Loading [MathJax]/jax/output/SVG/jax.js
Research article Special Issues

The dynamic nexus between economic factors, socioeconomic factors, green growth factors, and ecological footprint: evidence from GCC economies

  • Received: 26 May 2024 Revised: 15 August 2024 Accepted: 03 September 2024 Published: 19 September 2024
  • Industrialization, financial activities, and intensive human activities have reduced continuous habitats to smaller patches, threatening the safety of the ecosystem. However, as technological innovation and digitization increase, this negative impact will be somewhat neutralized. To address this issue, the current study examined the role of economic, socioeconomic, and green indicators on the ecological footprint in the Gulf Cooperation Council (GCC). By using data from 1990–2019, we have applied multiple panel tests to determine the long-run and short-run relationships among the variables. The findings show that economic growth increases the long-term ecological footprint in the GCC. The human development index and financial inclusion coefficients are also positively and significantly linked with the ecological footprint. The socioeconomic index, however, reveals a negative relationship between ecological footprint and GCC. Similarly, digitalization and environmental technologies have a negative and major impact on the ecological footprint. It indicates that green growth factors contribute to long-term improvements in environmental quality. So, GCC nations should emphasize investing in green growth factors and enact strict environmental regulations to safeguard their country from environmental problems.

    Citation: Majid Ibrahim Alsaggaf. The dynamic nexus between economic factors, socioeconomic factors, green growth factors, and ecological footprint: evidence from GCC economies[J]. AIMS Environmental Science, 2024, 11(5): 797-830. doi: 10.3934/environsci.2024040

    Related Papers:

    [1] Liqiong Pu, Zhigui Lin . A diffusive SIS epidemic model in a heterogeneous and periodically evolvingenvironment. Mathematical Biosciences and Engineering, 2019, 16(4): 3094-3110. doi: 10.3934/mbe.2019153
    [2] Cheng-Cheng Zhu, Jiang Zhu . Spread trend of COVID-19 epidemic outbreak in China: using exponential attractor method in a spatial heterogeneous SEIQR model. Mathematical Biosciences and Engineering, 2020, 17(4): 3062-3087. doi: 10.3934/mbe.2020174
    [3] Yongli Cai, Yun Kang, Weiming Wang . Global stability of the steady states of an epidemic model incorporating intervention strategies. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1071-1089. doi: 10.3934/mbe.2017056
    [4] Pannathon Kreabkhontho, Watchara Teparos, Thitiya Theparod . Potential for eliminating COVID-19 in Thailand through third-dose vaccination: A modeling approach. Mathematical Biosciences and Engineering, 2024, 21(8): 6807-6828. doi: 10.3934/mbe.2024298
    [5] Cheng-Cheng Zhu, Jiang Zhu, Xiao-Lan Liu . Influence of spatial heterogeneous environment on long-term dynamics of a reaction-diffusion SVIR epidemic model with relaps. Mathematical Biosciences and Engineering, 2019, 16(5): 5897-5922. doi: 10.3934/mbe.2019295
    [6] Yue Deng, Siming Xing, Meixia Zhu, Jinzhi Lei . Impact of insufficient detection in COVID-19 outbreaks. Mathematical Biosciences and Engineering, 2021, 18(6): 9727-9742. doi: 10.3934/mbe.2021476
    [7] Ke Guo, Wanbiao Ma . Global dynamics of an SI epidemic model with nonlinear incidence rate, feedback controls and time delays. Mathematical Biosciences and Engineering, 2021, 18(1): 643-672. doi: 10.3934/mbe.2021035
    [8] ZongWang, Qimin Zhang, Xining Li . Markovian switching for near-optimal control of a stochastic SIV epidemic model. Mathematical Biosciences and Engineering, 2019, 16(3): 1348-1375. doi: 10.3934/mbe.2019066
    [9] Rongjian Lv, Hua Li, Qiubai Sun, Bowen Li . Model of strategy control for delayed panic spread in emergencies. Mathematical Biosciences and Engineering, 2024, 21(1): 75-95. doi: 10.3934/mbe.2024004
    [10] Pan Yang, Jianwen Feng, Xinchu Fu . Cluster collective behaviors via feedback pinning control induced by epidemic spread in a patchy population with dispersal. Mathematical Biosciences and Engineering, 2020, 17(5): 4718-4746. doi: 10.3934/mbe.2020259
  • Industrialization, financial activities, and intensive human activities have reduced continuous habitats to smaller patches, threatening the safety of the ecosystem. However, as technological innovation and digitization increase, this negative impact will be somewhat neutralized. To address this issue, the current study examined the role of economic, socioeconomic, and green indicators on the ecological footprint in the Gulf Cooperation Council (GCC). By using data from 1990–2019, we have applied multiple panel tests to determine the long-run and short-run relationships among the variables. The findings show that economic growth increases the long-term ecological footprint in the GCC. The human development index and financial inclusion coefficients are also positively and significantly linked with the ecological footprint. The socioeconomic index, however, reveals a negative relationship between ecological footprint and GCC. Similarly, digitalization and environmental technologies have a negative and major impact on the ecological footprint. It indicates that green growth factors contribute to long-term improvements in environmental quality. So, GCC nations should emphasize investing in green growth factors and enact strict environmental regulations to safeguard their country from environmental problems.



    1. Introduction

    It is worth to start by quoting Bradley [15] "For real progress, the mathematical modeller, as well as the epidemiologist must have mud on his boots"!

    Indeed most of the pioneers in mathematical epidemiology have got "mud on their boots"; it is a duty and a pleasure to acknowledge here the ones who, apart from D. Bernoulli (1760) [14], established the roots of this field of research (in chronological order): W. Farr (1840) [41], W.H. Hamer (1906) [45], J. Brownlee (1911) [17], R. Ross (1911) [63], E. Martini (1921) [59], A. J. Lotka (1923) [57], W.O. Kermack and A. G. McKendrick (1927) [51], H. E. Soper (1929) [66], L. J. Reed and W. H. Frost (1930) [42], [1], M. Puma (1939) [62], E. B. Wilson and J. Worcester (1945) [69], M. S. Bartlett (1949) [12], G. MacDonald (1950) [58], N.T.J. Bailey (1950) [11], before many others; the pioneer work by En'ko (1989) [39] suffered from being written in Russian; historical accounts of epidemic theory can be found in [64], [35], [36]. After the late '70's there has been an explosion of interest in mathematical epidemiology, also thanks to the establishment of a number of new journals dedicated to mathematical biology. The above mentioned pioneers explored possible models to match real data, based on genuine epidemiological reasoning; further they did not choose a priori deterministic models as opposed to stochastic models. Unfortunately the most recent literature has suffered of a dramatic splitting in both approaches and methods, which has induced criticism among applied epidemiologists. About the relevance of mathematics in Life Sciences, Wilson and Worcester had since long [69] expressed a fundamental statement that we like to share: "Although mathematics is used to develop the logical inferences from known laws, it may also used to investigate the consequences of various assumptions when the laws are not known, .... one of the functions of mathematical and philosophical reasoning is to keep us alive to what may be only possibilities, when the actualities are not yet known".

    The scheme of this presentation is the following: in Section 2 a general structure of mathematical models for epidemic systems is presented in the form of compartmental systems; in Paragraph 2.1 the possible derivation of deterministic models is presented as an approximation, for large populations, of stochastic models; in Paragraph 2.2 nonlinear models are discussed as opposed to the standard epidemic models based on the "law of mass" action assumption; in Paragraph 2.3 the concept of field of forces of infection is discussed for structured populations. In Section 3 the particular case of man-environment-man infection is discussed, and, with respect to these models, in Section 4 optimal control problems are presented in the case of boundary feedback. Finally in Section 5 the most important problem of global eradication via regional control is presented.


    2. Compartmental models

    Model reduction for epidemic systems is obtained via the so-called compartmental models. In a compartmental model the total population (relevant to the epidemic process) is divided into a number (usually small) of discrete categories: susceptibles, infected but not yet infective (latent), infective, recovered and immune, without distinguishing different degrees of intensity of infection; possible structures in the relevant population can be superimposed when required (see e.g. Figure 1).

    Figure 1. The transfer diagram for an SEIR compartmental model including the susceptible class S, the exposed, but not yet infective, class E, the infective class I, and the removed class R.

    A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. The concepts of "force of infection" and "field of forces of infection" (when dealing with structured populations) will be the guideline of this presentation.

    We may like to remark here (see also [19]) that this concept is not very far from the medieval idea that infectious diseases were induced into a human being by a flow of bad air ("mal aria" in Italian). On the other hand in quantum field theory any field of forces is due to an exchange of particles: in this case bacteria, viruses, etc., so that the corpuscular and the continuous concepts of field are conceptually unified.

    It is of interest to identify the possible structures of the field of forces of infection which depend upon the specific mechanisms of transmission of the disease among different groups. This problem has been raised since the very first models when age and/or space dependence had to be taken into account.

    Suppose at first that the population in each compartment does not exhibit any structure (space location, age, etc.). The infection process (S to I) is driven by a force of infection (f.i.) due to the pathogen material produced by the infective population and available at time t

    (f.i.)(t)=[g(I(.))](t)

    which acts upon each individual in the susceptible class. Thus a typical rate of the infection process is given by the

    (incidence rate)(t)=(f.i.)(t)S(t).

    From this point of view, the so called "law of mass action" simply corresponds to choosing a linear dependence of g(I) upon I

    (f.i.)(t)=kI(t).

    The great advantage, from a mathematical point of view, is that the evolution of the epidemic is described (in the space and time homogeneous cases) by systems of ODE 's which contain at most bilinear terms.

    Indeed, for several models of this kind it is possible to prove global stability of nontrivial equilibria. A general result in this direction has been proposed in [13] where it has been shown that many bilinear epidemic systems can be expressed in the general form

    dzdt=diag(z)(e+Az)+b(z)

    where z(t)Rn+ is the state vector, eRn+ is a constant vector, A is an n×n constant matrix, and diag(z) is the diagonal matrix with diagonal entries zi. Further

    b(z)=c+Bz

    with cRn+ a constant vector, and B=(bij)i,j=1,,n a real constant matrix such that

    bij0,i,j=1,,n;bii=0,i=1,,n.

    Once a strictly positive equilibrium zRn+ has been somehow identified, the major "tool" in analyzing these systems is the so called Volterra-Goh Lyapunov function [44],

    V(z):=ni=1wi(zizizilnzizi),zRn

    where wi>0,i=1,,n, are real constants (the weights).

    Here we denote by

    Rn+:={zRnzi>0,i=1,,n},

    and clearly

    V:=Rn+R+.

    A discussion on V as a relative entropy can be found in [23].


    2.1. Deterministic approximation of stochastic models

    Actually for populations of a limited size, the stochastic version is more appropriate; but it is not difficult to show that for sufficiently large populations, the usual deterministic approximation can be gained via suitable laws of large numbers (see e.g. [40]).

    The stochastic process modelling an SIR epidemic, which takes into account the rescaling of the force of infection due to the size of the total population, is a multivariate jump Markov process (St,It,Rt)tR+, valued in N3.

    Considering the usual transitions

    SIR,

    by assuming the law of mass action, the only nontrivial transition rates are usually taken as

    q(S,I),(S1,I+1)=κINS:infection; (1)
    q(S,I),(S,I1)=δI:removal, (2)
    N=St+It+Rt=S0+I0=const. (3)

    We may notice that the above transition rates can be rewritten as follows

    q(S,I),(S1,I+1)=NκINSN; (4)
    q(S,I),(S,I1)=NδIN. (5)

    So that both transition rates are of the form

    q(N)k,k+l=Nβl(kN) (6)

    for

    k=(S,I) (7)

    and

    k+l={(S,I1),(S1,I+1). (8)

    Due to the constancy of the total population we may reduce the analysis to the Markov process ˆX(N):=(St,It), which satisfies a stochastic evolution equation of the form

    ˆX(N)(t)=ˆX(N)(0)+lZ2lYl(Nt0βl(ˆX(N)(τ)N)dτ), (9)

    for t<τ, the possible Markov time of explosion of the epidemic.

    Here the Yl are independent standard Poisson processes, and the sum is carried out only on the l's for which βl0.

    By setting

    F(x)=lZ2lβl(x),xR2 (10)

    for the scaled process

    X(N)=1NˆX(N), (11)

    we have

    X(N)(t)=X(N)(0)+t0F(X(N)(τ))dτ+lZ2lN˜Yl(Nt0βl(X(N)(τ))dτ) (12)

    where the

    ˜Yl(u)=Yl(u)u (13)

    are independent centered standard Poisson processes, so that the last term in the above equation is a zero-mean martingale.

    Of interest is the asymptotic behavior of the system for a large value of the scale parameter N.

    By the strong law of large numbers for Poisson processes (more generally for martingales), we know that

    limNsupuv|1N˜Yl(Nu)|=0,a.s., (14)

    for any v0. As a consequence, it is not a surprise the following result, based on Doob's inequality for martingales [40].

    Theorem 2.1. Under suitable regularity assumptions on βl and on F, if

    limNX(N)(0)=x0R2, (15)

    then, for every t0,

    limNsupτt|X(N)(τ)x(τ)|=0,a.s., (16)

    where x(t), tR+ is the unique solution of

    x(t)=x0+t0F(x(s))ds,t0, (17)

    wherever it exists.

    In our case the above deterministic system becomes the usual deterministic SIR model

    {ds(t)dt=κs(t)s(t)di(t)dt=κs(t)i(t)δi(t) (18)

    for

    s(t):=limNStN,i:=limNItN.

    A different scaling, may give rise to the diffusion approximation of the epidemic system (see [40], [22], and [67], for a variety of applications to Biology and Medicine).

    An interesting "pathology" arises when the relevant populations are very small, so that the deterministic approximation of the epidemic system may fail. Indeed for many epidemic models, above threshold the infective fraction of the relevant deterministic equations, while tending eventually to large values of a possible endemic level, may get very close to zero, but still never becomes extinct. This situation had been analyzed in [47] by suitable perturbation methods on the Fokker-Planck equation associated with the diffusion approximation of a typical SIR epidemic model, which lead to a non trivial extinction probability of the infective population, whenever its deterministic counterpart may get close to zero.

    It is worth mentioning that the discussion regarding the original stochastic model and its deterministic counterpart had involved J.L. Doob and others, who proposed (in 1945) [38] an algorithm for generating statistically correct trajectories of the stochastic system. It was presented by D. Gillespie in 1976 [43] as the Doob-Gillespie algorithm, well known in computational chemistry and physics.


    2.2. Nonlinear models

    Referring to the "Law of mass Action", Wilson and Worcester [69] stated the following:

    "It would in fact be remarkable, in a situation so complex as that of the passage of an epidemic over a community, if any simple law adequately represented the phenomenon in detail... even to assume that the new case rate should be set equal to any function... might be questioned?".

    Indeed Wilson and Worcester [69], and Severo [65] had been among the first epidemic modelers including nonlinear forces of infection of the form

    (f.i.)(t)=κI(t)pS(t)q

    in their investigations. Here I(t) denotes the number of persons who are infective, and S(t) denotes the number of persons who are susceptible to the infection.

    Independently, during the analysis of data regarding the spread of a cholera epidemic in Southern Italy during 1973, in [28] the authors suggested the need to introduce a nonlinear force of infection in order to explain the specific behavior emerging from the available data.

    A more extended analysis for a variety of proposed generalizations of the classical models known as Kermack-McKendrick models, appeared in [29], though nonlinear models became widely accepted in the literature only a decade later, after the paper [55].

    Nowadays models with nonlinear forces of infection are analyzed within the study of various kinds of diseases; typical expressions include the so called Holling type functional responses (see e.g. [29], [48])

    (f.i.)(t)=g(I(t));

    with

    g(I)=kIpα+βIq,p,q>0. (19)

    Particular cases are

    g(I)=kIp,p>0 (20)

    For the case p=q we have the behaviors described in Figure 2.

    Figure 2. Nonlinear forces of infection [29].

    A rather general analysis regarding existence and stability of nontrivial equilibria for model (19) has been carried out in a series of papers [61], [16], [56], [48] (see also [19], and [68]). The particular case p=q=2 in model (19) induces a saddle point behavior as analyzed in [26] and [31] (see Section 3 for the case with spatial structure).

    Additional shapes of g(I), as proposed in [29] which may decrease for large values of I, may be interpreted as "awareness" effects in the contact rates. Significant contributions to this concept and related epidemiological issues in recent literature can be found in [37].

    Further extensions include a nonlinear dependence upon both I and S, as discussed in modelling AIDS epidemics (see e.g. [32], [33], and references therein), where the social structure of the host population is analyzed too.


    2.3. Structured populations

    When dealing with populations which exhibit some structure (identified here by a parameter z), either discrete (e.g. social groups) or continuous (e.g. space location, age, etc.), the target of the infection process is a specific "subgroup" z in the susceptible class, so that the force of infection has to be evaluated with reference to that specific subgroup. This induces the introduction of a "field of forces of infection" (f.i.)(z;t) such that the incidence rate at time t at the specific "location" z will be given by

    (incidencerate)(z;t)=(f.i.)(z;t)s(z;t).

    When dealing with populations with space structure the relevant quantities are spatial densities, such as s(z;t) and i(z;t), the spatial densities of susceptibles and of infectives respectively, at a point z of the habitat Ω, and at time t0.

    The corresponding total populations are given by

    S(t)=Ωs(z;t)dz,I(t)=Ωi(z;t)dz

    In the law of mass action model, if only local interactions are allowed, the field at point zΩ is given by

    (f.i.)(z;t)=k(z)i(z;t).

    On the other hand if we wish to take distant interactions too into account, as proposed by D.G. Kendall in [50], the field at a point zΩ is given by

    (f.i.)(z;t)=Ωk(z,z)i(z;t)dz.

    For this case the emergence of travelling waves has been shown in [50] and [9]. The analysis of the diffusion approximation of Kendall's model can be found in [49].

    When dealing with populations with an age structure, we may interpret the parameter z as the age-parameter so that the first model above is a model with intracohort interactions while the second one is a model with intercohort interactions (see e.g. [18], and references therein).

    A large literature on the subject can be found in [19].


    3. Spatially structured man-environment-man epidemics

    A widely accepted model for the spatial spread of epidemics in an habitat Ω, via the environmental pollution produced by the infective population, e.g. via the excretion of pathogens in the environment, is the following, as proposed in [20], [21] (see also [19], and references therein).

    Typical real cases include typhoid fever, malaria, schistosomiasis, cholera, etc. (see e.g. [34], [6]).

    {u1t(x,t)=d1Δu1(x,t)a11u1(x,t)+Ωk(x,x)u2(x,t)dxu2t(x,t)=a22u2(x,t)+g(u1(x,t)) (21)

    in ΩRN (N1), a nonempty bounded domain with a smooth boundary Ω; for t(0,+), where a110, a220, d1>0 are constants.

    u1(x,t) denotes the concentration of the pollutant (pathogen material) at a spatial location x¯Ω, and a time t0;

    u2(x,t) denotes the spatial distribution of the infective population.

    ● The terms a11u1(x,t) and a22u2(x,t) model natural decays.

    ● The total susceptible population is assumed to be sufficiently large with respect to the infective population, so that it can be taken as constant.

    Environmental pollution is produced by the infective population, so that in the first equation of System (21), the integral term

    Ωk(x,x)u2(x,t)dx

    expresses the fact that the pollution produced at any point xΩ of the habitat is made available at any other point xΩ; when dealing with human pollution, this may be due to either malfunctioning of the sewage system, or improper dispersal of sewage in the habitat. Linearity of the above integral operator is just a simplifying option.

    Model (21) includes spatial diffusion of the pollutant, due to uncontrolled additional causes of dispersion (with a constant diffusion coefficient to avoid purely technical complications); we assume that the infective population does not diffuse (the case with diffusion would be here a technical simplification). As such, System (21) can be adopted as a good model for the spatial propagation of an infection in agriculture and forests, too.

    The above model is part of another important class of epidemics which exhibit a quasimonotone (cooperative) behavior (see [19]). For this class of problems stability of equilibria can be shown by monotone methods, such as the contracting rectangles technique (see [52], [53]).

    The local "incidence rate" at point x¯Ω, and time t0, is

    (i.r.)(t)=g(u1(x,t)),

    depending upon the local concentration of the pollutant.


    3.1. Seasonality.

    If we wish to model a large class of fecal-oral transmitted infectious diseases, such as typhoid fever, infectious hepatitis, cholera, etc., we may include the possible seasonal variability of the environmental conditions, and their impact on the habits of the susceptible population, so that the relevant parameters are assumed periodic in time, all with the same period T(0,+).

    As a purely technical simplification, we may assume that only the incidence rate is periodic, and in particular that it can be expressed as

    (i.r.)(x,t)=h(t,u1(x,t))=p(t)g(u1(x,t)),

    where h, the functional dependence of the incidence rate upon the concentration of the pollutant, can be chosen as in the time homogeneous case, with possible behaviors as shown in Figure 2.

    The explicit time dependence of the incidence rate is given via the function p(), which is assumed to be a strictly positive, continuous and Tperiodic function of time; i.e. for any tR,

    p(t)=p(t+T).

    Remark 1. The results can be easily extended to the case in which also a11, a22 and k are Tperiodic functions.

    In [21] the above model was studied, and sufficient conditions were given for either the asymptotic extinction of an epidemic outbreak, or the existence and stability of an endemic state; while in [27] the periodic case was additionally studied, and sufficient conditions were given for either the asymptotic extinction of an epidemic outbreak, or the existence and stability of a periodic endemic state with the same period of the parameters.


    3.2. Saddle point behaviour.

    The choice of g has a strong influence on the dynamical behavior of system (21). The case in which g is a monotone increasing function with constant concavity has been analyzed in an extensive way (see [19], [24], [26]); concavity leads to the existence (above a parameter threshold) of exactly one nontrivial endemic state and to its global asymptotic stability. In order to better clarify the situation, consider first the spatially homogeneous case (ODE system) associated with system (21); namely

    {dz1dt(t)=a11z1(t)+a12z2(t)du2dt(t)=a22z2(t)+g(z1(t)) (22)

    In [26] and [60] the bistable case (in which system (22) may admit two nontrivial steady states, one of which is a saddle point in the phase plane) was obtained by assuming that the force of infection, as a function of the concentration of the pollutant, is sigma shaped. In [60] this shape had been obtained as a consequence of the sexual reproductive behavior of the schistosomes. In [26] (see also [25]) the case of fecal-oral transmitted diseases was considered; an interpretation of the sigma shape of the force of infection was proposed to model the response of the immune system to environmental pollution: the probability of infection is negligible at low concentrations of the pollutant, but increases with larger concentrations; it then becomes concave and saturates to some finite level as the concentration of pollutant increases without limit.

    Let us now refer to the following simplified form of System (21), where as kernel we have taken k(x,x)=a12δ(xx),

    {u1t(x,t)=d1Δu1(x,t)a11u1(x,t)+a12u2(x,t)u2t(x,t)=a22u2(x,t)+g(u1(x,t)) (23)

    The concavity of g induces concavity of its evolution operator, which, together with the monotonicity induced by the quasi monotonicity of the reaction terms in (23), again imposes uniqueness of the possible nontrivial endemic state. On the other hand, in the case where g is sigma shaped, monotonicity of the solution operator is preserved, but as we have already observed in the ODE case, uniqueness of nontrivial steady states is no longer guaranteed. Furthermore, the saddle point structure of the phase space cannot be easily transferred from the ODE to the PDE case, as discussed in [26], [31]. In [26], homogeneous Neumann boundary conditions were analyzed; in this case nontrivial spatially homogeneous steady states are still possible. But when we deal with homogeneous Dirichlet boundary conditions or general third-type boundary conditions, nontrivial spatially homogeneous steady states are no longer allowed. In [31] this problem was faced in more detail; the steady-state analysis was carried out and the bifurcation pattern of nontrivial solutions to system (23) was determined when subject to homogeneous Dirichlet boundary conditions. When the diffusivity of the pollutant is small, the existence of a narrow bell-shaped steady state was shown, representing very likely a saddle point for the dynamics of (23). Numerical experiments confirm the bistable situation: "small" outbreaks stay localized under this bell-shaped steady state, while "large" epidemics tend to invade the whole habitat.


    4. Boundary feedback

    An interesting problem concerns the case of boundary feedback of the pollutant, which has been proposed in [24], and further analyzed in [30]; an optimal control problem has been later analyzed in [8].

    In this case the reservoir of the pollutant generated by the human population is spatially separated from the habitat by a boundary through which the positive feedback occurs. A model of this kind has been proposed as an extension of the ODE model for fecal-oral transmitted infections in Mediterranean coastal regions presented in [28].

    For this kind of epidemics the infectious agent is multiplied by the infective human population and then sent to the sea through the sewage system; because of the peculiar eating habits of the population of these regions, the agent may return via some diffusion-transport mechanism to any point of the habitat, where the infection process is restarted.

    The mathematical model is based on the following system of evolution equations:

    {u1t(x;t)=Δu1(x;t)a11u1(x;t)u2t(x;t)=a22u2(x;t)+g(u1(x;t))

    in Ω×(0,+), subject to the following boundary condition

    u1ν(x;t)+αu1(x;t)=Ωk(x,x)u2(x;t)dx

    on Ω×(0,+), and also subject to suitable initial conditions.

    Here Δ is the usual Laplace operator modelling the random dispersal of the infectious agent in the habitat; the human infective population is supposed not to diffuse. As usual a11 and a22 are positive constants. In the boundary condition the left hand side is the general boundary operator B:=ν+α() associated with the Laplace operator; on the right hand side the integral operator

    H[u2(,t)](x):=Ωk(x,x)u2(x;t)dx

    describes boundary feedback mechanisms, according to which the infectious agent produced by the human infective population at time t>0, at any point xΩ, is available, via the transfer kernel k(x,x), at a point xΩ.

    Clearly the boundary Ω of the habitat Ω can be divided into two disjoint parts: the sea shore Γ1 through which the feedback mechanism may occur, and Γ2 the boundary on the land, at which we may assume complete isolation.

    The parameter α(x) denotes the rate at which the infectious agent is wasted away from the habitat into the sea along the sea shore. Thus one may well assume that

    α(x),k(x,)=0, forxΓ2.

    A relevant assumption, of great importance in the control problems that we have been facing later, is that the habitat Ω is "epidemiologically" connected to its boundary by requesting that

     for anyxΩ there exists somexΓ1 such thatk(x,x)>0.

    This means that from any point of the habitat infective individuals contribute to polluting at least some point on the boundary (the sea shore).

    In the above model delays had been neglected and the feedback process had been considered to be linear; various extensions have been considered in subsequent literature.


    5. Regional control: Think Globally, Act Locally

    Let us now go back to System (21) in ΩRN (N1), a nonempty bounded domain with a smooth boundary Ω; for t(0,+), where a110, a220, d1>0 are constants.

    The public health concern consists of providing methods for the eradication of the disease in the relevant population, as fast as possible. On the other hand, very often the entire domain Ω, of interest for the epidemic, is either unknown, or difficult to manage for an affordable implementation of suitable environmental sanitation programmes. Think of malaria, schistosomiasis, and alike, in Africa, Asia, etc.

    This has led the first author, in a discussion with Jacques Louis Lions in 1989, to suggest that it might be sufficient to implement such programmes only in a given subregion ωΩ, conveniently chosen so to lead to an effective (exponentially fast) eradication of the epidemic in the whole habitat Ω. Though, a satisfactory mathematical treatment of this issue has been obtained only few years later in [2]. This practice may have an enormous importance in real cases with respect to both financial and practical affordability. Further, since we propose to act on the elimination of the pollution only, this practice means an additional nontrivial social benefit on the human population, since it would not be limited in his social and alimentation habits.

    Figure 3. Think Globally, Act Locally.

    In this section a review is presented of some results obtained by the authors, during 2002-2012, concerning stabilization (for both the time homogeneous case and the periodic case). Conditions have been provided for the exponential decay of the epidemic in the whole habitat Ω, based on the elimination of the pollutant in a subregion ωΩ. The case of homogeneous third type boundary conditions has been considered, including the homogeneous Neumann boundary conditions (to mean complete isolation of the habitat):

    u1ν(x,t)+αu1(x,t)=0 on Ω×(0,+),

    where α0 is a constant and ν denotes the normal derivative.

    For the time homogeneous case the following assumptions have been taken:

    (H1) g:R[0,+) is a function satisfying

    a) g(x)=0, for x(,0],

    b) g is Lipschitz continuous and increasing,

    c) g(x)a21x,  for any x[0,+), where a21>0;

    (H2) kL(Ω×Ω),k(x,x)0 a.e. in Ω×Ω,

    Ωk(x,x)dx>0 a.e. xΩ;

    (H3) u01, u02L(Ω),u01(x), u02(x)0 a.e. in Ω.

    Let ω⊂⊂Ω be a nonempty subdomain with a smooth boundary and Ω¯ω a domain. Denote by χω the characteristic function of ω (we use the convention

    χω(x)h(x)=0,xRN¯ω,

    even if function h is not defined on the whole set RN¯ω).

    Our goal is to study the controlled system

    {u1t(x,t)=d1Δu1(x,t)a11u1(x,t)+Ωk(x,x)u2(x,t)dx+χω(x)v(x,t),(x,t)Ω×(0,+)u1ν(x,t)+αu1(x,t)=0,(x,t)Ω×(0,+)u2t(x,t)=a22u2(x,t)+g(u1(x,t)),  (x,t)Ω×(0,+)u1(x,0)=u01(x),u2(x,0)=u02(x),xΩ,

    subject to a control vLloc(¯ω×[0,+)) (which implies that supp(v(t))¯ω for t0).

    We have to mention that existence, uniqueness and nonnegativity of a solution to the above system can be proved as in [10]. The nonnegativity of u1 and u2 is a natural requirement due to the biological significance of u1 and u2.

    Definition 5.1. We say that our system is zero-stabilizable if for any u01 and u02 satisfying (H3) a control vLloc(¯ω×[0,+)) exists such that the solution (u1,u2) satisfies

    u1(x,t)0,u2(x,t)0, a.e. xΩ,  for any t0

    and

    limtu1(t)L(Ω)=limtu2(t)L(Ω)=0.

    Definition 5.2. We say that our system is locally zero-stabilizable if there exists r0>0 such that for any u01 and u02 satisfying (H3) and u01L(Ω), u02L(Ω)r0, there exists vLloc(¯ω×[0,+)) such that the solution (u1,u2) satisfies u1(x,t)0, u2(x,t)0 a.e. xΩ,  for any t0 and limt+u1(t)L(Ω)=limt+u2(t)L(Ω)=0.

    Remark 2. It is obvious that if a system is zero-stabilizable, then it is also locally zero-stabilizable.

    A stabilization result for our system, in the case of time independent g, had been obtained in [2]. In case of stabilizability a complicated stabilizing control had been provided. A stronger result (which indicates also a simpler stabilizing control) has been established in [3] using a different approach. Later, in [4] the authors have further extended the main results to the case of a time Tperiodic function g and provided a very simple stabilizing feedback control.

    In [3], by Krein-Rutman Theorem, it has been shown that

    {d1Δφ+a11φa21a22Ωk(x,x)φ(x)dx=λφ, xΩ¯ωφ(x)=0,xωφν(x)+αφ(x)=0,xΩ,

    admits a principal (real) eigenvalue λ1(ω), and a corresponding strictly positive eigenvector φInt(K) where

    K={φL(Ω); φ(x)0  a.e. in Ω}.

    The following theorem holds [3]:

    Theorem 5.3. If λ1(ω)>0, then for γ0 large enough, the feedback control v:=γu1 stabilizes our system to zero.

    Conversely, if h is differentiable at 0 and h(0)=a21 and if our system is zero-stabilizable, then λ1(ω)0.

    Moreover, the proof of the main result in [3] shows that for a given affordable sanitation effort γ, the epidemic process can be diminished exponentially if λω1,γ>0, where λω1,γ is the principal eigenvalue to the following problem:

    {d1Δφ+a11φa21a22Ωk(x,x)φ(x)dx+γχωφ=λφ, xΩφν(x)+αφ(x)=0,xΩ. (24)

    A natural question related to the practical implementation of the sanitation policy is the following: "For a given sanitation effort γ>0 in the region ω, is the principal eigenvalue λω1,γ positive (and consequently can our epidemic system be stabilized to zero by the feedback control v:=γu1)?"

    So, the first problem to be treated is the estimation of λω1,γ. Since this eigenvalue problem is related to a non-self adjoint operator, we cannot use a variational principle (as Rayleigh's for selfadjoint operators); hence in [5] the authors have proposed an alternative method based on the following result:

    limt+Ωyω(x,t)dx=ζλω1,γ, (25)

    where yω is the unique positive solution to

    {ytd1Δy+a11y+γχωya21a22Ωk(x,x)y(x,t)dx                  ζy+(Ωy(x,t)dx)y=0,xΩ, t>0yν(x,t)+αy(x,t)=0,xΩ, t>0y(x,0)=1,xΩ, (26)

    and ζ>λω1,γ is a constant.

    Remark 3. Problem (26) is a logistic model for the population dynamics with diffusion and migration. Since the solutions to the logistic models rapidly stabilize, this means that (25) gives an efficient method to approximate λω1,γ. Namely, for T>0 large enough,

    ζΩyω(x,T)dx

    gives a very good approximation of λω1,γ. The above result leads to a concrete numerical estimation of λω1,γ by analyzing the "large-time" behavior of the system for different values of ζ.

    We may also remark that, if in (26)

    y(x,0)=y0,xΩ, (27)

    with y0 an arbitrary positive constant, then

    limt+Ωyω1(x,t)dx=ζλω1,γ,

    where yω1 is the solution to (26)-(27).

    Assume now that for a given sanitation effort γ, the principal eigenvalue to (24) satisfies λω1,γ>0, and consequently v:=γu1 stabilizes to zero the solution to (21).

    Let ω0 be a nonempty open subset of Ω, with a smooth boundary and such that ω0⊂⊂Ω and Ω¯ω0 is a domain. Consider O the set of all translations ω of ω0, satisfying ω⊂⊂Ω. Since, after all, our initial goal was to eradicate the epidemics, we are led to the natural problem of "Finding the translation ω of ω (ωO) which gives a small value (possibly minimal) of

    Rω=ω[uω1(x,T)+uω2(x,T)]dx,

    at some given finite time T>0. "

    Here (uω1,uω2) is the solution of (1.1) corresponding to v:=γu1, i.e. (uω1,uω2) is the solution to

    {u1t(x,t)=d1Δu1(x,t)a11u1(x,t)+Ωk(x,x)u2(x,t)dxγχω(x)u1(x,t),(x,t)Ω×(0,+)u1ν(x,t)+αu1(x,t)=0,(x,t)Ω×(0,+)u2t(x,t)=a22u2(x,t)+g(u1(x,t)),  (x,t)Ω×(0,+)u1(x,0)=u01(x),xΩu2(x,0)=u02(x),xΩ. (28)

    For this reason we are going to evaluate the derivative of Rω with respect to translations of ω. This will allow to derive a conceptual iterative algorithm to improve at each step the position (by translation) of ω in order to get a smaller value for Rω.


    5.1. The derivative of Rω with respect to translations

    For any ωO and VRn we define the derivative

    dRω(V)=limε0RεV+ωRωε.

    For basic results and methods in the optimal shape design theory we refer to [46].

    Theorem 5.4. For any ωO and VRn we have that

    dRω(V)=γT0ωuω1(x,t)pω1(x,t)ν(x)Vdσ dt,

    where (pω1,pω2) is the solution to the adjoint problem

    {p1t+d1Δp1a11p1γχωp1+g(uω1)p2=0,xΩ, t>0p2t+Ωk(x,x)p1(x,t)dxa22p2=0,xΩ, t>0p1ν(x,t)+αp(x,t)=0,xΩ, t>0p1(x,T)=p2(x,T)=1,xΩ. (29)

    Here ν(x) is the normal inward versor at xω (inward with respect to ω).

    For the construction of the adjoint problems in optimal control theory we refer to [54].

    Based on Theorem 5.4, in [5] the authors have proposed a conceptual iterative algorithm to improve the position (by translation) of ωO (in order to obtain a smaller value for Rω.


    5.2. The periodic case

    As a purely technical simplification, we have assumed that only the incidence rate is periodic, and in particular that it can be expressed as

    (i.r.)(x,t)=h(t,u1(x,t))=p(t)g(u1(x,t)),

    were g, the functional dependence of the incidence rate upon the concentration of the pollutant, can be chosen as in the time homogeneous case.

    In this case our goal is to study the controlled system

    {u1t(x,t)=d1Δu1(x,t)a11u1(x,t)+Ωk(x,x)u2(x,t)dx+χω(x)v(x,t),(x,t)Ω×(0,+)u1ν(x,t)+αu1(x,t)=0,(x,t)Ω×(0,+)u2t(x,t)=a22u2(x,t)+h(t,u1(x,t)),  (x,t)Ω×(0,+)u1(x,0)=u01(x),u2(x,0)=u02(x),xΩ, (30)

    with a control vLloc(¯ω×[0,+)) (which implies that supp(v(,t))¯ω for t0).

    The explicit time dependence of the incidence rate is given via the function p(), which is assumed to be a strictly positive, continuous and Tperiodic function of time; i.e. for any tR,

    p(t)=p(t+T).

    Remark 4. The results can be easily extended to the case in which also a11, a22 and k are Tperiodic functions.

    Consider the following (linear) eigenvalue problem

    {φtd1Δφ+a11φΩk(x,x)ψ(x,t)dx=λφ,xΩ¯ω, t>0φν(x,t)+αφ(x,t)=0,xΩ, t>0φ(x,t)=0,xω, t>0ψt(x,t)+a22ψ(x,t)a21p(t)φ(x,t)=0,xΩ¯ω, t>0φ(x,t)=φ(x,t+T),ψ(x,t)=ψ(x,t+T),xΩ¯ω, t0. (31)

    By similar procedures, as in the time homogeneous case, Problem (31) admits a principal (real) eigenvalue λT1(ω), and a corresponding strictly positive eigenvector φTInt(KT) where

    KT={φL(Ω×(0,T)); φ(x,t)0  a.e. in Ω×(0,T)}.

    Theorem 5.5. If λT1(ω)>0, then for γ0 large enough, the feedback control v:=γu1 stabilizes (30) to zero.

    Conversely, if g is differentiable at 0 and g(0)=a21, and if (30) is zero-stabilizable, then λT1(ω)0.

    Theorem 5.6. Assume that g is differentiable at 0. Denote by ˜λT1(ω) the principal eigenvalue of the problem

    {φtd1Δφ+a11φΩk(x,x)ψ(x,t)dx=λφ,xΩ¯ω, t>0φν(x,t)+αφ(x,t)=0,xΩ, t>0φ(x,t)=0,xω, t>0ψt(x,t)+a22ψ(x,t)g(0)p(t)φ(x,t)=0,xΩ¯ω, t>0φ(x,t)=φ(x,t+T),ψ(x,t)=ψ(x,t+T),xΩ¯ω, t0 (32)

    If ˜λT1(ω)>0, then the system is locally zero stabilizable, and for γ0 sufficiently large, v:=γu1 is a stabilizing feedback control.

    Conversely, if the system is locally zero stabilizable, then ˜λT1(ω)0.

    Remark 5. Since g(0)a21, it follows that λT1(ω)˜λT1(ω). We conclude now that

    10 If λT1(ω)>0, the system is zero-stabilizable;

    20 If ˜λT1(ω)>0 and λT1(ω)0, the system is locally zero-stabilizable;

    30 If ˜λT1(ω)<0, the system is not locally zero-stabilizable and consequently it is not zero stabilizable.

    Remark 6. Future directions. Another interesting problem is that when ω consists of a finite number of mutually disjoint subdomains. The goal is to find the best position for each subdomain. A similar approach can be used.

    In a recently submitted paper [7], the problem of the best choice of the subregion ω has been faced for a general harvesting problem in population dynamics as a shape optimization problem; our future aim is to apply those results to our problem of eradication of spatially structured epidemics.


    Acknowledgments

    The work of V. Capasso was supported by the MIUR-PRIN grant 200777BWEP003: "From the stochastic modelling to the statistics of space-time structured population dynamics". The work of Sebastian Aniţa was supported by the CNCS-UEFISCDI (Romanian National Authority for Scientific Research) grant 68/2.09.2013, PN-II-ID-PCE-2012-4-0270: "Optimal Control and Stabilization of Nonlinear Parabolic Systems with State Constraints. Applications in Life Sciences and Economics".

    It is a pleasure to acknowledge the contribution by Klaus Dietz regarding the bibliography on the historical remarks reported in the Introduction.

    Thanks are due to the Anonymous Referees for their precious advise and suggestions.




    [1] Jiakui C, Abbas J, Najam H, et al. (2023) Green technological innovation, green finance, and financial development and their role in green total factor productivity: Empirical insights from China. J Clean Prod 382: 135131. https://doi.org/10.1016/j.jclepro.2022.135131 doi: 10.1016/j.jclepro.2022.135131
    [2] Yang B, Jahanger A, Usman M, et al. (2021) The dynamic linkage between globalization, financial development, energy utilization, and environmental sustainability in GCC countries. Environ Sci Pollut Res 28: 16568–16588. https://doi.org/10.1007/s11356-020-11576-4 doi: 10.1007/s11356-020-11576-4
    [3] Sharif A, Meo MS, Chowdhury MAF, et al. (2021) Role of solar energy in reducing ecological footprints: An empirical analysis. J Clean Prod 292: 126028. https://doi.org/10.1016/j.jclepro.2021.126028 doi: 10.1016/j.jclepro.2021.126028
    [4] Haider S, Akram V (2019) Club convergence of per capita carbon emission: global insight from disaggregated level data. Environ Sci Pollut Res 26: 11074–11086. https://doi.org/10.1007/s11356-019-04573-9 doi: 10.1007/s11356-019-04573-9
    [5] Hussain MM, Pal S, Villanthenkodath MA (2023) Towards sustainable development: The impact of transport infrastructure expenditure on the ecological footprint in India. Innov Green Dev 2: 100037. https://doi.org/10.1016/j.igd.2023.100037 doi: 10.1016/j.igd.2023.100037
    [6] Elimelech M, Phillip WA (2011) The future of seawater desalination: Energy, technology, and the environment. Science 333: 712–717. https://doi.org/10.1126/science.1200488 doi: 10.1126/science.1200488
    [7] Al-Mulali U, Saboori B, Ozturk I (2015) Investigating the environmental Kuznets curve hypothesis in Vietnam. Energy Policy 76: 123–131. https://doi.org/10.1016/j.enpol.2014.11.019 doi: 10.1016/j.enpol.2014.11.019
    [8] Ansari MA, Ahmad MR, Siddique S, et al. (2020) An environment Kuznets curve for ecological footprint: Evidence from GCC countries. Carbon Manag 11: 355–368. https://doi.org/10.1080/17583004.2020.1790242 doi: 10.1080/17583004.2020.1790242
    [9] Charabi Y (2023) Deep near-term mitigation of short-lived climate forcers in Oman: grand challenges and prospects. Environ Sci Pollut Res 30: 3918–3928. https://doi.org/10.1007/s11356-022-22488-w doi: 10.1007/s11356-022-22488-w
    [10] Al Khars M, Miah F, Qudrat-Ullah H, et al. (2020) A Systematic Review of the Relationship Between Energy Consumption and Economic Growth in GCC Countries. Sustain 12: 3845. https://doi.org/10.3390/su12093845 doi: 10.3390/su12093845
    [11] Al-shammari ASA, Muneer S, Tripathi A (2022) Do Information Communication Technology and Economic Development Impact Environmental Degradation? Evidence From the GCC Countries. Front Environ Sci 10: 628. https://doi.org/10.3389/fenvs.2022.875932 doi: 10.3389/fenvs.2022.875932
    [12] Wackernagel M, Rees W (1998) Our ecological footprint: reducing human impact on the earth, New society publishers.
    [13] Hassan ST, Xia E, Khan NH, et al. (2019) Economic growth, natural resources, and ecological footprints: evidence from Pakistan. Environ Sci Pollut Res 26: 2929–2938. https://doi.org/10.1007/s11356-018-3803-3 doi: 10.1007/s11356-018-3803-3
    [14] Ullah A, Ahmed M, Raza SA, et al. (2021) A threshold approach to sustainable development: Nonlinear relationship between renewable energy consumption, natural resource rent, and ecological footprint. J Environ Manage 295: 113073. https://doi.org/10.1016/j.jenvman.2021.113073 doi: 10.1016/j.jenvman.2021.113073
    [15] Xue L, Haseeb M, Mahmood H, et al. (2021) Renewable Energy Use and Ecological Footprints Mitigation: Evidence from Selected South Asian Economies. Sustain 13: 1613. https://doi.org/10.3390/su13041613 doi: 10.3390/su13041613
    [16] Chen Y, Cheng L, Lee CC (2022) How does the use of industrial robots affect the ecological footprint? International evidence. Ecol Econ 198: 107483. https://doi.org/10.1016/j.ecolecon.2022.107483 doi: 10.1016/j.ecolecon.2022.107483
    [17] Solarin SA (2019) Convergence in CO 2 emissions, carbon footprint and ecological footprint: evidence from OECD countries. Environ Sci Pollut Res 26: 6167–6181. https://doi.org/10.1007/s11356-018-3993-8 doi: 10.1007/s11356-018-3993-8
    [18] Ozcan B, Ulucak R, Dogan E (2019) Analyzing long lasting effects of environmental policies: Evidence from low, middle and high income economies. Sustain Cities Soc 44: 130–143. https://doi.org/10.1016/j.scs.2018.09.025 doi: 10.1016/j.scs.2018.09.025
    [19] Bilgili F, Ulucak R (2018) Is there deterministic, stochastic, and/or club convergence in ecological footprint indicator among G20 countries? Environ Sci Pollut Res 25: 35404–35419. https://doi.org/10.1007/s11356-018-3457-1 doi: 10.1007/s11356-018-3457-1
    [20] Lin W, Li Y, Li X, et al. (2018) The dynamic analysis and evaluation on tourist ecological footprint of city: Take Shanghai as an instance. Sustain Cities Soc 37: 541–549. https://doi.org/10.1016/j.scs.2017.12.003 doi: 10.1016/j.scs.2017.12.003
    [21] Bliss-Guest P, Rodriguez A (1982) The Caribbean Action Plan: a framework for sustainable development. Ekistics A Rev Probl Sci Hum settlements Athenai 49: 182–183.
    [22] Caldwell LK (1984) Political Aspsects of Ecologically Sustainable Development. Environ Conserv 11: 299–308. https://doi.org/10.1017/S037689290001465X doi: 10.1017/S037689290001465X
    [23] Holden E, Linnerud K, Banister D (2017) The Imperatives of Sustainable Development. Sustain Dev 25: 213–226. https://doi.org/10.1002/sd.1647 doi: 10.1002/sd.1647
    [24] de Jong E, Vijge MJ (2021) From Millennium to Sustainable Development Goals: Evolving discourses and their reflection in policy coherence for development. Earth Syst Gov 7: 100087. https://doi.org/10.1016/j.esg.2020.100087 doi: 10.1016/j.esg.2020.100087
    [25] Todaro MP (1977) Economic Development in the Third World: An introduction to problems and policies in a global perspective, Pearson Education.
    [26] Brinkman RL, Brinkman JE (2014) GDP as a Measure of Progress and Human Development: A Process of Conceptual Evolution. 45: 447–456. https://doi.org/10.2753/JEI0021-3624450222
    [27] Costantini V, Monni S (2008) Environment, human development and economic growth. Ecol Econ 64: 867–880. https://doi.org/10.1016/j.ecolecon.2007.05.011 doi: 10.1016/j.ecolecon.2007.05.011
    [28] Chai J, Zhang X, Lu Q, et al. (2021) Research on imbalance between supply and demand in China's natural gas market under the double-track price system. Energy Policy 155: 112380. https://doi.org/10.1016/j.enpol.2021.112380 doi: 10.1016/j.enpol.2021.112380
    [29] Costanza R, Kubiszewski I, Giovannini E, et al. (2014) Development: Time to leave GDP behind. Nat 505: 283–285. https://doi.org/10.1038/505283a doi: 10.1038/505283a
    [30] do Carvalhal Monteiro RL, Pereira V, Costa HG (2018) A Multicriteria Approach to the Human Development Index Classification. Soc Indic Res 136: 417–438. ttps://doi.org/10.1007/s11205-017-1556-x
    [31] Chiappero-Martinetti E, von Jacobi N, Signorelli M (2015) Human Development and Economic Growth. Palgrave Dict Emerg Mark Transit Econ 223–244. https://doi.org/10.1007/978-1-137-37138-6_13 doi: 10.1007/978-1-137-37138-6_13
    [32] Jahanger A, Usman M, Murshed M, et al. (2022) The linkages between natural resources, human capital, globalization, economic growth, financial development, and ecological footprint: The moderating role of technological innovations. Resour Policy 76: 102569. https://doi.org/10.1016/j.resourpol.2022.102569 doi: 10.1016/j.resourpol.2022.102569
    [33] Usman M, Makhdum MSA, Kousar R (2021) Does financial inclusion, renewable and non-renewable energy utilization accelerate ecological footprints and economic growth? Fresh evidence from 15 highest emitting countries. Sustain Cities Soc 65: 102590. https://doi.org/10.1016/j.scs.2020.102590 doi: 10.1016/j.scs.2020.102590
    [34] Le TH, Le HC, Taghizadeh-Hesary F (2020) Does financial inclusion impact CO2 emissions? Evidence from Asia. Financ Res Lett 34: 101451. https://doi.org/10.1016/j.frl.2020.101451 doi: 10.1016/j.frl.2020.101451
    [35] Abbasi F, Riaz K (2016) CO2 emissions and financial development in an emerging economy: An augmented VAR approach. Energy Policy 90: 102–114. https://doi.org/10.1016/j.enpol.2015.12.017 doi: 10.1016/j.enpol.2015.12.017
    [36] Acheampong AO (2019) Modelling for insight: Does financial development improve environmental quality? Energy Econ 83: 156–179. https://doi.org/10.1016/j.eneco.2019.06.025 doi: 10.1016/j.eneco.2019.06.025
    [37] Ouedraogo NS (2013) Energy consumption and human development: Evidence from a panel cointegration and error correction model. Energy 63: 28–41. https://doi.org/10.1016/j.energy.2013.09.067 doi: 10.1016/j.energy.2013.09.067
    [38] UNDP (2022) Human Development Index Report 2021-22, New York.
    [39] UNDP (2022) Sustainable Development Goals | United Nations Development Programme 2022.
    [40] Kassouri Y, Altıntaş H (2020) Human well-being versus ecological footprint in MENA countries: A trade-off? J Environ Manage 263: 110405. https://doi.org/10.1016/j.jenvman.2020.110405 doi: 10.1016/j.jenvman.2020.110405
    [41] Jie H, Khan I, Alharthi M, et al. (2023) Sustainable energy policy, socio-economic development, and ecological footprint: The economic significance of natural resources, population growth, and industrial development. Util Policy 81: 101490. https://doi.org/10.1016/j.jup.2023.101490 doi: 10.1016/j.jup.2023.101490
    [42] Bilal, Khan I, Tan D, et al. (2022) Alternate energy sources and environmental quality: The impact of inflation dynamics. Gondwana Res 106: 51–63. https://doi.org/10.1016/j.gr.2021.12.011 doi: 10.1016/j.gr.2021.12.011
    [43] Wang Z, Yang L, Yin J, et al. (2018) Assessment and prediction of environmental sustainability in China based on a modified ecological footprint model. Resour Conserv Recycl 132: 301–313. https://doi.org/10.1016/j.resconrec.2017.05.003 doi: 10.1016/j.resconrec.2017.05.003
    [44] Huo W, Zaman BU, Zulfiqar M, et al. (2023) How do environmental technologies affect environmental degradation? Analyzing the direct and indirect impact of financial innovations and economic globalization. Environ Technol Innov 29: 102973. https://doi.org/10.1016/j.eti.2022.102973 doi: 10.1016/j.eti.2022.102973
    [45] Kahouli B, Chaaben N (2022) Investigate the link among energy Consumption, environmental Pollution, Foreign Trade, Foreign direct Investment, and economic Growth: Empirical evidence from GCC countries. Energy Build 266: 112117. https://doi.org/10.1016/j.enbuild.2022.112117 doi: 10.1016/j.enbuild.2022.112117
    [46] Wang H, Cui H, Zhao Q (2021) Effect of green technology innovation on green total factor productivity in China: Evidence from spatial durbin model analysis. J Clean Prod 288: 125624. https://doi.org/10.1016/j.jclepro.2020.125624 doi: 10.1016/j.jclepro.2020.125624
    [47] Ren S, Hao Y, Wu H (2022) Digitalization and environment governance: does internet development reduce environmental pollution? https://doi.org/10.1080/09640568.2022.2033959
    [48] Papworth S, Rao M, Oo MM, et al. (2017) The impact of gold mining and agricultural concessions on the tree cover and local communities in northern Myanmar OPEN. Nat Publ Gr. https://doi.org/10.1038/srep46594
    [49] Lailag U, Chen W (2022) How Does Digitization Affect Sports Industry Development and Public Health? Econ Anal Lett 1: 8–14. https://doi.org/10.58567/eal01010002 doi: 10.58567/eal01010002
    [50] Feng S, Chong Y, Yu H, et al. (2022) Digital financial development and ecological footprint: Evidence from green-biased technology innovation and environmental inclusion. J Clean Prod 380: 135069. https://doi.org/10.1016/j.jclepro.2022.135069 doi: 10.1016/j.jclepro.2022.135069
    [51] Awan U, Shamim S, Khan Z, et al. (2021) Big data analytics capability and decision-making: The role of data-driven insight on circular economy performance. Technol Forecast Soc Change 168: 120766. https://doi.org/10.1016/j.techfore.2021.120766 doi: 10.1016/j.techfore.2021.120766
    [52] Awan U, Sroufe R, Shahbaz M (2021) Industry 4.0 and the circular economy: A literature review and recommendations for future research. Bus Strateg Environ 30: 2038–2060. https://doi.org/10.1002/bse.2731 doi: 10.1002/bse.2731
    [53] Feng S, Zhang R, Li G (2022) Environmental decentralization, digital finance and green technology innovation. Struct Chang Econ Dyn 61: 70–83. https://doi.org/10.1016/j.strueco.2022.02.008 doi: 10.1016/j.strueco.2022.02.008
    [54] Zhou Y, Li Y, Liu Y (2020) The nexus between regional eco-environmental degradation and rural impoverishment in China. Habitat Int 96: 102086. https://doi.org/10.1016/j.habitatint.2019.102086 doi: 10.1016/j.habitatint.2019.102086
    [55] Li W, Qiao Y, Li X, et al. (2022) Energy consumption, pollution haven hypothesis, and Environmental Kuznets Curve: Examining the environment–economy link in belt and road initiative countries. Energy 239: 122559. https://doi.org/10.1016/j.energy.2021.122559 doi: 10.1016/j.energy.2021.122559
    [56] Harry B, Rafiq S, Salim R (2015) Economic growth with coal, oil and renewable energy consumption in China: Prospects for fuel substitution. Econ Model 104–115. https://doi.org/10.1016/j.econmod.2014.09.017 doi: 10.1016/j.econmod.2014.09.017
    [57] Liang W, Yang M (2019) Urbanization, economic growth and environmental pollution: Evidence from China. Sustain Comput Informatics Syst 21: 1–9. https://doi.org/10.1016/j.suscom.2018.11.007 doi: 10.1016/j.suscom.2018.11.007
    [58] Saqib N, Duran IA, Hashmi N (2022) Impact of Financial Deepening, Energy Consumption and Total Natural Resource Rent on CO2 Emission in the GCC Countries: Evidence from Advanced Panel Data Simulation. Int J Energy Econ Policy 12: 400–409. https://doi.org/10.32479/ijeep.12907 doi: 10.32479/ijeep.12907
    [59] Tamazian A, Chousa JP, Vadlamannati KC (2009) Does higher economic and financial development lead to environmental degradation: Evidence from BRIC countries. Energy Policy 37: 246–253. https://doi.org/10.1016/j.enpol.2008.08.025 doi: 10.1016/j.enpol.2008.08.025
    [60] Islam F, Shahbaz M, Ahmed AU, et al. (2013) Financial development and energy consumption nexus in Malaysia: A multivariate time series analysis. Econ Model 30: 435–441. https://doi.org/10.1016/j.econmod.2012.09.033 doi: 10.1016/j.econmod.2012.09.033
    [61] Shahbaz M, Hye QMA, Tiwari AK, et al. (2013) Economic growth, energy consumption, financial development, international trade and CO2 emissions in Indonesia. Renew Sustain Energy Rev 25: 109–121. https://doi.org/10.1016/j.rser.2013.04.009 doi: 10.1016/j.rser.2013.04.009
    [62] Destek MA, Sarkodie SA (2019) Investigation of environmental Kuznets curve for ecological footprint: The role of energy and financial development. Sci Total Environ 650: 2483–2489. https://doi.org/10.1016/j.scitotenv.2018.10.017 doi: 10.1016/j.scitotenv.2018.10.017
    [63] Naqvi B, Rizvi SKA, Mirza N, et al. (2023) Financial market development: A potentiating policy choice for the green transition in G7 economies. Int Rev Financ Anal 87: 102577. https://doi.org/10.1016/j.irfa.2023.102577 doi: 10.1016/j.irfa.2023.102577
    [64] Nyiwul L (2018) Income, environmental considerations, and sustainable energy consumption in Africa. 15: 264–276. https://doi.org/10.1080/15435075.2018.1439037
    [65] Hu Y, Jiang W, Dong H, et al. (2022) Transmission channels between financial efficiency and renewable energy consumption: Does environmental technology matter in high-polluting economies? J Clean Prod 368: 132885. https://doi.org/10.1016/j.jclepro.2022.132885 doi: 10.1016/j.jclepro.2022.132885
    [66] Smith HE, Ryan CM, Vollmer F, et al. (2019) Impacts of land use intensification on human wellbeing: Evidence from rural Mozambique. Glob Environ Chang 59: 101976. https://doi.org/10.1016/j.gloenvcha.2019.101976 doi: 10.1016/j.gloenvcha.2019.101976
    [67] Pinto LV, Inácio M, Ferreira CSS, et al. (2022) Ecosystem services and well-being dimensions related to urban green spaces – A systematic review. Sustain Cities Soc 85: 104072. https://doi.org/10.1016/j.scs.2022.104072 doi: 10.1016/j.scs.2022.104072
    [68] Panayotou T (1993) Empirical tests and policy analysis of environmental degradation at different stages of economic development.
    [69] Kaye AD, Okeagu CN, Pham AD, et al. (2021) Economic impact of COVID-19 pandemic on healthcare facilities and systems: International perspectives. Best Pract Res Clin Anaesthesiol 35: 293–306. https://doi.org/10.1016/j.bpa.2020.11.009 doi: 10.1016/j.bpa.2020.11.009
    [70] Bel G, Rosell J (2017) The impact of socioeconomic characteristics on CO2 emissions associated with urban mobility: Inequality across individuals. Energy Econ 64: 251–261. https://doi.org/10.1016/j.eneco.2017.04.002 doi: 10.1016/j.eneco.2017.04.002
    [71] Awodumi OB, Adewuyi AO (2020) The role of non-renewable energy consumption in economic growth and carbon emission: Evidence from oil producing economies in Africa. Energy Strateg Rev 27: 100434. https://doi.org/10.1016/j.esr.2019.100434 doi: 10.1016/j.esr.2019.100434
    [72] Kong YS, Khan R (2019) To examine environmental pollution by economic growth and their impact in an environmental Kuznets curve (EKC) among developed and developing countries. PLoS One 14: e0209532. https://doi.org/10.1371/journal.pone.0209532 doi: 10.1371/journal.pone.0209532
    [73] Ahmed Z, Ahmad M, Rjoub H, et al. (2022) Economic growth, renewable energy consumption, and ecological footprint: Exploring the role of environmental regulations and democracy in sustainable development. Sustain Dev 30: 595–605. https://doi.org/10.1002/sd.2251 doi: 10.1002/sd.2251
    [74] Ouyang X, Li Q, Du K (2020) How does environmental regulation promote technological innovations in the industrial sector? Evidence from Chinese provincial panel data. Energy Policy 139: 111310. https://doi.org/10.1016/j.enpol.2020.111310 doi: 10.1016/j.enpol.2020.111310
    [75] Hussain M, Dogan E (2021) The role of institutional quality and environment-related technologies in environmental degradation for BRICS. J Clean Prod 304: 127059. https://doi.org/10.1016/j.jclepro.2021.127059 doi: 10.1016/j.jclepro.2021.127059
    [76] Li W, Ullah S (2022) Research and development intensity and its influence on renewable energy consumption: evidence from selected Asian economies. Environ Sci Pollut Res 29: 54448–54455. https://doi.org/10.1007/s11356-022-19650-9 doi: 10.1007/s11356-022-19650-9
    [77] Kwakwa PA, Adusah-Poku F, Adjei-Mantey K (2021) Towards the attainment of sustainable development goal 7: what determines clean energy accessibility in sub-Saharan Africa? Green Financ 3: 268–287. https://doi.org/10.3934/GF.2021014 doi: 10.3934/GF.2021014
    [78] Lange S, Pohl J, Santarius T (2020) Digitalization and energy consumption. Does ICT reduce energy demand? Ecol Econ 176: 106760. https://doi.org/10.1016/j.ecolecon.2020.106760 doi: 10.1016/j.ecolecon.2020.106760
    [79] Paschou T, Rapaccini M, Adrodegari F, et al. (2020) Digital servitization in manufacturing: A systematic literature review and research agenda. Ind Mark Manag 89: 278–292. https://doi.org/10.1016/j.indmarman.2020.02.012 doi: 10.1016/j.indmarman.2020.02.012
    [80] Wang J, Zhu J, Luo X (2021) Research on the measurement of China's digital economy development and the characteristics. J Quant Tech Econ 38: 26–42.
    [81] Yang J, Li X, Huang S (2020) Impacts on environmental quality and required environmental regulation adjustments: A perspective of directed technical change driven by big data. J Clean Prod 275: 124126. https://doi.org/10.1016/j.jclepro.2020.124126 doi: 10.1016/j.jclepro.2020.124126
    [82] Yao Y, Hu D, Yang C, et al. (2015) The impact and mechanism of fintech on green total factor productivity. Green Financ 3: 198–221. https://doi.org/10.3934/GF.2021011 doi: 10.3934/GF.2021011
    [83] Galli A, Wackernagel M, Iha K, et al. (2014) Ecological Footprint: Implications for biodiversity. Biol Conserv 173: 121–132. https://doi.org/10.1016/j.biocon.2013.10.019 doi: 10.1016/j.biocon.2013.10.019
    [84] Tsuchiya K, Iha K, Murthy A, et al. (2021) Decentralization & local food: Japan's regional Ecological Footprints indicate localized sustainability strategies. J Clean Prod 292: 126043. https://doi.org/10.1016/j.jclepro.2021.126043 doi: 10.1016/j.jclepro.2021.126043
    [85] Caglar AE, Yavuz E, Mert M, et al. (2022) The ecological footprint facing asymmetric natural resources challenges: evidence from the USA. Environ Sci Pollut Res 29: 10521–10534. https://doi.org/10.1007/s11356-021-16406-9 doi: 10.1007/s11356-021-16406-9
    [86] Usman M, Yaseen MR, Kousar R, et al. (2021) Modeling financial development, tourism, energy consumption, and environmental quality: Is there any discrepancy between developing and developed countries? Environ Sci Pollut Res 28: 58480–58501. https://doi.org/10.1007/s11356-021-14837-y doi: 10.1007/s11356-021-14837-y
    [87] Kahouli B (2017) The short and long run causality relationship among economic growth, energy consumption and financial development: Evidence from South Mediterranean Countries (SMCs). Energy Econ 68: 19–30. https://doi.org/10.1016/j.eneco.2017.09.013 doi: 10.1016/j.eneco.2017.09.013
    [88] Baloch MA, Zhang J, Iqbal K, et al. (2019) The effect of financial development on ecological footprint in BRI countries: evidence from panel data estimation. Environ Sci Pollut Res 26: 6199–6208. https://doi.org/10.1007/s11356-018-3992-9 doi: 10.1007/s11356-018-3992-9
    [89] Pesaran MH, Smith R (1995) Estimating long-run relationships from dynamic heterogeneous panels. J Econom 68: 79–113. https://doi.org/10.1016/0304-4076(94)01644-F doi: 10.1016/0304-4076(94)01644-F
    [90] Pesaran MH, Pesaran MH, Shin Y, et al. (1999) Pooled Mean Group Estimation of Dynamic Heterogeneous Panels. J Am Stat Assoc 94: 621–634. https://doi.org/10.1080/01621459.1999.10474156 doi: 10.1080/01621459.1999.10474156
    [91] Osman M, Gachino G, Hoque A (2016) Electricity consumption and economic growth in the GCC countries: Panel data analysis. Energy Policy 98: 318–327. https://doi.org/10.1016/j.enpol.2016.07.050 doi: 10.1016/j.enpol.2016.07.050
    [92] Benhabib J, Bond S, Cummings J, et al. (2004) Financial development, financial fragility, and growth. JSTORNV Loayza, R RanciereJournal money, Credit banking, 2006•JSTOR.
    [93] Samargandi N, Fidrmuc J, Ghosh S (2014) Financial development and economic growth in an oil-rich economy: The case of Saudi Arabia. Econ Model 43: 267–278. https://doi.org/10.1016/j.econmod.2014.07.042 doi: 10.1016/j.econmod.2014.07.042
    [94] Mohanty S, Sethi N (2022) The energy consumption-environmental quality nexus in BRICS countries: the role of outward foreign direct investment. Environ Sci Pollut Res 29: 19714–19730. https://doi.org/10.1007/s11356-021-17180-4 doi: 10.1007/s11356-021-17180-4
    [95] Hashem Pesaran M, Yamagata T (2008) Testing slope homogeneity in large panels. J Econom 142: 50–93. https://doi.org/10.1016/j.jeconom.2007.05.010 doi: 10.1016/j.jeconom.2007.05.010
    [96] Chudik A, Pesaran MH (2015) Common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors. J Econom 188: 393–420. https://doi.org/10.1016/j.jeconom.2015.03.007 doi: 10.1016/j.jeconom.2015.03.007
    [97] Westerlund J (2008) Panel cointegration tests of the Fisher effect. J Appl Econom 23: 193–233. https://doi.org/10.1002/jae.967 doi: 10.1002/jae.967
    [98] Dogan E, Ulucak R, Kocak E, et al. (2020) The use of ecological footprint in estimating the Environmental Kuznets Curve hypothesis for BRICST by considering cross-section dependence and heterogeneity. Sci Total Environ 723: 138063. https://doi.org/10.1016/j.scitotenv.2020.138063 doi: 10.1016/j.scitotenv.2020.138063
    [99] Huang Y, Haseeb M, Usman M, et al. (2022) Dynamic association between ICT, renewable energy, economic complexity and ecological footprint: Is there any difference between E-7 (developing) and G-7 (developed) countries? Technol Soc 68: 101853. https://doi.org/10.1016/j.techsoc.2021.101853 doi: 10.1016/j.techsoc.2021.101853
    [100] Khalid K, Usman M, Mehdi MA (2021) The determinants of environmental quality in the SAARC region: a spatial heterogeneous panel data approach. Environ Sci Pollut Res 28: 6422–6436. https://doi.org/10.1007/s11356-020-10896-9 doi: 10.1007/s11356-020-10896-9
    [101] Usman M, Kousar R, Yaseen MR, et al. (2020) An empirical nexus between economic growth, energy utilization, trade policy, and ecological footprint: a continent-wise comparison in upper-middle-income countries. Environ Sci Pollut Res 27: 38995–39018. https://doi.org/10.1007/s11356-020-09772-3 doi: 10.1007/s11356-020-09772-3
    [102] Shen Y, Hu W, Hueng CJ (2021) Digital Financial Inclusion and Economic Growth: A Cross-country Study. Procedia Comput Sci 187: 218–223. https://doi.org/10.1016/j.procs.2021.04.054 doi: 10.1016/j.procs.2021.04.054
    [103] Amin A, Dogan E, Khan Z (2020) The impacts of different proxies for financialization on carbon emissions in top-ten emitter countries. Sci Total Environ 740: 140127. https://doi.org/10.1016/j.scitotenv.2020.140127 doi: 10.1016/j.scitotenv.2020.140127
    [104] Bhattacharya M, Awaworyi Churchill S, Paramati SR (2017) The dynamic impact of renewable energy and institutions on economic output and CO2 emissions across regions. Renew Energy 111: 157–167. https://doi.org/10.1016/j.renene.2017.03.102 doi: 10.1016/j.renene.2017.03.102
    [105] Ahmed Z, Nathaniel SP, Shahbaz M (2021) The criticality of information and communication technology and human capital in environmental sustainability: Evidence from Latin American and Caribbean countries. J Clean Prod 286: 125529. https://doi.org/10.1016/j.jclepro.2020.125529 doi: 10.1016/j.jclepro.2020.125529
    [106] Adewale Alola A, Ozturk I, Bekun FV (2021) Is clean energy prosperity and technological innovation rapidly mitigating sustainable energy-development deficit in selected sub-Saharan Africa? A myth or reality. Energy Policy 158: 112520. https://doi.org/10.1016/j.enpol.2021.112520 doi: 10.1016/j.enpol.2021.112520
    [107] Kihombo S, Ahmed Z, Chen S, et al. (2021) Linking financial development, economic growth, and ecological footprint: what is the role of technological innovation? Environ Sci Pollut Res 28: 61235–61245. https://doi.org/10.1007/s11356-021-14993-1 doi: 10.1007/s11356-021-14993-1
    [108] Acaravci A, Ozturk I, I. O (2010) On the Relationship between Energy Consumption, CO2 Emissions and Economic Growth in Europe. Energy 35: 5412–5420. https://doi.org/10.1016/j.energy.2010.07.009 doi: 10.1016/j.energy.2010.07.009
    [109] Yu Y, Ren H, Kharrazi A, et al. (2015) Exploring socioeconomic drivers of environmental pressure on the city level: The case study of Chongqing in China. Ecol Econ 118: 123–131. https://doi.org/10.1016/j.ecolecon.2015.07.019 doi: 10.1016/j.ecolecon.2015.07.019
    [110] Wu Y, Zhang Y (2022) The Impact of Environmental Technology and Environmental Policy Strictness on China's Green Growth and Analysis of Development Methods. J Environ Public Health 2022. https://doi.org/10.1155/2022/1052824
    [111] Ulucak R, Danish, Khan SUD (2020) Does information and communication technology affect CO2 mitigation under the pathway of sustainable development during the mode of globalization? Sustain Dev 28: 857–867. https://doi.org/10.1002/sd.2041 doi: 10.1002/sd.2041
    [112] He K, Ramzan M, Awosusi AA, et al. (2021) Does Globalization Moderate the Effect of Economic Complexity on CO2 Emissions? Evidence From the Top 10 Energy Transition Economies. Front Environ Sci 9: 778088. https://doi.org/10.3389/fenvs.2021.778088 doi: 10.3389/fenvs.2021.778088
    [113] Juodis A, Karavias Y, Sarafidis V (2021) A homogeneous approach to testing for Granger non-causality in heterogeneous panels. Empir Econ 60: 93–112. https://doi.org/10.1007/s00181-020-01970-9 doi: 10.1007/s00181-020-01970-9
    [114] Sinha A, Sengupta T (2019) Impact of natural resource rents on human development: What is the role of globalization in Asia Pacific countries? Resour Policy 63: 101413. https://doi.org/10.1016/j.resourpol.2019.101413 doi: 10.1016/j.resourpol.2019.101413
    [115] Charfeddine L, Kahia M (2019) Impact of renewable energy consumption and financial development on CO2 emissions and economic growth in the MENA region: A panel vector autoregressive (PVAR) analysis. Renew Energy 139: 198–213. https://doi.org/10.1016/j.renene.2019.01.010 doi: 10.1016/j.renene.2019.01.010
    [116] Douglas I (2017) Ecosystems and human well-being. https://doi.org/10.1016/B978-0-12-809665-9.09206-5
    [117] Steffen W, Richardson K, Rockström J, et al. (2015) Planetary boundaries: Guiding human development on a changing planet. Science (80-) 347. https://doi.org/10.1126/science.1259855
    [118] Zhang Q, Yu Z, Kong D (2019) The real effect of legal institutions: Environmental courts and firm environmental protection expenditure. J Environ Econ Manage 98: 102254. https://doi.org/10.1016/j.jeem.2019.102254 doi: 10.1016/j.jeem.2019.102254
  • This article has been cited by:

    1. Xueying Wang, Ruiwen Wu, Xiao-Qiang Zhao, A reaction-advection-diffusion model of cholera epidemics with seasonality and human behavior change, 2022, 84, 0303-6812, 10.1007/s00285-022-01733-3
    2. Sebastian Aniţa, Vincenzo Capasso, Matteo Montagna, Simone Scacchi, 2024, Chapter 1, 978-3-031-60772-1, 1, 10.1007/978-3-031-60773-8_1
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1174) PDF downloads(110) Cited by(2)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog