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

Exploring the impact of green HRM practices on pro-environmental behavior via interplay of organization citizenship behavior

  • Received: 30 May 2022 Revised: 30 June 2022 Accepted: 05 July 2022 Published: 13 July 2022
  • JEL Codes: M10, M19

  • Using Green human resource management practices (HRMPs) as a multi-component construct, this study investigated the influence of bundle of Green HRMPs on pro-environmental behavior (Pro-EB) and organizational citizenship behavior towards the environment (OCBE), and examined the mediating effect of OCBE as a psychological mechanism that defines Green HRMPs and Pro-EB relationships. Data were obtained using self-administered questionnaires from a sample of 247 full-time academics working in public sector higher education institutions of Pakistan. The hypotheses were verified using partial least squares structural equation modelling (PLS-SEM). The results revealed that Green HRMPs bundle had a significant and positive effect on both Pro-EB and OCBE, and OCBE, in return, had a positive relationship with Pro-EB. It was further revealed that OCBE positively mediated the association between Green HRMPs bundles and Pro-EB. The originality of the study lies in conceptualizing Green HRMPs bundles as a multi-component construct and examining the relationships between Green HRMPs bundle, OCBE, and Pro-EB in the context of Pakistan's higher education institutions. Besides, exploring OCBE as a mediator between Green HRMPs bundles and Pro-EB is one of the novel contributions of this study. This study helps management and practitioners in developing Green strategies that can promote Green and Pro-EB among academics/faculty members.

    Citation: Abdul Samad Kakar, Mrestyal Khan. Exploring the impact of green HRM practices on pro-environmental behavior via interplay of organization citizenship behavior[J]. Green Finance, 2022, 4(3): 274-294. doi: 10.3934/GF.2022013

    Related Papers:

    [1] Hui Xu, Jun Kong, Mengyao Liang, Hui Sun, Miao Qi . Video behavior recognition based on actional-structural graph convolution and temporal extension module. Electronic Research Archive, 2022, 30(11): 4157-4177. doi: 10.3934/era.2022210
    [2] Xite Yang, Ankang Zou, Jidi Cao, Yongzeng Lai, Jilin Zhang . Systemic risk prediction based on Savitzky-Golay smoothing and temporal convolutional networks. Electronic Research Archive, 2023, 31(5): 2667-2688. doi: 10.3934/era.2023135
    [3] Min Li, Ke Chen, Yunqing Bai, Jihong Pei . Skeleton action recognition via graph convolutional network with self-attention module. Electronic Research Archive, 2024, 32(4): 2848-2864. doi: 10.3934/era.2024129
    [4] Jiangtao Zhai, Haoxiang Sun, Chengcheng Xu, Wenqian Sun . ODTC: An online darknet traffic classification model based on multimodal self-attention chaotic mapping features. Electronic Research Archive, 2023, 31(8): 5056-5082. doi: 10.3934/era.2023259
    [5] Bingsheng Li, Na Li, Jianmin Ren, Xupeng Guo, Chao Liu, Hao Wang, Qingwu Li . Enhanced spectral attention and adaptive spatial learning guided network for hyperspectral and LiDAR classification. Electronic Research Archive, 2024, 32(7): 4218-4236. doi: 10.3934/era.2024190
    [6] Huimin Qu, Haiyan Xie, Qianying Wang . Multi-convolutional neural network brain image denoising study based on feature distillation learning and dense residual attention. Electronic Research Archive, 2025, 33(3): 1231-1266. doi: 10.3934/era.2025055
    [7] Chengyong Yang, Jie Wang, Shiwei Wei, Xiukang Yu . A feature fusion-based attention graph convolutional network for 3D classification and segmentation. Electronic Research Archive, 2023, 31(12): 7365-7384. doi: 10.3934/era.2023373
    [8] Zengyu Cai, Liusen Xu, Jianwei Zhang, Yuan Feng, Liang Zhu, Fangmei Liu . ViT-DualAtt: An efficient pornographic image classification method based on Vision Transformer with dual attention. Electronic Research Archive, 2024, 32(12): 6698-6716. doi: 10.3934/era.2024313
    [9] Shaohu Zhang, Jianxiao Ma, Boshuo Geng, Hanbin Wang . Traffic flow prediction with a multi-dimensional feature input: A new method based on attention mechanisms. Electronic Research Archive, 2024, 32(2): 979-1002. doi: 10.3934/era.2024048
    [10] Jiange Liu, Yu Chen, Xin Dai, Li Cao, Qingwu Li . MFCEN: A lightweight multi-scale feature cooperative enhancement network for single-image super-resolution. Electronic Research Archive, 2024, 32(10): 5783-5803. doi: 10.3934/era.2024267
  • Using Green human resource management practices (HRMPs) as a multi-component construct, this study investigated the influence of bundle of Green HRMPs on pro-environmental behavior (Pro-EB) and organizational citizenship behavior towards the environment (OCBE), and examined the mediating effect of OCBE as a psychological mechanism that defines Green HRMPs and Pro-EB relationships. Data were obtained using self-administered questionnaires from a sample of 247 full-time academics working in public sector higher education institutions of Pakistan. The hypotheses were verified using partial least squares structural equation modelling (PLS-SEM). The results revealed that Green HRMPs bundle had a significant and positive effect on both Pro-EB and OCBE, and OCBE, in return, had a positive relationship with Pro-EB. It was further revealed that OCBE positively mediated the association between Green HRMPs bundles and Pro-EB. The originality of the study lies in conceptualizing Green HRMPs bundles as a multi-component construct and examining the relationships between Green HRMPs bundle, OCBE, and Pro-EB in the context of Pakistan's higher education institutions. Besides, exploring OCBE as a mediator between Green HRMPs bundles and Pro-EB is one of the novel contributions of this study. This study helps management and practitioners in developing Green strategies that can promote Green and Pro-EB among academics/faculty members.



    Tungiasis is a parasitic skin condition brought on by female sand fleas and is sometimes referred to as jiggers or sand flea infestation. Tropical and subtropical regions, especially the regions of America, Asia, Africa and the Caribbean, are infected with this disease. The flea enters into the skin, usually in areas where the skin is thin, such as the toes, heels and the spaces between toes and fingers [1]. The female sand flea burrows into the skin and grows into a small, swollen, and painful lesion, often resembling a tiny white or black dot. The flea then lays eggs inside this lesion and after development to complete the life cycle. The primary symptom of tungiasis is intense itching, leading to scratching, which can cause secondary bacterial infections. The affected area may become red, swollen, and painful. Over time, the lesions may grow larger and more uncomfortable [2]. Tungiasis is usually diagnosed based on clinical signs and symptoms. The presence of a specific lesion in the toes or feet, especially in areas with a history of sand flea infestations, helps with diagnosis [3]. The most effective treatment for tungiasis is the removal of the embedded sand fleas using sterilized instruments or a needle. The lesion should be cleaned and disinfected to prevent infections. In severe cases, topical antibiotics may be prescribed if secondary infections have developed [4]. Preventive measures include avoiding walking barefoot in sandy or contaminated areas and wearing protective footwear.

    Surgical extraction of embedded sand fleas under sterile medical conditions [5] can also be considered an efficacious therapeutic approach for its management. Tungiasis is a preventable condition, but it can cause significant discomfort and complications if left untreated [6]. If you suspect you have tungiasis or are experiencing symptoms, it is essential to seek medical attention for proper diagnosis and treatment. The infected areas often experience subpar living conditions and inadequate sanitation, making the inhabitants particularly susceptible to the infestation [7]. The afflicted populations face serious health and economical difficulties as a result of this neglected tropical illness. The mechanics of tungiasis transmission must be understood in order to adopt effective control measures and lessen the disease's effects. Jiggers, chigoe flea infection, and pulex penetrans infestation are a few of the historical names for tungiasis [8]. The female sand flea that transmits the disease burrows into the skin, concentrating on the feet, causing painful sores, inflammatory reactions, and secondary infections if left untreated.

    Mathematical models have significantly contributed to enhancing comprehension of the fundamental mechanisms of biological processes for public health [9][15]. Over the years, researchers and public health experts have dedicated significant efforts to gain insight into the spread of various infections [16]. Previous research has concentrated on a variety of disease-related topics [17], [18], from clinical symptoms and epidemiology to control methods and therapies. The frequency and geographic distribution of tungiasis have been examined in studies, revealing insight on the disease's burden and its effects on afflicted people [19], [20]. Kahuru et al conducted a study focused on employing an optimal control approach within a mathematical model to analyze the dynamics of tungiasis within a community [21]. The researchers in [22] established the stability results of the transmission dynamics of the disease. After that, the theory of optimal control is utilized, all with the ultimate goal of reducing the numbers of infested humans, infested animals, and sand flea populations [23]. The processes of disease transmission and the potential effects of interventions like better sanitation, health education, and treatment campaigns have both benefited greatly from these modeling studies [24]. Mathematical modeling of infectious diseases enhances our understanding of the diseases, facilitates evidence-based decision-making, and helps implement targeted interventions to reduce the burden of the condition in affected communities. In this work, we will enhance our scientific comprehension of tungiasis dynamics to provide more valuable perspectives for efficient management approaches. Through the utilization of mathematical modeling and simulation methods, we will evaluate the prospective consequences of treatments and facilitate decision-making within the realm of public health to improve the effectiveness of interventions and control measures.

    Fractional calculus is a branch of mathematics that deals with derivatives and integrals of non-integer orders. It extends the concepts of traditional calculus, which involves integer-order derivatives and integrals. Fractional calculus has found applications in various scientific fields [25][30], including epidemiology, where it can be used to model the spread of infectious diseases. It has been acknowledged that fractional calculus offers a more flexible framework for describing complex real-world problems [31], [32]. The Atangana-Baleanu fractional derivative is a type of fractional derivative that has been applied to various mathematical models, including epidemic models [33], [34]. Fractional calculus generalizes the concept of traditional derivatives and integrals to non-integer orders, allowing for a more flexible representation of complex phenomena, such as anomalous diffusion or power-law behaviors [35]. In the context of epidemic models, the Atangana-Baleanu fractional derivative has been utilized to introduce memory effects and long-range interactions into the system. In addition to this, these models can capture more realistic scenarios and provide insights into the long-term behavior of infectious diseases. Hence, we choose to represent the dynamics of tungiasis using a fractional framework to obtain more precise results.

    This article is organized as follows: The fundamental concepts and results of the fractional theory related to the ABC operator is presented in Section 2. In Section 3, we formulated a mathematical model for tungiasis through the ABC operator in the fractional framework. In Section 4, the suggested model is subsequently examined. In Section 5, the solution of the recommended model is investigated with the help of fixed-point theory. Then, we introduced a numerical scheme to highlight the dynamical behaviour of the system in Section 6. Finally, ending remarks of the work are presented with future work in Section 7.

    The main relevant findings and definitions of classical Caputo[36] and Atangana-Baleanu fractional derivatives[37] will be presented here and will be useful in the following portion of the paper.

    Definition 2.1. Let f:[p,q]R be a given function, then the fractional derivative of Caputo fractional derivative of order j is given by

    CpDjt(u(t))=1Γ(nj)tpun(κ)(tκ)nj1dκ,

    for j(n1,n), where nZ.

    Definition 2.2. The Atangana-Beleanu fractional derivative for a given function f in the Caputo form is introduced as

    ABCpDjtf(t)=B(j)1jtpf(κ)Ej[j(tκ)j1j]dκ,

    where fH1(p,q), q > p, and j[0,1]. In addition to this, B(j) is the normalization function which satisfies the condition B(0) = B(1) = 1.

    Definition 2.3. The integral of the ABC derivative is denoted by ABCpIjtf(t) and is defined as:

    ABCpIjtf(t)=1jB(j)f(t)+jB(j)Γ(j)tpf(κ)(tκ)j1dκ.

    Theorem 2.1. Assume f in a manner that fC[p,q], then we have the equation below mentioned in [37]:

    ABCpDȷt(f(t))<B(ȷ)1ȷf(t),wheref(t)=maxptq|f(t)|.

    Furthermore, it has been established that ABC derivatives satisfy the Lipschitz condition [37].

    ABCpDȷtf1(t)ABCpDȷtf2(t)<ϑ1f1(t)f2(t).

    Here we present a mathematical model of Tungiasis disease. In this approach, the total population is divided into four categories: group that practices good hygiene (P), susceptible (S), infected (I), and treated (T) groups. Then, the total population is

    N(t)=P(t)+S(t)+I(t)+T(t).

    At birth, the population that is most susceptible is recruited at a rate of (1γ)υ, whereas the group that practices good hygiene is recruited at γυ where υ represents the rate of recruitment at birth and γ represents the likelihood of being recruited into the category of good hygiene practices. The appropriate hygiene practice group (P) develops susceptibility (S) at a rate of φ. Individuals from the class (S) move to the class (I) with a rate Г. The infected individuals (I) transfer to the treated group (T) at a rate of ρ following therapy. We indicated the natural death rate by µ. The infection rate Г is defined as

    Γ=σεIN,

    where ϵ is the contact rate with infected people and σ is the likelihood of being infected after repeated exposure to infected people. Then our model with the above assumptions for tungiasis disease is as follows:

    {dPdt=γυ(φ+μ)P,dSdt=(1γ)υ+φP(Γ+μ)S,dIdt=ΓS(ω+ϱ+μ)I,dTdt=ϱIμT, (3.1)

    with appropriate initial condition

    P(0)>0, S(0)>0, I(0)>0, T(0)>0. (3.2)
    Table 1.  Parameter values with interpretation used in the proposed system.
    Parameter Interpretation
    γ Probability of recruitment in P(t)
    υ Birth or recruitment rate
    φ The losing rate of protection
    µ Death occurs naturally in each class
    Г Infection rate from susceptible to infected class
    ω Disease induced mortality rate
    ρ Treatment rate for the infection
    σ Rate of transmission of the infection
    ϵ Contact rate of infection

     | Show Table
    DownLoad: CSV

    It is acknowledged that epidemic models through the Atangana-Baleanu fractional derivative can more accurately represents the dynamics of infectious diseases than conventional integer derivatives. This inclusion enables a more comprehensive exploration of epidemic spread in intricate settings characterized by long-range interactions and memory effects, fostering an improved comprehension of the underlying mechanisms. Consequently, the refined insights gained from these fractional derivative-based models hold the potential to enhance the precision of epidemic predictions and facilitate the development of more efficacious control strategies. Nonetheless, it is crucial to acknowledge that the introduction of fractional derivatives into mathematical models may introduce increased system complexity, necessitating the utilization of specialized mathematical and numerical techniques for rigorous analysis and simulation. Thus, the model (3.1) recommended above can be written in fractional form as

    {ABC0DȷtP=γυ(φ+μ)P,ABC0DȷtS=(1γ)υ+φP(Γ+μ)S,ABC0DȷtI=ΓS(ω+ϱ+μ)I,ABC0DȷtT=ϱIμT. (3.3)

    All of the parameters in the recommended model (3.1) for tungiasis disease are considered to be positive. Furthermore, the term ABC0Djt in the above model indicates the ABC derivative. The effects of memory which arise in the epidemiological process but are not incorporated in the classical operators, are the driving force behind fractional order models. In Table 1, we illustrated the parameters of the recommended model with description.

    In this section, we deal with some analysis of the model, like steady-state analysis, and find the basic reproduction ratio R0 for the above model (3.3). As the system (3.3) models the population of humans, all state variable solutions with nonnegative beginning conditions are nonnegative t>0 and have a feasible region bound as follows:

    Ξ=((P,S,I,T)R4+;S,P,I,T0;Nυμ).

    In the upcoming step, we will focus on the steady-states of the suggested system of the infection. First, we take the following:

    ABC0DȷtP=ABC0DȷtS=ABC0DȷtI=ABC0DȷtT=0,

    then, the model (3.3) becomes

    {0=γυ(φ+μ)P,0=(1γ)υ+φP(Γ+μ)S,0=ΓS(ω+ϱ+μ)I,0=ϱIμT. (4.1)

    The disease-free equilibrium of an epidemic model refers to a stable state where the infectious disease has been eliminated from the population. Understanding the disease-free equilibrium is essential in assessing the effectiveness of control strategies and vaccination programs. It serves as a benchmark to measure the success of public health interventions in eliminating or controlling infectious diseases and preventing outbreaks. For the infection-free steady-state, we set

    P=Po,S=So,I=Io,T=To  and  N=No.

    Thus, we have

    Eo=(Po,So,Io,To)=(0,(1γ)υ(Γ+μ),0,0).

    The endemic equilibrium (EE) of an epidemic model refers to a stable state where the prevalence of the infectious disease remains constant over time. Understanding the endemic equilibrium of an epidemic model is crucial in assessing the long-term behavior of the infection and evaluating the quality of control measures in maintaining the disease at a manageable level. It provides valuable insights into the stability and persistence of the infection in a population and is a fundamental concept in the study of infectious disease dynamics. We indicate the EE of the system by (E*) and substitute Γ=σεIN. Then from (4.1), we have

    {0=γυ(φ+μ)P,0=(1γ)υ+φP(σεIN+μ)S,0=σεINS(ω+ϱ+μ)I,0=ϱIμT. (4.2)

    Solving the above system (4.2), we have

    E(PSIT)=E(γυφ+μN(ω+ϱ+μ)σε1(ω+ϱ+μ)[(φγμ+μ)υ(φ+μ)Nμ(ω+ϱ+μ)σε]ϱμ(ω+ϱ+μ)[(φγμ+μ)υ(φ+μ)Nμ(ω+ϱ+μ)σε]).

    The basic reproduction number is a fundamental concept in epidemiology that quantifies the potential of an infection to spread. It represents the average number of secondary infections generated by a single infected individual in a fully susceptible environment. If the basic reproduction number is less than 1, it means that, on average, each infected individual will cause fewer than one new infection during their infectious period. In this case, the disease will not be able to sustain itself in the population, and it will eventually die out. If this parameter is equal to 1, this implies that, on average, each infected individual will cause exactly one new infection during their infectious period. The disease will reach a stable endemic equilibrium, where the number of new infections is balanced by the number of recoveries, resulting in a constant prevalence of the disease in the population. If this parameter is greater than 1, this implies that each infected individual, on average, will cause more than one new infection during their infectious period. In this case, the disease has the potential to spread, and if left uncontrolled, it may lead to an epidemic outbreak.

    We symbolized this number as R0 and calculate it through the next-generation matrix method [38]. We take the infected class of the system (3.1), so we have

    ABC0DȷtI=ΓS(ω+ϱ+μ)I. (4.3)

    Let F be the matrix containing parameters that are entering into infected class and V be the matrix containing those parameters that leave infected classes while neglecting the negative signs, so we get

    F=ΓS=σεISN,

    and

    V=(ω+ϱ+μ)I.

    This implies that R0=σεω+ϱ+μ, which is the required R0 of the recommended system.

    Theorem 4.1. For j = 1, the infection-free steady-state E0 of the system (3.3) is locally asymptotically stable if R0<1, otherwise it is unstable.

    Proof. Let j = 1 and take the Jacobian matrix of the model (3.3) at infection-free steady-state E0 as

    J(Eo)=[(φ+μ)000φ(σεIoN+μ)σεIoN00σεIoNσεSoN(ϱ+ω+μ)000ϱμ].

    The above Jacobian matrix has the following characteristic equation:

    |J(Eo)λI|=0,

    furthermore, we have

    |(φ+μ)λ000φ(σεIoN+μ)λσεIoN00σεIoNσεSoN(ϱ+ω+μ)λ000ϱμλ|=0,

    and simplifying, we have

    ((φ+μ)λ)|(σεIoN+μ)λσεIoN0σεIoNσεSoN(ϱ+ω+μ)λ00ϱμλ|=0,

    which implies that λ1=(ϕ+µ) and

    |(σεIoN+μ)λσεIoN0σεIoNσεSoN(ϱ+ω+μ)λ00ϱμλ|=0,

    the simplification of which implies that

    (μλ)|(σεIoN+μ)λσεIoNσεIoNσεSoN(ϱ+ω+μ)λ|=0.

    From the above, we have λ2=µ and

    |(σεIoN+μ)λσεIoNσεIoNσεSoN(ϱ+ω+μ)λ|=0

    Hence, all the eigen values are negative. Furthermore, we have J1(E0) given by

    J1(E0)=[(σεIoN+μ)σεIoNσεIoNσεSoN(ϱ+ω+μ)]=0.

    To show the required result, we have to show that Tace(J1(Eo))<0 and Det(J1(Eo))>0, so

    Trace(J1(Eo))=(σεIoN+μ)+σεSoN(ϱ+ω+μ),
    =μ+σε(ϱ+ω+μ),
    =μ+σεϱωμ,
    =2μ+σε(ϱ+ω),
    Trace(J1(E0))=(2μσε+(ϱ+ω))<0,

    which implies that

    Trace(J1(Eo))<0.

    Also, we have

    Det(J1(E0))=|(σεIoN+μ)σεIoNσεIoNσεSoN(ϱ+ω+μ)|
    =[(σεIoN+μ)(σεSoN(ϱ+ω+μ))(σεIoN)(σεIoN)].

    Because R0<1 is given, so the Det will be positive, that is, Det(J1(E0))>0. Hence, the infection-free steady-state of the recommended system is locally asymptotically stable (LAS) for R0<1 and unstable in other cases.

    Theorem 4.2. For j = 1, the endemic steady-state (E*) of system (3.3) is LAS if R0>1 and is unstable in other circumstances.

    Proof. Let j = 1 and take the Jacobian matrix of system (3.3) at endemic steady-state (E*) as

    J(E)=[(φ+μ)000φ(σεIN+μ)σεIN00σεINσεSN(ϱ+ω+μ)000ϱμ,],

    furthermore, we get

    J(E)=[(φ+μ)000φ(σεWN+μ)σεWN00σεWN(ϱ+ω+μ)000ϱμ,],

    in which W=1(ω+ϱ+μ)[(φγμ+μ)υ(φ+μ)Nμ(ω+ϱ+μ)σε]. The characteristic equation is (φ+μ+λ)(μ+λ)[λ2+(σεWN+μ)λ+σε(ω+ϱ+μ)WN]=0, which implies that λ1=(ϕ+µ) and λ2=µ with the following

    λ2+(σεWN+μ)λ+σε(ω+ϱ+μ)WN=0. (4.4)

    Substituting the value of W into (4.4), we get

    λ2+mλ+n=0, (4.5)

    in which m=Ro((φγμ+μ)υ)(φ+μ)N and n=σε(φγμ+μ)υ(φ+μ)N(ω+ϱ+μ)μ. Hence it is clear that m,n>1, also R0=σεω+ϱ+μ>1. The eigenvalues provided by equation (4.5) are negative according to the Routh-Hurwitz criteria. Thus, whenever R0>1, the EE of the proposed model of tungiasis is locally asymptotically stable.

    In this section of the paper, we utilize fixed point theory to demonstrate the existence and uniqueness of the fractional order model (3.3) solution. The system of equations can be represented in the following way:

    {ABC0Dȷts(t)=U(t,v(t)),v(0)=v0,0<t<T<. (5.1)

    In the above (5.1), v(t)=(P,S,I,T) is the vector form of the state variables and U is a continuous vector function. Moreover, U is given by

    U=(U1U2U3U4)=(γυ(φ+μ)P,(1γ)υ+φP(Γ+μ)S,ΓS(ω+ϱ+μ)I,ϱIμT),

    and v0(t)=(P(0),S(0),I(0),T(0)) are initial conditions. In addition to this, the Lipschitz condition is fulfilled by U as

    U(t,v1(t))U(t,v2(t))Nv1(t)v2(t). (5.2)

    In the upcoming step, the existence and uniqueness of the fractional order dynamical model (3.3) will be proved.

    Theorem 5.1. The solution of fractional order (FO) model of equations (3.3) will be unique if the below mentioned condition satisfies:

    (1ȷ)ABC(ȷ)N+ȷABC(ȷ)Γ(ȷ)TȷmaxN<1. (5.3)

    Proof. In order to demonstrate the desired result, we utilize the Atangana-Beleanu (AB) fractional integral, as defined in (2.3), on system (5.1). This yields a non-linear Volterra integral equation as follows:

    v(t)=v0+1ȷABC(ȷ)U(t,r(t))+ȷABC(ȷ)Γ(ȷ)t0(tκ)ȷ1U(κ,v(κ))dκ. (5.4)

    Take I=(0,T) and the operator Φ:G(I,R4)G(I,R4) defined by

    Φ[v(t)]=v0+1ȷABC(ȷ)U(t,v(t))+ȷABC(ȷ)Γ(ȷ)t0(tκ)ȷ1U(κ,v(κ))dκ. (5.5)

    Equation (5.4) takes the following form

    v(t)=Φ[v(t)], (5.6)

    and the supremum norm on I is indicated by .I and is

    v(t)I=suptIv(t),v(t)G. (5.7)

    Certainly, G(I,R4) with norm .I becomes a Banach space and

    t0F(t,κ)v(κ)dκTF(t,κ)Iv(t)I, (5.8)

    with v(t)G(I,R4), F(t,κ)G(I2,R) in a manner that

    F(t,κ)I=supt,κI|F(t,κ)|. (5.9)

    Here, utilizing the definition of Φ shown in (5.6), we have

    Φ[v1(t)]Φ[v2(t)]I(1ȷ)ABC(ȷ)(U(t,v1(t))U(t,v2(t))+ȷABC(ȷ)Γ(ȷ)×t0(tκ)ȷ1(U(κ,v1(κ))U(κ,v2(κ)))dκI (5.10)

    Additionally, by applying the Lipschitz condition (5.2) and the triangular inequality, in combination with the result in (5.8), we arrive at the below expression after simplification:

    Φ[v1(t)]Φ[v1(t)]I((1ȷ)NABC(ȷ)+ȷABC(ȷ)Γ(ȷ)NTȷmax)v1(t)v2(t)I. (5.11)

    Consequently, we have the following:

    Φ[v1(t)]Φ[v1(t)]IBv1(t)v2(t)I, (5.12)

    in which

    B=(1ȷ)NABC(ȷ)+ȷABC(ȷ)Γ(ȷ)NTȷmax.

    It is evident that when condition (5.3) is met, Φ becomes a contraction, implying that the fractional order dynamical system (5.1) possesses a unique solution.

    In this section, we will present an iterative scheme for the numerical solution of the recommended model (3.3) of the infection. First, an iterative scheme will be developed and then the the solution pathways of the system will be represented through the scheme to understand the dynamics. We use the newly established numerical approach (iterative) proposed for the approximation of the AB integral operator [39]. We briefly describe and apply the aforesaid approach to our dynamical system (3.3) in order to show the impact of different parameters on the infection.

    Here, rewriting system (5.4) of the infection into the fractional integral equation form using the fundamental theorem of fractional calculus:

    s(t)s(0)=(1ȷ)ABC(ȷ)U(t,s(t))+ȷABC(ȷ)×Γ(ȷ)t0U(κ,x(ξ))(tκ)ȷ1dξ. (6.1)

    At t=tξ+1, ξ=0,1,2,..., we have

    s(tξ+1)s(0)=1ȷABC(ȷ)U(tξ,s(tξ))+ȷABC(ȷ)×Γ(ȷ)tξ+10U(κ,s(κ))(tξ+1κ)ȷ1dȷ,=1ȷABC(ȷ)U(tξ,s(tξ))+ȷABC(ȷ)×Γ(ȷ)ξj=0tj+1tjU(κ,s(κ))(tξ+1κ)ȷ1dȷ. (6.2)

    The function U(κ,s(κ)) can be estimated over the interval [tj,tj+1], and we apply the interpolation polynomial

    U(κ,s(κ))U(tj,s(tj))h(ttj1)U(tj1,s(tj1))h(ttj), (6.3)

    then substituting in (6.2), we get

    s(tξ+1)=s(0)+1ȷABC(ȷ)U(tξ,s(tξ))+ȷABC(ȷ)×Γ(ȷ)ξj=0(U(tj,s(tj))htj+1tj(ttj1)(tξ+1t)ȷ1dtU(tj1,s(tj1))htj+1tj(ttj)(tξ+1t)ȷ1dt). (6.4)

    After computing these integrals, the approximate answer is as follows:

    s(tξ+1)=s(t0)+1ȷABC(ȷ)U(tξ,s(tξ))+ȷABC(ȷ)ξj=0(hȷU(tj,s(tj))Γ(ȷ+2)((ξ+1j)ȷ(ξj+2+ȷ)(ξj)ȷ(ξj+2+2ȷ))hȷU(tj1,s(tj1))Γ(ȷ+2)((ξ+1j)ȷ+1(ξj)ȷ(ξj+1+ȷ))). (6.5)

    Finally, for the suggested model, we achieved the following recursive formulae:

    P(tξ+1)=P(t0)+1ȷABC(ȷ)U1(tξ,s(tξ))+ȷABC(ȷ)ξj=0(hȷU1(tj,s(tj))Γ(ȷ+2)((ξ+1j)ȷ(ξj+2+ȷ)(ξj)ȷ(ξj+2+2ȷ))hȷU1(tj1,s(tj1))Γ(ȷ+2)((ξ+1j)ȷ+1(ξj)ȷ(ξj+1+ȷ)))S(tξ+1)=S(t0)+1ȷABC(ȷ)U2(tξ,s(tξ))+ȷABC(ȷ)kj=0(fȷU2(tj,s(tj))Γ(ȷ+2)((ξ+1j)ȷ(ξj+2+ȷ)(ξj)ȷ(ξj+2+2ȷ))hȷU2(tj1,s(tj1))Γ(ȷ+2)((ξ+1j)ȷ+1(ξj)ȷ(ξj+1+ȷ)))I(tξ+1)=I(t0)+1ȷABC(ȷ)U3(tξ,s(tξ))+ȷABC(ȷ)ξj=0(hȷU3(tj,s(tj))Γ(ȷ+2)((ξ+1j)ȷ(ξj+2+ȷ)(ξj)ȷ(ξj+2+2ȷ))hȷU3(tj1,s(tj1))Γ(ȷ+2)((ξ+1j)ȷ+1(ξj)ȷ(ξj+1+ȷ)))T(tξ+1)=T(t0)+1ȷABC(ȷ)U4(tξ,s(tξ))+ȷABC(ȷ)ξj=0(fȷU4(tj,s(tj))Γ(ȷ+2)((ξ+1j)ȷ(ξj+2+ȷ)(ξj)ȷ(ξj+2+2ȷ))fȷU4(tj1,s(tj1))Γ(ȷ+2)((n+1j)ȷ+1(ξj)ȷ(ξj+1+ȷ))). (6.6)
    Figure 1.  Visualization of the tracking path behavior of the suggested model under varying fractional parameter values j, i.e., j = 0.5, 0.6, 0.7, 0.8.
    Figure 2.  Illustration of the solution pathways of the suggested model with varying values of the losing rate of protection φ, i.e., φ = 0.40, 0.45, 0.50, 0.55.
    Figure 3.  Illustration of the solution pathways of the suggested model with varying values of the treatment rate ρ, i.e., ρ = 0.02, 0.04, 0.06, 0.08.
    Figure 4.  Representing the time series of the class of the proposed system of the infection with varying values of the transmission probability σ, i.e., σ = 0.40, 0.50, 0.60, 0.70.
    Figure 5.  Visualization of the tracking path behavior of the suggested model under varying fractional parameter values j, i.e., j = 0.85, 0.90, 0.95, 1.00.

    We will utilize the above alterative approach to investigate the dynamical behaviour of the recommended fractional model of tungiasis. It is well-known that the graphical view analysis of epidemic models provide a comprehensive exploration of the model's behavior, leading to a better understanding of the epidemic's spread and potential control strategies. Here, we will perform different simulations to visualize the impact of different input factors on the system.

    The values of the input parameter and state variables of the system are assumed for numerical purposes. For our investigation, we conducted a series of simulations to analyze the behavior of the system under different conditions. In these simulations, we varied specific parameters and observed their impact on the solution pathways of the system. First, in Figure 1 and Figure 5, we examined the effect of the fractional parameter j on the dynamics of the system. By changing the fractional order, we aimed to understand its role in shaping the infection spread in the society. Notably, we observed that decreasing the fractional parameter led to a reduction in the infection rate within the community. This finding indicates that the fractional parameter can serve as a crucial control parameter for managing the epidemic. In Figure 2, we focused on the losing rate of protection and its influence on the dynamics of the tungiasis infection. The results clearly indicate that this parameter plays a pivotal role in determining the risk of infection within the population. A higher losing rate of protection was found to increase the susceptibility to infection, posing a potential threat to public health.

    The treatment rate was the primary parameter of interest in Figure 3. By varying the treatment rate ρ, we explored its impact on the transmission dynamics of the system. The simulation revealed that the treatment rate significantly affects the control of the infection. Higher values of ρ demonstrated a more effective reduction in infection rates, suggesting its importance in implementing effective intervention strategies. Lastly, Figure 4 focused on understanding the influence of the transmission probability on the tungiasis dynamics. Through this simulation, we visualized how changes in the transmission probability affect the overall dynamics of the infection. The results clearly illustrated that the transmission probability is a critical factor in shaping the infection spread within the community.

    Our numerical analysis provided valuable insights into the control and dynamics of tungiasis. The fractional parameter, losing rate of protection, treatment rate, and transmission probability all emerged as significant factors that influence the infection's behavior. In the realm of tungiasis control and intervention, our discovered insights provide a foundational framework for the formulation of effective strategies aimed at managing and mitigating the spread of the infection within affected populations. It is, however, crucial to acknowledge that the values employed in this analysis were assumptions crafted for numerical expediency and may not faithfully replicate real-world scenarios. Consequently, for heightened precision in predictions and practical implications, an imperative next step involves the meticulous validation and refinement of our model using authentic real-world data. This process is indispensable for aligning our theoretical framework with the intricacies of tangible scenarios and enhancing the applicability of our findings in the context of tungiasis control and management.

    In this study, we formulated an epidemic model for tungiasis disease in the framework of fractional Atangana-Baleanu derivative to conceptualize the transmission route of the infection. The biologically meaningful steady-states of the system are investigated through analytic methods. We determined the basic reproduction number of our fractional model, symbolized by R0. The existence and uniqueness of the model's solution has been demonstrated. We have shown that the infection-free steady-states of the recommended model are locally asymptotically stable if R0<1 and unstable in other cases, while the endemic steady-state is locally asymptotically stable if R0>1 and unstable in other circumstances. A numerical scheme is presented to illustrate the solution pathways of the recommended system of the infection. The dynamical behaviour of the model is presented with the variation of different input parameters. We recommended the most critical factors of the system for the control and subsequent of tungiasis. It is acknowledged that delays play a fundamental role in capturing the temporal dynamics of systems [40]. Incorporating delays into mathematical models enhances their predictive power and allows for a more accurate representation of real-world phenomena [41][43]. In the future work, we will incorporate time delay in the transmission dynamics of the disease to comprehend the dynamics of the disease and provide more accurate information for prevention.

    The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.



    [1] Amrutha VN, Geetha SN (2020) A systematic review on green human resource management: Implications for social sustainability. J Clean Prod 247: 119131. https://doi.org/10.1016/j.jclepro.2019.119131 doi: 10.1016/j.jclepro.2019.119131
    [2] Anwar N, Mahmood NHN, Yusliza MY, et al. (2020) Green Human Resource Management for organisational citizenship behaviour towards the environment and environmental performance on a university campus. J Clean Prod 256: 120401. https://doi.org/10.1016/j.jclepro.2020.120401 doi: 10.1016/j.jclepro.2020.120401
    [3] Appelbaum E, Bailey T, Berg P, et al. (2000) Manufacturing Advantage: Why High-Performance Work Systems Pay Off. Cornell University Press. https://doi.org/10.5465/amr.2001.4845847
    [4] Becker JM, Klein K, Wetzels M (2012) Hierarchical Latent Variable Models in PLS-SEM: Guidelines for Using Reflective-Formative Type Models. Long Range Plann 45: 359-394. https://doi.org/10.1016/j.lrp.2012.10.001 doi: 10.1016/j.lrp.2012.10.001
    [5] Bissing-Olson MJ, Iyer A, Fielding KS, et al. (2013) Relationships between daily affect and pro-environmental behavior at work: The moderating role of pro-environmental attitude. J Organ Behav 34: 156-175. https://doi.org/10.1002/job.1788 doi: 10.1002/job.1788
    [6] Boiral O (2009) Greening the corporation through organizational citizenship behaviors. J Bus Ethics 87: 221-236. https://doi.org/10.1007/s10551-008-9881-2 doi: 10.1007/s10551-008-9881-2
    [7] Boiral O, Paillé P (2012) Organizational citizenship behaviour for the environment: Measurement and validation. J Bus ethics 109: 431-445. https://doi.org/10.1007/s10551-011-1138-9 doi: 10.1007/s10551-011-1138-9
    [8] Boiral O, Talbot D, Paillé P (2015) Leading by example: A model of organizational citizenship behavior for the environment. Bus Strateg Environ 24: 532-550. https://doi.org/10.1002/bse.1835 doi: 10.1002/bse.1835
    [9] Bowen A, Kuralbayeva K, Tipoe EL (2018) Characterising green employment: The impacts of 'greening' on workforce composition. Energy Econ 72: 263-275. https://doi.org/10.1016/j.eneco.2018.03.015 doi: 10.1016/j.eneco.2018.03.015
    [10] Boxall P, Guthrie JP, Paauwe J (2016) Editorial introduction: Progressing our understanding of the mediating variables linking HRM, employee well-being and organisational performance. Hum Resour Manag J 26: 103-111. https://doi.org/10.1111/1748-8583.12104 doi: 10.1111/1748-8583.12104
    [11] Chaudhary R (2018) Can green human resource management attract young talent? An empirical analysis. in Evidence-based HRM: A global forum for empirical scholarship (Emerald Publishing Limited). https://doi.org/10.1108/EBHRM-11-2017-0058
    [12] Cheema S, Afsar B, Al-Ghazali BM, et al. (2020) How employee's perceived corporate social responsibility affects employee's pro-environmental behaviour? The influence of organizational identification, corporate entrepreneurship, and environmental consciousness. Corp Soc Responsib Environ Manag 27: 616-629. https://doi.org/10.1002/csr.1826 doi: 10.1002/csr.1826
    [13] Daniyal M, Khan M (2020) The role of HRM practices in retaining employees: Evidence from the banking sector. J Manag Info 7: 232-247. https://doi.org/10.31580/jmi.v7i4.1654 doi: 10.31580/jmi.v7i4.1654
    [14] Daily BF, Bishop JW, Govindarajulu N (2009) A conceptual model for organizational citizenship behavior directed toward the environment. Bus Soc 48: 243-256. https://doi.org/10.1177/0007650308315439 doi: 10.1177/0007650308315439
    [15] Dumont J, Shen J, Deng X (2017) Effects of green HRM practices on employee workplace green behavior: The role of psychological green climate and employee green values. Hum Resour Manage 56: 613-627. https://doi.org/10.1002/hrm.21792 doi: 10.1002/hrm.21792
    [16] Emerson RM (1976) Social exchange theory, annual review of sociology. Annu Rev https://doi.org/10.1146/annurev.so.02.080176.002003 doi: 10.1146/annurev.so.02.080176.002003
    [17] Faul F, Erdfelder E, Lang A-G, et al. (2007) G* Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behav Res Methods 39: 175-191.
    [18] Fawehinmi O, Yusliza MY, Mohamad Z, et al. (2020) Assessing the green behaviour of academics. Int J Manpow. https://doi.org/10.1108/IJM-07-2019-0347 doi: 10.1108/IJM-07-2019-0347
    [19] Fornell C, Larcker DF (1981) Evaluating Structural Equation Models with Unobservable Variables and Measurement Error J Mark Res 18: 39. https://doi.org/10.2307/3151312 doi: 10.2307/3151312
    [20] Gilal FG, Ashraf Z, Gilal NG, et al. (2019) Promoting environmental performance through green human resource management practices in higher education institutions: A moderated mediation model. Corp Soc Responsib Environ Manag 26: 1579-1590. https://doi.org/10.1002/csr.1835 doi: 10.1002/csr.1835
    [21] Graves LM, Sarkis J (2018). The role of employees' leadership perceptions, values, and motivation in employees' provenvironmental behaviors. J Clean Prod 196: 576-587. https://doi.org/10.1016/j.jclepro.2018.06.013 doi: 10.1016/j.jclepro.2018.06.013
    [22] Graves LM, Sarkis J, Gold N (2019) Employee proenvironmental behavior in Russia: The roles of top management commitment, managerial leadership, and employee motives. Resour Conserv Recycl. 140: 54-64. https://doi.org/10.1016/j.resconrec.2018.09.007 doi: 10.1016/j.resconrec.2018.09.007
    [23] Hair JF, Hult GTM, Ringle CM, et al. (2017) A primer on partial least squares structural equation modeling (PLS-SEM). Sage Publications.
    [24] Hair JF, Ringle CM, Sarstedt M (2011) PLS-SEM: Indeed a Silver Bullet. J Mark Theory Pract 19: 139-152. doi: 10.2753/MTP1069-6679190202 doi: 10.2753/MTP1069-6679190202
    [25] Hair Jr JF, Hult GTM, Ringle C, et al. (2016) A primer on partial least squares structural equation modeling (PLS-SEM). Sage publications.
    [26] Haldorai K, Kim WG, Garcia RLF (2022) Top management green commitment and green intellectual capital as enablers of hotel environmental performance: The mediating role of green human resource management. Tour Manag 88: 104431. https://doi.org/10.1016/j.tourman.2021.104431 doi: 10.1016/j.tourman.2021.104431
    [27] Hanna MD, Newman WR, Johnson P (2000) Linking operational and environmental improvement through employee involvement. Int J Oper Prod Manag https://doi.org/10.1108/01443570010304233 doi: 10.1108/01443570010304233
    [28] Henseler J, Ringle CM, Sarstedt M (2015) A new criterion for assessing discriminant validity in variance-based structural equation modeling. J Acad Mark Sci 43: 115-135. https://doi.org/10.1007/s11747-014-0403-8. doi: 10.1007/s11747-014-0403-8
    [29] Hicklenton C, Hine DW, Loi NM (2019) Can work climate foster pro-environmental behavior inside and outside of the workplace? PLoS One 14. https://doi.org/10.1371/journal.pone.0223774 doi: 10.1371/journal.pone.0223774
    [30] Huselid MA (1995) The Impact Of Human Resource Management Practices On Turnover, Productivity, And Corporate Financial Performance. Acad Manag J 38: 635-872. https://doi.org/10.5465/256741 doi: 10.5465/256741
    [31] Jabbour CJC (2011) How green are HRM practices, organizational culture, learning and teamwork? A Brazilian study. Ind Commer Train. https://doi.org/10.1108/00197851111108926 doi: 10.1108/00197851111108926
    [32] Jravis CB, MacKenzie SB, Podsakoff PM (2003) A Critical Review of Construct Indicators and Measurement Model Misspecification in Marketing and Consumer Research. J Consum Res 30: 199-218. https://doi.org/10.1086/376806 doi: 10.1086/376806
    [33] Khan M, Daniyal M, Ashraf MZ (2020) The Relationship Between Monetary Incentives and Job Performance: Mediating Role of Employee Loyalty. Int J Multi Curr Edu Res. 2: 12-21.
    [34] Khan M, Rubab S, Awan TM, et al. (2022) The Relationship Between Social Media Marketing Activities and Brand Attachment: An Empirical Study from Pakistan. J Asian Fin Econ Bus 9: 219-230. https://doi.org/10.13106/jafeb.2022.vol9.no6.0219 doi: 10.13106/jafeb.2022.vol9.no6.0219
    [35] Kollmuss A, Agyeman J (2002) Mind the gap: why do people act environmentally and what are the barriers to pro-environmental behavior? Environ Educ Res 8: 239-260. https://doi.org/10.1080/13504620220145401 doi: 10.1080/13504620220145401
    [36] Kooij DTAM, Boon C (2018) Perceptions of HR practices, person-organisation fit, and affective commitment: The moderating role of career stage. Hum Resour Manag J 28: 61-75. https://doi.org/10.1111/1748-8583.12164 doi: 10.1111/1748-8583.12164
    [37] Kuvaas B (2008) An exploration of how the employee-organization relationship affects the linkage between perception of developmental human resource practices and employee outcomes. J Manag Stud 45: 1-25. https://doi.org/10.1111/j.1467-6486.2007.00710.x doi: 10.1111/j.1467-6486.2007.00710.x
    [38] Lamm E, Tosti-Kharas J, Williams EG (2013) Read this article, but don't print it: Organizational citizenship behavior toward the environment. Gr Organ Manag 38: 163-197. https://doi.org/10.1177/1059601112475210 doi: 10.1177/1059601112475210
    [39] Larson LR, Stedman RC, Cooper CB, et al. (2015). Understanding the multi-dimensional structure of pro-environmental behavior. J Environ Psychol 43: 112-124. https://doi.org/10.1016/j.jenvp.2015.06.004 doi: 10.1016/j.jenvp.2015.06.004
    [40] Lu H, Zhang L, Miethe TD (2002) Interdependency, communitarianism and reintegrative shaming in China. Soc Sci J 39: 189-201. https://doi.org/10.1016/S0362-3319(02)00162-3 doi: 10.1016/S0362-3319(02)00162-3
    [41] Lülfs R, Hahn R (2013) Corporate greening beyond formal programs, initiatives, and systems: A conceptual model for voluntary pro-environmental behavior of employees. Eur Manag Rev 10: 83-98. https://doi.org/10.1111/emre.12008 doi: 10.1111/emre.12008
    [42] Luu TT (2018) Employees' green recovery performance: the roles of green HR practices and serving culture. J Sustain Tour 26: 1308-1324. https://doi.org/10.1080/09669582.2018.1443113 doi: 10.1080/09669582.2018.1443113
    [43] Luu TT (2019) Green human resource practices and organizational citizenship behavior for the environment: the roles of collective green crafting and environmentally specific servant leadership. J Sustain Tour 27: 1167-1196. https://doi.org/10.1080/09669582.2019.1601731 doi: 10.1080/09669582.2019.1601731
    [44] Malik SY, Cao Y, Mughal YH, et al. (2020) Pathways towards Sustainability in Organizations: Empirical Evidence on the Role of Green Human Resource Management Practices and Green Intellectual Capital. Sustainability 12: 3228. https://doi.org/10.3390/su12083228 doi: 10.3390/su12083228
    [45] Mishra P (2017) Green human resource management: A framework for sustainable organizational development in an emerging economy. Int J Organ Anal 25: 762-788. https://doi.org/10.1108/IJOA-11-2016-1079 doi: 10.1108/IJOA-11-2016-1079
    [46] Mousa SK, Othman M (2020) The impact of green human resource management practices on sustainable performance in healthcare organisations: A conceptual framework. J Clean Prod 243: 118595. https://doi.org/10.1016/j.jclepro.2019.118595 doi: 10.1016/j.jclepro.2019.118595
    [47] Niyomdecha L, Yahya KK (2019) Examining The Relationship Between Human Resource Managemnt Practices And Organizational Citizenship Behavior For Environment Among Administrative Staff In A Thailand University. Sains Humanika 11. https://doi.org/10.11113/sh.v11n2-2.1653 doi: 10.11113/sh.v11n2-2.1653
    [48] Paillé P, Chen Y, Boiral O, et al. (2014). The impact of human resource management on environmental performance: An employee-level study. J Bus Ethics 121: 451-466. https://doi.org/10.1007/s10551-013-1732-0 doi: 10.1007/s10551-013-1732-0
    [49] Pham NT, Phan QPT, Tučková Z, et al. (2018) Enhancing the organizational citizenship behavior for the environment: the roles of green training and organizational culture. Manag Mark Challenges Knowl Soc 13: 1174-1189. https://doi.org/10.2478/mmcks-2018-0030 doi: 10.2478/mmcks-2018-0030
    [50] Pham NT, Thanh TV, Tučková Z, et al. (2019a) The role of green human resource management in driving hotel's environmental performance: Interaction and mediation analysis. Int J Hosp Manag 88: 102392. https://doi.org/10.1016/j.ijhm.2019.102392 doi: 10.1016/j.ijhm.2019.102392
    [51] Pham NT, Tučková Z, Phan QPT (2019b) Greening human resource management and employee commitment toward the environment: an interaction model. J Bus Econ Manag 20: 446-465. https://doi.org/10.3846/jbem.2019.9659 doi: 10.3846/jbem.2019.9659
    [52] Pinzone M, Guerci M, Lettieri E, et al. (2016) Progressing in the change journey towards sustainability in healthcare: the role of 'Green' HRM. J Clean Prod 122: 201-211. https://doi.org/10.1016/j.jclepro.2016.02.031 doi: 10.1016/j.jclepro.2016.02.031
    [53] Podsakoff PM, MacKenzie SB, Lee JY, et al (2003) Common Method Biases in Behavioral Research: A Critical Review of the Literature and Recommended Remedies. J Appl Psychol 88: 879-903. https://doi.org/10.1037/0021-9010.88.5.879 doi: 10.1037/0021-9010.88.5.879
    [54] Preacher KJ, Hayes AF (2004) SPSS and SAS procedures for estimating indirect effects in simple mediation mode. Behav Res Methods Instruments Comput 36: 717-731. https://doi.org/10.3758/BF03206553 doi: 10.3758/BF03206553
    [55] Preacher KJ, Hayes AF (2008) Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behav Res Methods 40: 879-891. https://doi.org/10.3758/BRM.40.3.879 doi: 10.3758/BRM.40.3.879
    [56] Ragas SFP, Tantay FMA, Chua LJC, et al. (2017) Green lifestyle moderates GHRM's impact on job performance. Int J Product Perform Manag. https://doi.org/10.1108/IJPPM-04-2016-0076 doi: 10.1108/IJPPM-04-2016-0076
    [57] Ren S, Tang G, Jackson SE (2018) Green human resource management research in emergence: A review and future directions. Asia Pacific J Manag 35: 769-803. https://doi.org/10.1007/s10490-017-9532-1 doi: 10.1007/s10490-017-9532-1
    [58] Renwick DWS, Redman T, Maguire S (2013) Green human resource management: A review and research agenda. Int J Manag Rev 15: 1-14. https://doi.org/10.1111/j.1468-2370.2011.00328.x doi: 10.1111/j.1468-2370.2011.00328.x
    [59] Robertson JL, Barling J (2017) Toward a new measure of organizational environmental citizenship behavior. J Bus Res 75: 57-66. https://doi.org/10.1016/j.jbusres.2017.02.007 doi: 10.1016/j.jbusres.2017.02.007
    [60] Saeed B Bin, Afsar B, Hafeez S, Khan I, Tahir M, Afridi MA (2019). Promoting employee's proenvironmental behavior through green human resource management practices. Corp Soc Responsib Environ Manag 26: 424-438. https://doi.org/10.1002/csr.1694 doi: 10.1002/csr.1694
    [61] Singh S, Darwish TK, Costa AC, et al. (2012) Measuring HRM and organisational performance: concepts, issues, and framework. Manag Decis. https://doi.org/10.1108/00251741211220282 doi: 10.1108/00251741211220282
    [62] Singh SK, Del Giudice M, Chierici R, et al. (2020) Green innovation and environmental performance: The role of green transformational leadership and green human resource management. Technol Forecast Soc Change 150: 119762. https://doi.org/10.1016/j.techfore.2019.119762 doi: 10.1016/j.techfore.2019.119762
    [63] Steg L, Bolderdijk JW, Keizer K, et al. (2014) An integrated framework for encouraging pro-environmental behaviour: The role of values, situational factors and goals. J Environ Psychol 38: 104-115. https://doi.org/10.1016/j.jenvp.2014.01.002 doi: 10.1016/j.jenvp.2014.01.002
    [64] Steg L, Vlek C (2009) Encouraging pro-environmental behaviour: An integrative review and research agenda. J Environ Psychol 29: 309-317. https://doi.org/10.1016/j.jenvp.2008.10.004 doi: 10.1016/j.jenvp.2008.10.004
    [65] Tang G, Chen Y, Jiang Y, et al. (2018) Green human resource management practices: scale development and validity. Asia Pacific J Hum Resour 56: 31-55. https://doi.org/10.1111/1744-7941.12147 doi: 10.1111/1744-7941.12147
    [66] Terrier L, Kim S, Fernandez S (2016) Who are the good organizational citizens for the environment? An examination of the predictive validity of personality traits. J Environ Psychol 48: 185-190. https://doi.org/10.1016/j.jenvp.2016.10.005 doi: 10.1016/j.jenvp.2016.10.005
    [67] Wall TD, Wood SJ (2005) The romance of human resource management and business performance, and the case for big science. Hum relations 58: 429-462. https://doi.org/10.1177/0018726705055032 doi: 10.1177/0018726705055032
    [68] Yong JY, Yusliza M-Y, Fawehinmi OO (2019) Green human resource management. Benchmarking An Int J 7: 2005-2027. https://doi.org/10.1108/BIJ-12-2018-0438 doi: 10.1108/BIJ-12-2018-0438
    [69] Yuriev A, Boiral O, Francoeur V, et al (2018) Overcoming the barriers to pro-environmental behaviors in the workplace: A systematic review. J Clean Prod 182: 379-394. https://doi.org/10.1016/j.jclepro.2018.02.041 doi: 10.1016/j.jclepro.2018.02.041
    [70] Yusoff Y (2019) Linking Green Human Resource Management Bundle to Environmental Performance in Malaysia's Hotel Industry: The Mediating Role of Organizational Citizenship Behaviour Towards Environment. Int J Innov Technol Explor Eng (IJITEE) 8: 1625-1630. https://doi.org/10.1177/0972150918779294 doi: 10.1177/0972150918779294
    [71] Zaid AA, Jaaron AAM, Bon AT (2018) The impact of green human resource management and green supply chain management practices on sustainable performance: An empirical study. J Clean Prod 204: 965-979. https://doi.org/10.1016/j.jclepro.2018.09.062 doi: 10.1016/j.jclepro.2018.09.062
    [72] Zibarras LD, Coan P (2015) HRM practices used to promote pro-environmental behavior: a UK survey. Int J Hum Resour Manag 26: 2121-2142. https://doi.org/10.1080/09585192.2014.972429 doi: 10.1080/09585192.2014.972429
    [73] Zientara P, Zamojska A, Maciejewski G, et al. (2019) Environmentalism and Polish coal mining: a multilevel study. Sustainability 11: 3086. https://doi.org/10.3390/su11113086 doi: 10.3390/su11113086
  • GF-04-03-013-s001.pdf
  • This article has been cited by:

    1. Dongfei Gao, A deep learning approach for energy management systems in smart buildings towards a low-carbon economy, 2025, 20, 1748-1325, 1136, 10.1093/ijlct/ctaf063
  • Reader Comments
  • © 2022 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(2249) PDF downloads(292) Cited by(6)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog