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Research article

Affordability, negative experiences, perceived racism, and health care system distrust among black American women aged 45 and over

  • Black Americans (AA) face a confluence of challenges when seeking care including unaffordable costs, negative experiences with providers, racism, and distrust in the healthcare system. This study utilized linear regressions and mediation analysis to explore the interconnectedness of these challenges within a community-based sample of 313 AA women aged 45 and older. Approximately 23% of participants reported affordability problems, while 44% had a negative experience with a provider. In the initial linear regression model excluding perceived racism, higher levels of distrust were observed among women reporting affordability problems (β = 2.66; p = 0.003) or negative experiences with a healthcare provider (β = 3.02; p = <0.001). However, upon including perceived racism in the model, it emerged as a significant predictor of distrust (β = 0.81; p = < 0.001), attenuating the relationships between affordability and distrust (β = 1.74; p = 0.030) and negative experience with a provider and distrust (β = 1.79; p = 0.009). Mediation analysis indicated that perceived racism mediated approximately 35% and 41% of the relationships between affordability and distrust and negative experience with a provider and distrust, respectively. These findings underscore the critical imperative of addressing racism in the efforts to mitigate racial disparities in healthcare. Future research should explore the applicability of these findings to other marginalized populations.

    Citation: Jacqueline Wiltshire, Carla Jackie Sampson, Echu Liu, Myra Michelle DeBose, Paul I Musey, Keith Elder. Affordability, negative experiences, perceived racism, and health care system distrust among black American women aged 45 and over[J]. AIMS Public Health, 2024, 11(4): 1030-1048. doi: 10.3934/publichealth.2024053

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  • Black Americans (AA) face a confluence of challenges when seeking care including unaffordable costs, negative experiences with providers, racism, and distrust in the healthcare system. This study utilized linear regressions and mediation analysis to explore the interconnectedness of these challenges within a community-based sample of 313 AA women aged 45 and older. Approximately 23% of participants reported affordability problems, while 44% had a negative experience with a provider. In the initial linear regression model excluding perceived racism, higher levels of distrust were observed among women reporting affordability problems (β = 2.66; p = 0.003) or negative experiences with a healthcare provider (β = 3.02; p = <0.001). However, upon including perceived racism in the model, it emerged as a significant predictor of distrust (β = 0.81; p = < 0.001), attenuating the relationships between affordability and distrust (β = 1.74; p = 0.030) and negative experience with a provider and distrust (β = 1.79; p = 0.009). Mediation analysis indicated that perceived racism mediated approximately 35% and 41% of the relationships between affordability and distrust and negative experience with a provider and distrust, respectively. These findings underscore the critical imperative of addressing racism in the efforts to mitigate racial disparities in healthcare. Future research should explore the applicability of these findings to other marginalized populations.



    In recent years, the problems of resource shortage and fragile ecological environment have appeared frequently, threatening the survival and development of posterity to a large extent. Therefore, many people have a keen interest in studying biological systems. Considering the maximization of net economic income, a bio-economic model was proposed in [1] which was based on differential-algebraic equation. Biological and economic stability by adding a popular dynamic was studied in [2,3,4]. The problem of how to obtain best harvest in the bio-economic model was studied in [5,6], which provides a theoretical basis for the rational development of biological resources. The optimal cost control problem of Markov jump system was solved in [7,8]. For the purpose of protecting the environment and maintaining the economic development stably and rapidly, it is very urgent and necessary to research the analysis of the bio-economic system.

    Singular systems have a larger application background in bio-economic systems [9]. The singular systems is different from the normal system in that its stability is more complex. It is well-known that a singular system can be stabilized only when it is regular and impulse-free [10,11]. Therefore, much effort was devoted to singular system and its applications. In the recent years, some singular bio-economic system models with stochastic and bifurcation properties are established, which shows that the research of the singular system is very broad and has good development prospects. A singular biological economy markov jump system is proposed in [12], which takes commodity price as markov chain. The bio-economic singular Markov jumping system was studied and the corresponding control design was proposed in [13].

    In natural environment, environmental fluctuation is a very important part of bio-economic system in real life. To a large extent, there are limitations in the application of deterministic methods in mathematical modeling. Therefore, the future dynamics of the system are difficult to accurately predict. In the various dynamic analysis of the system, the stochastic differential equation model is a important part. The ecological population system model was established using randomness in [14]. Some problems of T-S fuzzy system was researched and the applicaton of this type of system in bio-economy was explored in [15,16]. According to the theory of fishery resource economics, a stochastic singular bio-economic system which based on the T-S fuzzy model was established in [17].

    In practice, some systems can maintain asymptotic stability in an infinite time interval but they do not have good transient characteristics. Consequently, it is meaningful to study the transient behavior within a limited time interval. Several sufficient conditions for the continuous-time systems and discrete-time systems to maintain stability in a finite-time are given in [18,19]. In the singular system, the finite-time stability was redefined which have impulsive effects. Then at this time, sufficient conditions were derived in [20]. The conditions which linear stochastic systems can achieve finite-time stability was studied in [21]. The linear matrix inequality theory was used to obtain a series of properties of linear systems, nonlinear systems and stochastic systems in [22,23]. However, up to now, there are few studies on stochastic singular systems with parameter uncertainties and external disturbances. These problems are very important in practical application and also the main content of our research.

    The purpose of this paper is to research stability in finite-time and achieve control of the singular bio-economic system with stochastic fluctuations. It is undoubtedly challenging to control the density of biological population within a certain range and eliminate the influence of some unfavorable factors. This is also the motivation of this paper. The knowledge of the singular stochastic bio-economic system combined with the application of T-S fuzzy control in [24,25]. Firstly, the T-S fuzzy control model which based on the T-S fuzzy control method is established. Then, it provides a new sufficient condition for the system to achieve stochastic stability in finite-time. On this basis, a state feedback controller which can control the biological populations in a limited range through open resource management is designed. Finally, the effectiveness of the method is verified through simulation in the feasible region.

    Notations: The superscript T of a matrix represents its matrix transpose. A is a positive definite matrix if A>0. deg() represents the degree of the determinant. ε(x) represents expectation of stochastic variable x. diag() denotes a diagonal matrix. λmax(A) and λmin(A) stand for the largest eigenvalue and the smallest eigenvalue of matrix A.

    A single kind of dynamic model which has stage structure proposed by [26] is introduced as follows:

    {˙x1(t)=αx2(t)r1x1(t)βx1(t)ηx21(t),˙x2(t)=βx1(t)r2x2(t), (2.1)

    where x1(t) represents the population density of immature species at time t. x2(t) represents the population density of mature species at time t. α represents the inherent growth rate of the immature. β denotes the transition rate which from the immature species grow into mature species. r1 represents the death rate of immature species. r2 represents the death rate of mature species. ηx21(t) reflects restriction on the growth of immature species density.

    The economic profit is often affected by tax, season, market demand, capture costs and other factors. By the bio-economic theory, the sustainable economic profit should be the sustainable total revenue minus the sustainable total cost. If the population captured in the model (2.1) and the economic benefits of the young population captured are considered, and the economic profit m(t) changes with time, then the singular bio-economic system model can be established as follows:

    {˙x1(t)=αx2(t)r1x1(t)βx1(t)ηx21(t),˙x2(t)=βx1(t)r2x2(t),0=E1(p(t)x1(t)c)m(t), (2.2)

    where E1 represtents harvested effort of the immature species, c denotes the cost coefficient so cE1 represents the total cost, p(t) and m(t) represent the price coefficient and the economic benefits of each individual at time t, respectively.

    We notice that there are many random factors in nature and many other random factors caused by human activities, affecting or interfering the changes of immature population density and mature population density in the real environment. It is assumed that the parameters involved in the deterministic model (2.2) are deterministic and have nothing to do with environmental fluctuations. By considering these factors, we can replace the parameters r1 and r2 to introduce randomness into the model. Firstly, it is supposed that the white noise can affects the mortality rate of biological species by r1r1α1ξ(t) and r2r2α2ξ(t). Secondly, it is assumed that the population density will also be directly affected through the external random parameter ω(t).

    Therefore, the stochastic differential-algebraic equations is established as follows:

    {˙x1(t)=αx2(t)r1x1(t)βx1(t)ηx21(t)E1x1(t)+α1x1(t)ξ(t)+x1(t)w(t),˙x2(t)=βx1(t)r2x2(t)+α2x2(t)ξ(t),0=E1(p(t)x1(t)c)m(t), (2.3)

    where α1, α2 are used to represent two different intensities of the white noises. It is assumed that ξ(t) and ω(t) are independent of each other, the mean value is zero and the standard deviation is Gaussian white noises, that is E[ω(t)]=0, E[ω(t)ω(t+τ)]=δ(τ), δ(τ) is the Dirac function. In the context of biological systems, all the coefficients in Eq (2.3) are non-negative.

    There is a positive equilibrium point and a non-positive equilibrium point in system (2.3). In other words, there are two equilibrium points in total, and only the positive balance point is considered in the context of biological. Therefore, this paper only considers the positive equilibrium point under some certain conditions.

    For express more clearly, it is supposed that the equilibrium point is p=(x1x2m). In order to facilitate further study, the following transformations can be used:

    {ς1(t)=x1(t)x1,ς2(t)=x2(t)x2,ς3(t)=m(t)m. (3.1)

    The system (2.3) can be converted to:

    {˙ς1(t)=α(ς2(t)+x2)r1(ς1(t)+x1)β(ς1(t)+x1)η(ς1(t)+x1)2,E1(ς1(t)+x1)+α1(ς1(t)+x1)ξ(t)+(ς1(t)+x1)w(t)˙ς2(t)=β(ς1(t)+x1)r2(ς2(t)+x2)+α2(ς2(t)+x2)ξ(t),0=E1(p(t)(ς1(t)+x1)c)(ς3(t)+m). (3.2)

    The Eq (3.2) is obviously a nonlinear system. Since species density saturation exists, it can be assumed that ςi(t)(i=1,2,3) are bounded. Make the following changes to the system (3.2) to make expression more concise:

    E˙ς(t)=[Ω11α0βr2+α2ξ(t)0E1p(t)01]ς(t)+[αx2r1x1βx1ηx12E1x1+x1α1ξ(t)+x1ω(t)+ς1(t)w(t)βx1r2x2+x2α2ξ(t)E1p(t)x1E1cm], (3.3)

    where

    Ω11=r1βης1(t)2ηx1E1+α1ξ(t)
    ς(t)=[ς1(t)ς2(t)ς3(t)],E=[100010000].

    Let

    z(t)=r1βης1(t)2ηx1E1+α1ξ(t),

    so

    maxz(t)=r1βηςmin1(t)2ηx1E1+α1ξ(t),minz(t)=r1βηςmax1(t)2ηx1E1+α1ξ(t).

    z(t) is expressed as follows by the max-min values

    z(t)=M11(z(t))maxz(t)+M12(z(t))minz(t)

    where M11+M12=1 and M11, M12 denote the membership functions. Given the fuzzy rules as follows:

    Model rule 1:

    If z(t) is M11(z1(t)), then E.ς(t)=A1ς(t)+B1ς(t)w(t)

    Model rule 2:

    If z(t) is M12(z1(t)), then E.ς(t)=A2ς(t)+B2ς(t)w(t)

    The system (3.3) can be changed into Eq (3.8) by using the fuzzy rules:

    Edς(t)=Ahς(t)dt+Bς(t)dw(t) (3.4)

    where Ah=2i=1hi(z(t))Aihi(z(t))02i=1hi(z(t))=1B=B1=B2.

    Definition 3.1. (ⅰ) If there is a constant λ such that det(λEAh)0, then the system (3.4) is regular.

    (ⅱ) If rank(E)=deg(det(λEAh)), then the system (3.4) is impulse-free.

    Definition 3.2. Given a positive definite matrix R, for any two positive numbers l1, l2 then satisfy l1l2, the system (3.4) for (l1,l2,T,R) is stochastic finite-time admissible if

    ε{ςT(0)ETREς(0)}l1ε{ςT(t)ETREς(t)}l2,t[0,T]

    Definition 3.3. [27] Given a stochastic Lyapunov function V(x(t),t), where x(t) satisfies the following equation which is a stochastic differential equation in a stochastic system:

    dx(t)=f(t)dt+g(t)dw(t) (3.5)

    The definition of the weak infinitesimal operator L in the random process is given as {x(t),t>0}:

    LV(x(t),t)=V(x(t),t)t+V(x(t),t)xf(t)+12tr[gT(t)Vxx(x(t),t)g(t)] (3.6)

    Lemma 3.4. ([28] Gronwalls inequality) Given a non-negative function g(t), for any two constants m,n and they satisfy m,n0

    g(t)m+nt0g(s)ds,0tT (3.7)

    then

    g(t)mexp(nt) (3.8)

    Lemma 3.5. (Schur's complement) Exist any real matrix A,B,C, among them BT=B and CT=C>0, the following three conditions are equivalent:

    (i)B+AC1AT<0
    (ii)(BAATC)<0
    (iii)(BAATC)<0

    Lemma 3.6. [29](i) For two orthogonal matrices U and V, if rank(E)=r, then E can be decomposed as follows

    E=U[r00]VT=U[Ir00]vT (3.9)

    where r=diag{δ1,δ2,,δr},δk>0,k=1,2,,r

    Partition U=[U1U2],V=[V1V2],v=[V1rV2] with V2=0,UT2E=0.

    (ii)If P satisfies

    EPT=PET (3.10)

    Then

    ˜P=UTPv=[p11p120p22]. (3.11)

    We can have P110, det(P22)0 if P is nonsingular. Furthermore, P that satisfied Eq (3.10) can be set as follows

    P=EvTYv1+UZVT2 (3.12)

    where Y=diag{P11,Φ},Z=[PT11PT22]T, among this ΦR(nr)×(nr) is an arbitrary parameter matrix.

    (iii) The following equation holds if P is a nonsingular matrix, C and Φ are two positive definite matrices, Y is a diagonal matrix in Eq (3.12), P and E satisfy Eq (3.13)

    P1E=ETC12SC12E (3.13)

    Then the solution of Eq (3.13) can be expressed by S=C12UY1UTC12, where S is a positive definite matrix.

    In this section, we discuss whether the model (3.4) can be stable in a finite-time.

    Theorem 4.1. If there is a non-singular symmetric positive definite matrix Q makes any given time constant T>0 and scalar α>0 satisfy

    PET=EPT0 (4.1)
    P1E=ETR12QR12E (4.2)
    λmax(Q)l1eαTl2λmin(Q)<0 (4.3)

    and satisfy the following matrix inequalities:

    [A1PT+PAT1αEPT(EBPT)TEBPT˜Q]<0 (4.4)
    [A2PT+PAT2αEPT(EBPT)TEBPT˜Q]<0 (4.5)

    where ˜Q=R12Q1R12. Then the system (3.4) is tolerable in a stochastic finite-time for (l1,l2,T,R).

    Proof. Introduce the following Lyapunov function

    V(ς(t),t)=ςT(t)P1Eς(t) (4.6)

    Let L be the infinitesimal generator. We can get the following inequality:

    LV(ς(t),t)<αV(ς(t),t) (4.7)

    In the following, we can prove that the three conditions Eqs (4.7), (4.4) and (4.5) are equivalent. Applying Itˆo formula, we can get

    LV(ς(t),t)=ςT(t)(AThPT+P1Ah+BTP1EB)ς(t) (4.8)

    then

    LV(ς(t),t)αV(ς(t),t)=ςT(t)(AThPT+P1Ah+BTP1EBαP1E)ς(t) (4.9)

    Combining condition Eq (4.2) with ˜Q=R12Q1R12, Eq (4.9) can be transformed as

    LV(ς(t),t)αV(ς(t),t)=ςT(t)(AThPT+P1Ah+BTET˜Q1EBαP1E)ς(t) (4.10)

    Therefore, from Eq (4.10), Eq (4.7) is equivalent to

    AThPT+P1Ah+BTET˜Q1EBαP1E<0 (4.11)

    The left is multiplied by P and on the right multiplied by PT, we get

    PATh+AhPT+PCTET˜Q1EBPTαEPT<0 (4.12)

    It can be obtained that Eq (4.12) is equivalent to Eqs (4.4) and (4.5) by using matrix factorization and Schur's complement lemma. Integrating the left and right sides of Eq (4.7) from 0 to t at the same time and then taking the expected value, we can get

    ε{V(ς(t),t)}<V(ς(0),0)+αt0ε{V(ς(s),s)}ds (4.13)

    From Lemma 3.4, we have

    ε{V(ς(t),t)}<V(ς(0),0)eαt (4.14)

    from inequalities

    ε{V(ς(t),t)}=ε{ςT(t)ETR12QR12Eς(t)}λmin(Q)ε{ςT(t)ETREς(t)} (4.15)

    and

    V(ς(0),0)eαt=ςT(0)ETR12QR12Eς(0)eαtλmax(Q)ςT(0)ETREς(0)eαtλmax(Q)l1e (4.16)

    then, we get

    ε{ςT(t)ETREς(t)}<λmax(Q)λmin(Q)l1eαT (4.17)

    Considering condition Eq (4.3) and inequality (4.17), for the t[0,T], have

    ε{ςT(t)ETREς(t)}<l2 (4.18)

    In practice, the bio-economic system is more or less disturbed by the external environment. For example, the growth of a population can be affected by environmental factors such as the intensity of sunlight and the temperature. This section considers this random environment that affects populations as a zero-mean Gauss white noise. In order to achieve effective planning of capture strategies and maintain the sustainable development of market economy, some measures must be taken to stabilize the biological population. Therefore, control is added to the singular stochastic bioeconomic system model (2.3):

    {˙x1(t)=αx2(t)r1x1(t)βx1(t)ηx21(t)E1x1(t)+α1x1(t)ξ(t)+u(t)+x1(t)w(t),˙x2(t)=βx1(t)r2x2(t)+α2x2(t)ξ(t),0=E1(p(t)x1(t)c)m(t), (4.19)

    where u(t) represents the management degree of open resources and it is a control variable.

    Through the method which is similar to the T-S fuzzy method mentioned in Section 3, we get

    Edς(t)=2i=1hi(z(t))((Aiς(t)+Cu(t))dt+Bς(t)dw(t)) (4.20)

    Consider the following state feedback controller:

    u(t)=2i=1hi(z(t))Giς(t) (4.21)

    By designing the state feedback gain Gi.

    Thus, the corresponding closed-loop system can be expressed as

    Edς(t)=2i=1hi(z(t))2j=1hj(z(t))[(Ai+CGj)ς(t)dt+Bς(t)dw(t)] (4.22)

    where C=[100]T

    Next, design parameters of the fuzzy state feedback controller Eq (4.21), a new sufficient condition for the closed-loop singular stochastic bio-economic system to be stable in a finite-time is given.

    Theorem 4.2. The closed-loop system (4.22) is stochastic finite-time admissible for a state feedback controller Eq (4.21) relative to (l1,l2,T,R), if P is a nonsingular matrix, Q is a symmetric positive definite matrix and any matrix Yj,j=1,2 which can make Eqs (4.1)–(4.3) hold, and the following matrix inequalities can be satisfied:

    [γii(EBPT)TEBPT˜Q]<0,i=j,i,j=1,2 (4.23)
    [γij+γji(EBPT)TEBPT˜Q]<0,i<j,i,j=1,2 (4.24)

    where γij=PATi+YTjCT+AiPT+CYjαEPT and ˜Q=R12Q1R12, Next, we can choose the state feedback Gj=YjPT which we need.

    Proof. First, regularity and impulse-free of the system can be proved. Without loss of generality, denoting

    E=[Ir000]

    where rank(E)=rank(Ir)=rn.

    Suppose that there are two non-singular matrices H and K, then

    HEK=[Ir000]H(Ai+CGj)K=[Ai11Ai12Ai21Ai22]HBK=[B1B200]HTPK1=[P11P12P21P22] (4.25)

    Now, if (E,Ai+CGj) is impulse-free, we can prove the impulselessness of the system (4.22). The system (4.22) is impulse-free if

    rank[EAi+CGj0E]=n+rank(E) (4.26)

    It can be computed from Eq (4.25) that

    rank[EAi+CGj0E]=rank[Ir0Ai11Ai1200Ai21Ai2200Ir00000]=2r+rank(Ai22) (4.27)

    This shows Eq (4.26) is equivalent to n=r+rank(Ai22), then (E,Ai+CGj) is regular and impulse-free if Ai22 is non-singular simultaneously.

    Considering Theorem 4.1 and the system (4.22), the following matrix inequality can be obtained:

    2i=12j=1hi(z(t))hj(z(t))Δij<0 (4.28)

    where

    Δij=P(Ai+CGj)T+(Ai+CGj)PT+PCTET˜Q1EBPTαEPT

    Let

    Yj=GjPT

    Then

    2i=12j=1hi(z(t))hj(z(t))(PATi+YTjC+AiPT+CYj+PCTET˜Q1ECPTαEPT)<0 (4.29)

    Obviously, Eq (4.29) is equivalent to

    2i=1h2i(z(t))(γii+PCTET˜Q1ECPT)+2i=12j=1hi(z(t))hj(z(t))[(γij+γji+PCTET˜Q1ECPT)]<0 (4.30)

    Using matrix decomposition and Lemma 3.5, the above inequality (4.30) is equivalent to inequalities (4.23) and (4.24). Next, by using Eqs (4.2)–(4.3) and similar proof of Theorem 4.1, the system (4.22) is stochastic finite-time admissible for (l1,l2,T,R).

    Remark 1. By designing a fuzzy state feedback controller, the government's management of open resource development can be better expressded. The density of biological population can be controlled within a limited range and some unfavorable phenomena can be eliminated. In real life, managers should take some effective measures, such as adjusting taxes, introducing some preferential policies to stimulate the development of fisheries, reducing environmental pollution and so on. Thus, the population density can be strictly controlled and the economic benefits can be maintained steadily.

    We use the following special circumstances to prove that the results obtained are true and effective. Selection of ecological parameters based on Nile tilapia data from Lake Tanganyika in Africa.

    Consider the finite-time stability of bio-economic model with white noise, we choose the ecological parameters of the appropriate unit:

    α=0.4,r1=0.5,β=0.5,η=0.1α1=0.1,r2=0.1,α2=0.1,p(t)=1E1=0.8,c=3,ξ(t)=1,w(t)=0.1

    Then, the singular bioeconomic system can be obtained:

    {˙x1(t)=0.4x2(t)0.5x1(t)0.5x1(t)0.1x21(t)0.8x1(t)+0.1x1(t)ξ(t)+u(t)+x1(t)w(t),˙x2(t)=0.5x1(t)0.1x2(t)+0.1x2(t)ξ(t),0=0.8(p(t)x1(t)3)m(t), (5.1)

    where

    x1(t)[0,5],x2(t)[0,10],m(t)[0,5]

    We can get the system (5.1) has an equilibrium point p(5,15,1.225) when u(t)=0.

    For achieveing the transition from the equilibrium point to origin, a following fuzzy models can be constructed by using linear transformation (3.1):

    E.ζ(t)=[Ω110.400.50.1+0.1ξ(t)00.8p(t)01]ζ(t)+[5.5+0.5ξ(t)+5w(t)+ζ1(t)w(t)+u(t)11.5ξ(t)4p(t)3.625], (5.2)

    where

    ζ1(t)[5,0],ζ2(t)[15,5],ζ3(t)[1.225,3.775]
    Ω11=2.80.1ζ1(t)+0.1ξ(t)

    we have

    maxz(t)=3.3+0.1ξ(t)minz(t)=2.8+0.1ξ(t)

    By using the fuzzy rules mentioned above, we can execute the fuzzy model as:

    Edς(t)=2i=1hi(z(t))2j=1hj(z(t))[(Ai+CGj)ς(t)dt+Bς(t)dw(t)] (5.3)

    where

    E=[100010000],A1=[3.20.400.5000.801]A2=[2.70.400.5000.801],B=[4.50.50.375]C=[100]T

    Let

    α=0.001,l1=10000,l2=10000000,T=1000,R=I

    Then we get

    G1=[8.657947.25910.0345]G2=[8.622147.27850.0364]

    Therefore, we can get that ε{ζT(t)ETREζ(t)}<10000000, for all t[0,1000].

    From Figure 1, we can see the trajectory of a stochastic singular bio-economic system which is open-loop and considers the white noise. It can be seen that the species density and average price are unstable within a limited time. The economic interests fluctuates randomly in Figure 1, on account of the economic interests is affected by the population unit price and the species density of biological economic model which proposed in this paper in a randomly disturbed environment.

    Figure 1.  Trajectory of the open-loop stochastic singular system.

    From Figure 2, through the state feedback controller Eq (4.21), we can see the trajectory of a stochastic singular bio-economic system which is closed-loop and considers the white noise. It can be seen from Figure 2 that economic profits tend to be stabilize within a limited time.

    Figure 2.  Trajectory of the closed-loop stochastic singular system.

    In this paper, the finite time stability and control of a kind of singular bio-economic system with stochastic fluctuations which based on T-S fuzzy model are studied. Through two theorems, we derived some new sufficient conditions to guarantee the stability of system in finite time. The corresponding controller design method is also given. Finally, the effectiveness of the method is verifies through a numerical simulation. The results are also applicable to other types of systems which is similar to the system of this paper.

    From a biological point of view, the biological species density can be controlled within a certain range through the fuzzy state feedback controller which designed in this paper, eliminating influence of some unfavorable factors, It can better control the density of the population and keep the economic profit stable.

    This work is supported by National Natural Science Foundation of China under Grant 61673099.

    The authors declare there is no conflict of interest.


    Acknowledgments



    This study is not funded by any agency and is being conducted by the authors independently.

    Authors' contribution



    Jacqueline Wiltshire devised the project, the main conceptual ideas, and wrote the manuscript. Carla Jackie Sampson contributed to the conceptualization and writing of the manuscript. Echu Liu contributed to the methods, statistical analysis, results, and discussion sections of the manuscript. Myra Michelle DeBose, Paul I Musey, and Keith Elder contributed to the conceptual ideas and worked on the discussion section of the manuscript.

    Conflict of interest



    Keith Elder is an editor-in-chief for AIMS Public Health and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.

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