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Effect of combining acid modification and heat-moisture treatment (HMT) on resistant starch content: A systematic review

  • Type 2 diabetes mellitus (DMT2) is a metabolic disease that is increasingly attracting public attention. Diabetes mellitus is expected to reach 439 million in the world in 2030. Resistant starch (RS) is an indigestible starch which has health properties which has health properties that can be used for preventing diabetes mellitus type 2. In order to increase the RS content, a dual modification method consisted of acidification and heat moisture treatment (HMT) can be applied. The Acid-HMT method is affected by various factors, i.e., acid types, acid concentration, water content ratio, HMT temperature and HMT processing time, and different treatments may result in different RS yields. This study aimed to analyze the effective treatment in the Acid-HMT dual modification to enhance RS content by using a systematic review based on the PRISMA method. The studies revealed that there were 11 articles (n = 68 data) which utilized various acid types combined with HMT. The utilization of acid-alcohol, HCl, and organic acid such as citric acid, acetic acid, and lactic acid resulted in different results of RS content in modified starch. In addition to acid types, treatment conditions such as acid concentration, acidification time, acidification temperature, water content ratio, HMT time, and HMT temperature also affected the resulted RS. The treatment with 0.2 M citric acid for 24 hours at 25 ℃ combined with HMT with 30% moisture at 110 ℃ for 8 hours resulted in the highest increase in RS content of modified starch.

    Citation: Ratu Reni Budiyanti, Didah Nur Faridah, Nur Wulandari, Anuraga Jayanegara, Frendy Ahmad Afandi. Effect of combining acid modification and heat-moisture treatment (HMT) on resistant starch content: A systematic review[J]. AIMS Agriculture and Food, 2023, 8(2): 479-495. doi: 10.3934/agrfood.2023025

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  • Type 2 diabetes mellitus (DMT2) is a metabolic disease that is increasingly attracting public attention. Diabetes mellitus is expected to reach 439 million in the world in 2030. Resistant starch (RS) is an indigestible starch which has health properties which has health properties that can be used for preventing diabetes mellitus type 2. In order to increase the RS content, a dual modification method consisted of acidification and heat moisture treatment (HMT) can be applied. The Acid-HMT method is affected by various factors, i.e., acid types, acid concentration, water content ratio, HMT temperature and HMT processing time, and different treatments may result in different RS yields. This study aimed to analyze the effective treatment in the Acid-HMT dual modification to enhance RS content by using a systematic review based on the PRISMA method. The studies revealed that there were 11 articles (n = 68 data) which utilized various acid types combined with HMT. The utilization of acid-alcohol, HCl, and organic acid such as citric acid, acetic acid, and lactic acid resulted in different results of RS content in modified starch. In addition to acid types, treatment conditions such as acid concentration, acidification time, acidification temperature, water content ratio, HMT time, and HMT temperature also affected the resulted RS. The treatment with 0.2 M citric acid for 24 hours at 25 ℃ combined with HMT with 30% moisture at 110 ℃ for 8 hours resulted in the highest increase in RS content of modified starch.



    In December 2019, the world is facing the emergence of a new pandemic, which is called coronavirus disease 2019 (COVID-19). Then, COVID-19 spreads to world widely over the first two months in 2020. There were 492,510 confirmed cases of COVID-19 infection and 22,185 dead cases in world [1], [2]. Therefore, it poses a continuing threat to human health because of its high transmission efficiency and serious infection consequences as well, it transmits by direct contact. Many researchers have tried to study and understand the dynamical behavior of COVID-19 through the transmission dynamics and calculate the basic reproduction number of COVID-19. It has become a key quantity to determine the spread of epidemics and control it. For example, in [3], Li et al. conducted a study of the first 425 confirmed cases in Wuhan, China, showing that the reproduction number of COVID-19 was 2.2, and revealed that person to person transmission occurred between close contacts. Other research [4] shows that the reproduction number of COVID-19 becomes 2.90, which is being increasing. In [5], Riou et al. studied pattern of early human to human transmission of COVID-19 in Wuhan, China. In [6], Hellewell et al. investigated the feasibility of controlling 2019-nCoV outbreaks by isolation of cases and contacts. Chen et al.[7], suggested mathematical model for simulation the phase-based transmissibility of novel coronavirus. Bentout et al. [8] developed an susceptible exposed infectious recovered model to estimation and prediction for COVID-19 in Algeria. Belgaid et al.[9] suggested and analysis of a model for Coronavirus spread. Owolabi et al. [10] proposed and analyzed a nonlinear epidemiological model for SARS CoV-2 virus with quarantine class. Flaxman et al. [11] suggested and estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe. Kennedy et al. [12] suggested a mathematical model involving the effects of intervention strategies on COVID-19 transmission dynamics. Feng et al. [13] studied a COVID-19 model with the effects of media and quarantine in UK. In this present study, we will show effects of the quarantine strategy and media reports on the spread of COVID-19.

    We propose a mathematical model for COVID-19 transmission dynamics with the quarantine strategy and media effects. We start the model formulation by denoting the total size of the population by N which is classified further into five classes, the susceptible S(t), the exposed E(t), the infected I(t), the hospital quarantined Q(t) and the recovery R(t) at any time t, So, N=S+E+I+Q+R. The exposed class means low-level virus carrier, which is considered to be non infectious. The quarantined class in which the individual who is in the process in hospital, we suppose that only those who treat it will be in contact with the infected population. Accordingly, the flow of corona virus pandemic along with the above assumptions can be representing in the following block diagram:

    Figure 1.  Flow diagram of the compartmental model of COVID-19.

    And the corresponding dynamical model has formulated through the nonlinear differential equations as follows,

    dS(t)dt=A(β1β2Im+I)SIdS,dE(t)dt=(1c)(β1β2Im+I)SIk(β1β2Im+I)EIdE,dI(t)dt=c(β1β2Im+I)SI+k(β1β2Im+I)EI(ϵ+γ1+d+µ)I,dQ(t)dt=ϵI(d+γ2)Q,dR(t)dt=γ1I+γ2QdR,

    with initial conditions

    S(0)>0,E(0)>0,I(0)>0,Q(0)>0,R(0)>0.

    In model (1), the birth rate A is taken into susceptible class and natural death rate of population is given by the parameter d. The susceptible will be infected through sufficient direct contacts with infected people in the absence of media alerts by β1, with fraction parameter c, where c[0,1]. The term β2Im+I reduce the transmission as media continuously alert the susceptible and exposed regarding infected cases and possible preventive measures. Usually, we assume that β1β2. As well, we consider the media awareness cannot stop the outbreak of COVID-19 but can aware the population to minimize the transmission risk through half saturation of media constant m. The death due to disease rate µ affecting from infected class only. k represent to a fraction denoting the level of exogenous re-infection. The quarantined rate is given by ϵ. And the mean recovery rates of class I, Q are γi,i=1,2, respectively.

    It is easy see that the 4th and 5th equations are a linear differential equation with respect to variables I(t) and R(t), which are not appear in the other equations of model (1). Hence model (1) can be reduced to the following model:

    dS(t)dt=A(β1β2Im+I)SIdS,dE(t)dt=(1c)(β1β2Im+I)SIk(β1β2Im+I)EIdE,dI(t)dt=c(β1β2Im+I)SI+k(β1β2Im+I)EI(ϵ+γ1+d+µ)I.

    In this paper, we will discuss the dynamics of model (3) with initial conditions

    S(0)>0,  E(0)>0,  I(0)>0.

    This paper is organized as follows. In section 2, we will build the basic properties of model such as (positivity, boundedness of solutions and basic reproduction number). Existence of equilibrium points is presented in section 3. In section, the phenomenon of backward bifurcation is considered. The local and global stability of equilibrium points are studied in sections 4. In section 5, numerical simulation results are given. We conclude this paper with a brief conclusion.

    On the positivity of solutions for model (3), we have the following result.

    Theorem 2.1 Every solution of (3) with initial values (4) is positive as t > 0.

    Proof. Let t1=sup{t>0:S(t)>0,  E(t)>0,  I(t)>0}>0. It follows (3) that

    dS(t)dt=A(β1β2Im+I)SIdS,

    which can be written as

    ddt{S(t)exp[dt+t0(β1β2I(τ)m+I(τ))S(τ)I(τ)dτ]}          =Aexp[dt+t0(β1β2I(τ)m+I(τ))S(τ)I(τ)dτ].

    thus,

    S(t1)exp[dt1+t0(β1β2I(τ)m+I(τ))S(τ)I(τ)dτ]S(0)          =t10Aexp[dy+y0(β1β2I(τ)m+I(τ))S(τ)I(τ)dτ]dy,

    so that

    S(t1)=S(0)exp[dt110(β1β2I(τ)m+I(τ))S(τ)I(τ)dτ]          +exp[dt110(β1β2I(τ)m+I(τ))S(τ)I(τ)dτ]          ×t10Aexp[dy+y0(β1β2I(τ)m+I(τ))S(τ)I(τ)dτ]dy>0.

    Similarly, it can be shown that E(t) > 0 and I(t) > 0 for all time t > 0. Hence all solutions of the model (3) remain positive for all non-negative initial conditions, as required.

    Theorem 2.2 All solutions of model (1) which initiate in 5+ are uniformly bounded.

    Proof. Define the function N(t)=S(t)+E(t)+I(t)+Q(t)+R(t) and then take the time derivative of N(t) along the solution of model (1) gives dNdtALN. Then, dNdt+LNA, where L=min{d,d+µ}.

    Now, it is easy to verify that the solution of the above linear differential inequalities can be written as

    N(t)AL+(N0AL)eLt,

    where N0=(S(0),E(0),I(0),Q(0),R(0)). Hence,

    limsuptN(t)AL.

    and N(t)AL for t>0. Thus all solutions are uniformly bounded and the proof is complete.

    It is easy to see that model (3) always has a disease-free equilibrium P0(S0,0,0), where S0=Ad. We can calculate the reproduction number 0 of model (3) by using the next-generation matrix method illustrated by van den Driessche and Watmough in [14].

    0=cβ1Ad(ϵ+γ1+d+µ).

    Consequently, from Theorem 2 of [14], we have the following result.

    Theorem 2.3 The disease-free equilibrium P0 of the model (3) is locally asymptotically when 0<1 and P0 is unstable when 0>1.

    The basic reproduction number for COVID-19 infection 0 measures the average number of new COVID-19 infections generated by a single infected individual in a completely susceptible population [14], [15]. Theorem 2.3 implies that COVID-19 can be eliminated from the community (when 0<1) if the initial sizes of the sub-populations of the model (3) are in the attraction basin of the disease-free equilibrium P0. To ensure that COVID-19 elimination is independent of the initial sizes of the sub-populations, it is necessary to show that the disease-free equilibrium P0 is globally asymptotically stable when 0<1.

    In this section, we consider the number of equilibrium solutions the model (3). To do so, let P*(S*,E*,I*) be any arbitrary equilibrium of the model (3). Setting the right sides of the model (3) to zero gives

    S*=AX*I*+d,E*=(1c)AX*I*(kXI*+d)(X*I*+d).

    here

    X*=β1β2I*m+I*.

    Since we assume β1>β2, S* and E* are positive. now, substituting (12) in 3rd equation of the model (3) and simplifying it, we get

    D1I*4+D2I*3+D3I*2+D4I*+D5=0,

    where

    D1=k(ϵ+γ1+d+µ)(β1β2)2,D2=kA(β1β2)2(ϵ+γ1+d+µ)(β1β2)[d(k+1)+2kmβ1],D3=A(β1+β2)(2kmβ1+cd)(ϵ+γ1+d+µ)[md(k+1)(2β1+β2)+d2+kβ21m2],D4=kAβ21m2+cdA[β1(m+1)β2md(ϵ+γ1+d+µ)(2d+mβ1),D5=d2m2(ϵ+γ1+d+µ)(01).

    From (15), we can find that D1<0. And D5>0 when 0>1, D5<0 when 0<1. Thus, the number of possible positive real roots the polynomial (12) can have depends on the signs of D2, D3 and D4. Let f(x)=D1x4+D2x3+D3x2+D4x+D5. The various possibilities for the roots of f(x) can be analyzed using the Descartes Rule of Signs. The various possibilities for the roots of f(x) are tabulated in Table 1.

    Table 1.  Number of possible positive real roots of equation (14).
    Cases D1 D2 D3 D4 D5 R0 Number of sign changes Number of possible positive real roots
    1 + + + + 0 > 1 1 1
    + + + 0 < 1 2 0,2
    2 + + + 0 > 1 3 1,3
    + + 0 < 1 2 0,2
    3 + + + 0 > 1 3 1,3
    + + 0 < 1 4 0,2,4
    4 + + 0 > 1 3 1,3
    + 0 < 1 2 0,2
    5 + + + 0 > 1 1 1
    + + 0 < 1 2 0,2
    6 + + 0 > 1 3 1,3
    + 0 < 1 2 0,2
    7 + + 0 > 1 1 1
    + 0 < 1 2 0,2
    8 + 0 > 1 1 1
    0 < 1 0 0

     | Show Table
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    Theorem 3.1 The model (3)

    (i) has a unique endemic equilibrium if 0>1 and whenever Cases 1, 5, 7 and 8 are satisfied;

    (ii) could have more than one endemic equilibrium if 0>1 and Cases 2, 3, 4 and 6 are satisfied;

    (iii) could have 2 or more endemic equilibria if 0<1 and Cases 1–7 are satisfied.

    From the 4th and 5th equations of model (1) we can determent the values of Q* and R* through

    Q*=ϵI*d+γ2,R*=γ1I*+γ2Q*d.

    The existence of multiple endemic equilibria when 0<1 suggests the possibility of backward bifurcation [16], where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when 0<1. This is can be obtained using Centre Manifold Theory.

    Theorem 3.2 The model (3) exhibits backward bifurcation whenever m>(1c)2Aβ2d2 and no backward bifurcation otherwise.

    Proof. To prove existence of backward bifurcation in the model (3) the Center Manifold approach as outlined by Castillo-Chavez and Song in [17] is used.

    Firstly, for clarity and understanding of the Center Manifold Theory the model (3) variables are transformed as follows x1=S,  x2=E,  x3=I. Define X=(x1,x2,x3)Τ (Τ denotes transpose), such that the model (3) can be rewritten as dXdt=F(X) where F=(f1,f2,f3). Hence,

    dx1(t)dt=f1=A(β1β2x3m+x3)x1x3dx1,dx2(t)dt=f2=(1c)(β1β2x3m+x3)x1x3k(β1β2x3m+x3)x2x3dx2,dx3(t)dt=f3=c(β1β2x3m+x3)x1x3+k(β1β2x3m+x3)x2x3(ϵ+γ1+d+µ)x3.

    Now let β1=β*1 be the bifurcation parameter. Observe that at 0=1,

    β1=β*1=d(ϵ+γ1+d+µ)cA.

    With β1=β*1 the transformed model equation (17) has a simple eigenvalue with zero real part and all other eigenvalues are negative (that is has a hyperbolic equilibrium point). Thus, Center Manifold Theory can be applied to investigate the local dynamics of the transformed system (17) near β1=β*1. Now the Jacobian matrix of the transformed system evaluated at COVID-19 free equilibrium P0 is obtained as

    J(P0)=(d0β1S00d(1c)β1S000cβ1S0(ϵ+γ1+d+µ)).

    It is easy to obtain the right eigenvectors of this Jacobian matrix as V=(v1,v2,v3)Τ, where (v1,v2,v3)Τ=(β1S0d,(1c)β1S0d,1). Similarly, it is possible to obtain the left eigenvectors which are denoted by W=(w1,w2,w3)=(0,0,1). Now proceeding to obtain the bifurcation coefficients a and b as defined in Theorem 4.1 in [17].

    First the non-vanishing partial derivatives of the transformed model (17) evaluated at COVID-19 free equilibrium are obtained as

    2f1x1x3=2f1x3x1=mβ2β1,  2f1x23=2βS0m,

    2f2x1x3=2f2x3x1=(1c)β1,  2f2x2x3=2f2x3x2=kβ1,  2f2x23=2(1c)β2S0m,2f3x1x3=2f3x3x1=cβ1,  2f3x23=2cβ2m,

    so that

    a=3k,i,j=1wkvivj2fkxixj      =2w3v1v32f3x1x3+w3v232f3x23      =2cβ21S0d2(1(1c)2β2S0dm).

    The sign of the bifurcation parameter b is associated with the following non-vanishing partial derivatives of F(X), also evaluated at the disease free equilibrium P0:

    2f1x3β1=S0,  2f2x3β1=(1c)S0,  2f3x3β1=cS0.

    The bifurcation coefficient b is obtained as

    b=3k,i=1vkwi2fkxiβ1      =v1w32f1x3β1+v2w32f2x3β1+v3w32f3x3β1      =cS0(1+(2cβ1)Ad2)>0.

    Obviously, b is always positive. From Theorem 3.2 the system (17) will exhibit backward bifurcation phenomena if the bifurcation coefficient a is positive. The positivity of a in (22) gives the condition for backward bifurcation, which leads to

    m>(1c)2Aβ2d2.

    In this section, the stability analysis of the all equilibrium points of model (3) studied as shown in the following theorems by used some criterion.

    Theorem 4.1 The COVID-19 equilibrium point P* of the model (3) is locally asymptotically if the following conditions are hold

    β2I*(2m+I*)(m+I*)2<β1,

    [(β1β2I*(2m+I*)(m+I*)2)((1c)S*kE*)]+d(d1+k)k<XI*<cdk(1c)c.

    Proof. The Jacobian matrix of model (3) at P* can be written as

    J(P*)=(a110a13a21a22a23a31a320),

    here

    a11=(XI*+d),a13=β2S*I*(2m+I*)(m+I*)2β1S*,                         a21=(1c)XI*,a22=(kXI*+d),                                   a23=(1c)(β1S*β2S*I*(2m+I*)(m+I*)2)k(β1E*β2E*I*(2m+I*)(m+I*)2),a31=cXI*,a32=kXI*.

    clearly, the characteristics equation of J(P*) is given by

    λ3+B1λ2+B2λ+B3=0,

    where

    B1=[a11+a22],                                           B2=a11a22a13a31a23a32,                         B3=[a11(a23a32)+a13(a21a32a22a31)].

    furthermore, we have that

    Δ=B1B2B3                                                                          =a11a22[a11+a22]+a11a13a31+a22a23a32+a13a21a32.

    Now, according to Routh-huewitz criterion P* will be locally asymptotically stable provided that B1>0,B3>0 and Δ>0. It is clear that if above conditions (26)–(27) hold.

    The purpose of this section is to investigate the global stability by using Lyapunov function for COVID-19 free equilibrium point and COVID-19 equilibrium point respectively. We obtain the result in the following theorems

    Theorem 4.2 The disease-free equilibrium P0 is globally asymptotically stable provided that the following condition holds:

    0c<1.

    Proof. Consider the following function

    V0(S,E,I)=(SS0S0lnSS0)+E+I.

    clearly, V0:3+ is a continuously differentiable function such that V0(S0,0,0)=0 and V0(S,E,I)>0,  (S,E,I)(S0,0,0). Further, we have

    dV0dt=(SS0S)[A(β1β2Im+I)SIdS]                                                      +[(1c)(β1β2Im+I)SIk(β1β2Im+I)EIdE]                +[c(β1β2Im+I)SI+k(β1β2Im+I)EI(ϵ+γ1+d+µ)I].

    now, by doing some algebraic manipulation and using the condition (33), we get

    dV0dtdS(SS0)2β2S0I2m+IdE[(ϵ+γ1+d+µ)β1S0]I.

    Obviously, dV0/dt=0 at P0=(S,0,0), moreover dV0/dt<0 otherwise. Hence dV0/dt is negative definite and then the solution starting from any initial point satisfy the condition (33), will approaches asymptotically to COVID-19 free equilibrium point. Hence the proof is complete.

    Theorem 4.3 P* in case i of Th. (3.1) is globally asymptotically stable if 0>1.

    Proof. At the COVID-19 equilibrium point P*=(S*,E*,I*),S*,E* and I* satisfies the following equations

    A(β1β2Im+I)SIdS=0,(1c)(β1β2Im+I)SIk(β1β2Im+I)EIdE=0,c(β1β2Im+I)SI+k(β1β2Im+I)EI(ϵ+γ1+d+µ)I=0

    By above equations (4.4) and assumptions

    SS*=x,  EE*=y,  II*=u

    we obtian

    ˙x=x[AS*(1x1)β1I*(u1)+β2I2*m+I*(u2(m+I*)m+I1)]˙y=y{(1c)[β1S*I*E*(xuy1)β2S*I2*(m+I*)E*((m+I*)xu2(m+I)y1)]kβ1I*(u1)+kβ2I2*m+I*((m+I*)u2m+I1)}˙u=u[cβ1S*(x1)cβ2S*I*m+I*((m+I*)xum+I1)+kβ1E*(y1)kβ2E*I*m+I*((m+I*)yum+I1)]

    now, define the Lyapunov function

    V1=S*(x1lnx)+E*(y1lny)+I*(u1lnu)

    clearly, by derivative of V1 we get

    dV1dt=S*x1x˙x+E*y1y˙y+I*u1u˙u

    dV1dt=(x1)[A(1x1)β1S*I*(u1)+β2S*I2*m+I*(u2(m+I*)m+I1)]        +(y1){(1c)[β1S*I*(xuy1)β2S*I2*m+I*((m+I*)xu2(m+I)y1)]+kβ2E*I2*m+I*((m+I*)u2m+I1)}        +(u1)[cβ1S*I*(x1)cβ2S*I2*m+I*((m+I*)xum+I1)kβ2E*I2*m+I*((m+I*)yum+I1)]
    furthermore, by simplifying the resulting terms, we get that

    =A[2x1x]+β1S*I*[x+uc(x+u)(1c)(y+xuy)]    β2S*I2*m+I*[xy(1c)cu+(u2(1c)xu2ycxu)(m+I*m+I)]    kβ2E*I2*m+I*[yu+(u2uy)(m+I*m+I)]

    Since the arithmetical mean is greater than, or equal to the geometrical mean, then 2x1x0 for x>0 and 2x1x=0 if and only if x=1; x+uc(x+u)(1c)(y+xuy)0 for x,y,u>0 and x+uc(x+u)(1c)(y+xuy)=0 if and only if x=y=u=1; yu+(u2uy)(m+I*m+I)0 for y,u>0 and yu+(u2uy)(m+I*m+I)=0 if and only if y=u=1. Therefore, ˙V10 for x,y,u>0 and ˙V1=0 if and only if x=y=u=1, the maximum invariant set of model (3) on the set {(x,y,u):˙V1=0} is the singleton (1,1,1). Thus, the COVID-19 equilibrium point P* is globally asymptotically stable if 0>1,by LaSalle Invariance Principle [18]. Hence, the proof is complete.

    For the parameters values of model (1.1), we can chosen the parameters values from real data available sense Feb. 24 2020 to Apr. 5 2020. The total population of the Iraq for the year 2020 is approximately 40 × 106 [19]. The life expectancy in Iraq is approximatily 71.08 [19]. Clearly, we can obtain that the natural death rate d=3.8545×105 per day. The birth rate is estimated from A/d=N, and assumed that this is to be the bound population in the disease absence. So, A=1541.8 per day and the other parameters of our model shows that in Table 2.

    Table 2.  Definitions and values of model parameters.
    Parameter Definition Value Source
    A Birth rate 1541.8 [19]
    β1 Transmission contact rate between S and I 0.5 Estimated
    c Fraction constant [0–1] Estimated
    β2 Awareness rate 0.1 Estimated
    m Half saturation of media constant 70 Estimated
    d Natural death rate 3.854510−5 [19],[20]
    k Fraction denoting the level of exogenous re-infection 0.05 Estimated
    ϵ Quarantined rate 1/7 [13]
    γ1 Recovery rate from infected wihout quarantin strategy 0.033 Estimated
    γ2 Recovery rate from quarantin class 1/18 [13]
    µ Death due to disease rate 0.38 [19]

     | Show Table
    DownLoad: CSV

    We plot the solution trajectories of model (1) with initial point (15,20,500,1000,150) which converges to COVID-19 equilibrium point P*=(1,27,2773,5428,19371), shown that in Figure 2.

    Figure 2.  Solution trajectories converge to COVID-19 equilibrium point P*=(1,27,2773,5428,19371), by parameter value in Table 2.
    Table 3.  Different government control measures and corresponding β1 values.
    No. Date Government measures β1
    1 Feb. 24 2020 (1) detection of the first case of COVID-19 in Iraq 0.3
    (2) quarantined as preliminary control
    2 Feb. 25 2020 (1) medical examination for all individuals who are in contact with the affected case 0.1
    (2) cancellation of some mass gatherings
    (3) increase the awareness programs about prevention measures
    3 Feb. 25-Mar. 24 2020 (1) cancellation of all religious and social events throughout Iraq 0.09
    (2) preventing movement between all provinces
    (3) the suspension of attendance at universities and schools
    (4) providing a number of hospitals to be places for prevention confirmed cases
    4 Mar. 24-Apr. 5 2020 (1) close all borders with neighboring countries 0.08
    (2) to declare a state of emergency and impose a curfew
    (3) medical support from the government
    (4) methodological improvement on the diagnosis and treatment strategy
    (5) spontaneous household quarantine by citizens
    (6) more newly-hospitals put into use
    (7) massive online teaching in postponed semester
    (8) addition of new diagnosis method clinically diagnosis in Baghdad and some provinces

     | Show Table
    DownLoad: CSV

    In the face of the COVID-19 outbreak, many stringent measures were taken by Iraqi government will show in Table 3, to simulate the impact of different government control measures on the number of all S(t),E(t),I(t),Q(t) and R(t). We assumed that some values to contact rates with awareness Table 3, with the other parameters in Table 2 staying still on the all stages.

    The following Figure 3 shows the values of S(t),E(t),I(t),Q(t) and R(t) under government measures that above to control of COVID-19 outbreak.

    Figure 3.  Time series to value simulation curve of different values of contact rates β1=0.3,0.1,0.09,0.08 respectively with keeping other parameters values are taken in Table 2.

    Clearly, from above figure for effect of contact rate Table 3, We obtain that in case decrease the contact rate (social isolation) the reproduction number less than one and the dynamical behavior of model (1.1) still approaches to COVID-19 equilibrium point. Hence, the backward bifurcation is occur. Now, to investigate the effect of the quarantined strategy it is given by ϵ on the dynamical behavior of model (1.1) and to control to COVID-19 outbreak in Iraq. We study the impact of this parameter on values of S(t),E(t),I(t),Q(t) and R(t) in follows Table 4 and shows the results in Figure 4.

    Table 4.  Different government control measures and corresponding ϵ values.
    No. Date Government measures ϵ
    1 Feb. 24 2020 (1) quarantined as preliminary control in Iraq 0.2
    2 Feb. 25 2020 (1) medical examination for all individuals who are in contact with the affected case 0.4
    (2) cancellation of some mass gatherings
    (3) increase the awareness programs about prevention measures
    3 Feb. 25-Mar. 24 2020 (1) direct the media to explain the symptoms of the epidemic 2.5
    (2) Preventing movement between all provinces
    (3) Providing a number of hospitals to be places for prevention confirmed cases
    4 Mar. 24-Apr. 5 2020 (1) to declare a state of emergency and impose a curfew to reduce the contact between people 4.5
    (2) medical support from the government
    (3) methodological improvement on the diagnosis and treatment strategy
    (4) spontaneous household quarantine by citizens
    (5) addition of new diagnosis method clinically diagnosis in Baghdad and some provinces

     | Show Table
    DownLoad: CSV

    The following Figure 4 shows the values of S(t),E(t),I(t),Q(t) and R(t) under government measures that above to control of COVID-19 outbreak.

    Figure 4.  Time series to value simulation curve of different values of quarantined rates ϵ=0.2,0.4,2.5,4.5 respectively with keeping other parameters values are taken in Table 2.

    Clearly, from above investigate to impact of the quarantined strategy Table 4, when the quarantine strategy increasing we get the number of infected is decrease and other classes are increase. Here, we ask whether the quarantine strategy is the best solution? The answer is possible, but for specific numbers. Whereas, if the quarantine is more than the capacity of the health institutions. We get the dynamical behavior of model (1.1) lose the stability as shown in Figure 5.

    Figure 5.  Time series to value simulation curve of different values of quarantined rates 20.5 ≤ ϵ ≤ 30.5. With keeping other parameters values are taken in Table 2.

    In this research, a mathematical model of COVID-19 transmission has been proposed by compartment the total population into five epidemiological status, namely, susceptible S(t), exposed E(t), infected I(t), quarantine Q(t) and recovered R(t). The model incorporates the impact of social awareness programs conducted by public health officials with quarantine strategy in hospital. It has been noticed that these awareness programs and quarantine strategy result in human behavioral changes in order to avoid risk of disease transmission. The model mainly accounts for the reduction in disease class due to awareness. While we can say the disease goes away due to applied the quarantine it well. The proposed model has two biological equilibrium points are COVID-19 free and COVID-19. The COVID-19 free has been local stability when 0<1. Otherwise when 0>1, the COVID-19 free point becomes unstable and the dynamical behavior of the model converges to COVID-19 equilibruim point. The backward bifurcation occur if 0=1 at the parameter bifurcation β1=β*1=d(ϵ+γ1+d+µ)/cA. As well as the different government control measures have been also discussed. Furthermore, to shown and understand the effect of quarantine rate of disease we have choosed many different value of it say parameter then we have obtained some different results see Table 4 and Figure 4.



    [1] Cummings JH, Stephen AM (2007) Carbohydrate terminology and classification. Eur J Clin Nutr 61 (Suppl 1): S5–S18. https://doi.org/10.1038/sj.ejcn.1602936 doi: 10.1038/sj.ejcn.1602936
    [2] Kusnandar F (2020) Kimia Pangan Komponen Makro, Jakarta: Bumi Aksara, 133–141.
    [3] Englyst HN, Kingman SM, Cummings JH (1992) Classification and measurement of nutritionally important starch fractions. Eur J Clin Nutr 46 (Suppl 2): S33–50. https://pubmed.ncbi.nlm.nih.gov/1330528/
    [4] Wei HX, Liang BD, Chai YR, et al. (2020) Effect of Different Heat Treatments on Physicochemical Properties and Structural and Digestibility of Water Caltrop Starch. Starch 72:1–11. https://doi.org/10.1002/star.201900275 doi: 10.1002/star.201900275
    [5] Haralampu SG (2000) Resistant starch-a review of the physical properties and biological impact of RS3. Carbohydr Polym 41: 285–292. https://doi.org/10.1016/S0144-8617(99)00147-2 doi: 10.1016/S0144-8617(99)00147-2
    [6] Li Y, Su X, Shi F, et al. (2017) High-temperature air-fluidization-induced changes in the starch texture, rheological properties, and digestibility of germinated brown rice. Starch 69:1–10. https://doi.org/10.1002/star.201600328 doi: 10.1002/star.201600328
    [7] Weickert M, Mohlig C, Koebnick C, et al. (2005) Impact of cereal fibre on glucose-regulating factors. Diabetologia 48: 2343–2353. https://doi.org/10.1007/s00125-005-1941-x doi: 10.1007/s00125-005-1941-x
    [8] Shaikh F, Ali TM, Mustafa G, et al. (2021) Comparative study on effects of xanthan gum at different concentrations on the functional, thermal, and digestibility characteristics of corn and sorghum starch extrudates. Starch 73: 2000206. https://doi.org/10.1002/star.202000206 doi: 10.1002/star.202000206
    [9] Esfahani A, Wong JMW, Mirrahimi A, et al. (2009) The glycemic index: Physiological significance. J Am Coll Nutr 28: 439S–445S. https://doi.org/10.1080/07315724.2009.10718109 doi: 10.1080/07315724.2009.10718109
    [10] Maache-Rezzoug Z, Zarguili I, Loisel C, et al. (2008) Structural modifications and thermal transitions of standard maize starch after DIC hydrothermal treatment. Carbohydr Polym 74: 802–812. https://doi.org/10.1016/j.carbpol.2008.04.047 doi: 10.1016/j.carbpol.2008.04.047
    [11] Faridah DN, Damaiyanti S, Indrasti D, et al. (2021) Effect of heat moisture treatment on resistant starch content among carbohydrate sources: A meta-analysis. Int J Food Sci Technol 57: 1965–1974. https://doi.org/10.1111/ijfs.15276 doi: 10.1111/ijfs.15276
    [12] Hung P Van, My NTH, Phi NTL (2014) Impact of acid and heat-moisture treatment combination on physicochemical characteristics and resistant starch contents of sweet potato and yam starches. Starch 66: 1013–1021. https://doi.org/10.1002/star.201400104 doi: 10.1002/star.201400104
    [13] Massuquetto A, Durau JF, Ezaki Barrilli LN, et al. (2020) Thermal processing of corn and physical form of broiler diets. Poult Sci 99: 3188–3195. https://doi.org/10.1016/j.psj.2020.01.027 doi: 10.1016/j.psj.2020.01.027
    [14] Barretti BRV, Almeida VS de, Ito VC, et al. (2020) Combination of organic acids and heat-moisture treatment on the normal and waxy corn starch: thermal, structural, pasting properties, and digestibility. Food Sci 2061: 1–7. https://doi.org/10.1590/fst.33120 doi: 10.1590/fst.33120
    [15] Shaikh F, Ali TM, Mustafa G, et al. (2019) Comparative study on effects of citric and lactic acid treatment on morphological, functional, resistant starch fraction and glycemic index of corn and sorghum starches. Int J Biol Macromol 135: 314–327. https://doi.org/10.1016/j.ijbiomac.2019.05.115 doi: 10.1016/j.ijbiomac.2019.05.115
    [16] Maior L de O, de Almeida VS, Barretti BRV, et al. (2021) Combination of organic acid and heat–moisture treatment: impact on the thermal, structural, pasting properties and digestibility of maize starch. J Therm Anal Calorim 143: 265–273. https://doi.org/10.1007/s10973-019-09241-1 doi: 10.1007/s10973-019-09241-1
    [17] Van Hung P, Huong NTM, Phi NTL, et al. (2017) Physicochemical characteristics and in vitro digestibility of potato and cassava starches under organic acid and heat-moisture treatments. Int J Biol Macromol 95: 299–305. https://doi.org/10.1016/j.ijbiomac.2016.11.074 doi: 10.1016/j.ijbiomac.2016.11.074
    [18] Moher D, Liberati A, Tetzlaff J, et al. (2009) Academia and clinic annals of internal medicine preferred reporting items for systematic reviews and meta-analyses. Annu Intern Med 151: 264–269.
    [19] Afandi FA (2020) Meta-analisis Faktor-faktor Penentu Nilai Indeks Glikemik Bahan Pangan Pati-patian dan Verifikasinya dengan Menggunakan Model Pangan, Bogor: IPB University.
    [20] Afandi FA, Wijaya CH, Faridah DN, et al. (2021) Evaluation of various starchy foods: A systematic review and meta-analysis on chemical properties affecting the glycemic index values based on in vitro and in vivo experiments. Foods 10: 364. https://doi.org/10.3390/foods10020364 doi: 10.3390/foods10020364
    [21] Higgins J, Green S (2008) Cochrane Handbook for Systematic Reviews of Intervention. Hoboken: Wiley-Blackwell.
    [22] Lin JH, Lee SY, Chang YH (2003) Effect of acid-alcohol treatment on the molecular structure and physicochemical properties of maize and potato starches. Carbohydr Polym 53: 475–482. https://doi.org/10.1016/S0144-8617(03)00145-0 doi: 10.1016/S0144-8617(03)00145-0
    [23] Chang YH, Lin JH, Chang SY (2006) Physicochemical properties of waxy and normal corn starches treated in different anhydrous alcohols with hydrochloric acid. Food Hydrocoll 20: 332–339. https://doi.org/10.1016/j.foodhyd.2005.02.024 doi: 10.1016/j.foodhyd.2005.02.024
    [24] Lin J-HH, Singh H, Wen C-YY, et al. (2011) Partial-degradation and heat-moisture dual modification on the enzymatic resistance and boiling-stable resistant starch content of corn starches. J Cereal Sci 54: 83–89. https://doi.org/10.1016/j.jcs.2011.05.001 doi: 10.1016/j.jcs.2011.05.001
    [25] Hoover R, Vasanthan T (1994) Effect of heat-moisture treatment on the structure and physicochemical properties of cereal, legume, and tuber starches. Carbohydr Res 252: 33–53. https://doi.org/10.1016/0008-6215(94)90004-3 doi: 10.1016/0008-6215(94)90004-3
    [26] Shi YC, Capitani T, Trzasko P, et al. (1998) Molecular structure of a low-amylopectin starch and other high-amylose maize starches. J Cereal Sci 27: 289–299. https://doi.org/10.1006/jcrs.1997.9998 doi: 10.1006/jcrs.1997.9998
    [27] Li C, Dhital S, Gidley MJ (2022) High-amylose wheat bread with reduced in vitro digestion rate and enhanced resistant starch content. Food Hydrocoll 123: 107181. https://doi.org/10.1016/j.foodhyd.2021.107181 doi: 10.1016/j.foodhyd.2021.107181
    [28] Aparicio-Saguilán A, Valera-Zaragoza M (2015) Lintnerization of banana starch isolated from underutilized variety: morphological, thermal, functional properties, and digestibility. CyTA-Journal 13:1, 3–9. https://doi.org/10.1080/19476337.2014.902864 doi: 10.1080/19476337.2014.902864
    [29] Adhiyamaan PS, Parimalavalli R (2020) Effect of dual modification on crystalline formation of resistant starch from cassava. J Food Meas 14: 3520–3528. https://doi.org/10.1007/s11694-020-00580-4 doi: 10.1007/s11694-020-00580-4
    [30] Jayakody L, Hoover R (2002) The effect of lintnerization on cereal starch granules. Food Res Int 35: 665–680. https://doi.org/10.1016/S0963-9969(01)00204-6 doi: 10.1016/S0963-9969(01)00204-6
    [31] Ng JQ, Siew CK, Mamat H, et al. (2018) Effect of Acid Methanol Treatment and Heat Moisture Treatment on In Vitro Digestibility and Estimated Glycemic Index of Raw and Gelatinized Sago (Metroxylon Sagu) Starch. Starch 70: 776–780. https://doi.org/10.1002/mdc3.13341 doi: 10.1002/mdc3.13341
    [32] Brumovsky JO, Thompson DB (2001) Production of boiling‐stable granular resistant starch by partial acid hydrolysis and hydrothermal treatments of high‐amylose maize starch. Cereal Chem 78:680–689. https://doi.org/10.1094/CCHEM.2001.78.6.680 doi: 10.1094/CCHEM.2001.78.6.680
    [33] Kim JY, Huber KC (2013) Heat-moisture treatment under mildly acidic conditions alters potato starch physicochemical properties and digestibility. Carbohydr Polym 98: 1245–1255. https://doi.org/10.1016/j.carbpol.2013.07.013 doi: 10.1016/j.carbpol.2013.07.013
    [34] Schmiedl D, Bäuerlein M, Bengs H, et al. (2000) Production of heat-stable, butyrogenic resistant starch. Carbohydr Polym 43: 183–193. https://doi.org/10.1016/S0144-8617(00)00147-8 doi: 10.1016/S0144-8617(00)00147-8
    [35] De La Rosa-Millán J (2017) Physicochemical, Molecular, and digestion characteristics of annealed and heat-moisture treated starches under acidic, neutral, or alkaline pH. Cereal Chem 94: 770–779. https://doi.org/10.1094/CCHEM-03-16-0068-FI doi: 10.1094/CCHEM-03-16-0068-FI
    [36] Horstmann SW, Lynch KM, Arendt EK (2017) Starch characteristics linked to gluten-free products. Foods 6(29): 1–21. https://doi.org/10.3390/foods6040029 doi: 10.3390/foods6040029
    [37] Gidley MJ, Cooke D, Darke AH, et al. (1995) Molecular order and structure in enzyme-resistant retrograded starch. Carbohydr Polym 28: 23–31. https://doi.org/10.1016/0144-8617(96)81387-7 doi: 10.1016/0144-8617(96)81387-7
    [38] Waduge RN, Warkentin TD, Donner E, et al. (2017) Structure, Physicochemical Properties, and In Vitro Starch Digestibility of Yellow Pea Flour Modified with Different Organic Acids. Cereal Chem 94: 142–150. https://doi.org/10.1094/CCHEM-03-16-0068-FI doi: 10.1094/CCHEM-03-16-0068-FI
    [39] Sánchez-Rivera MM, Núñez-Santiago M del C, Bello-Pérez LA, et al. (2017) Citric acid esterification of unripe plantain flour: Physicochemical properties and starch digestibility. Starch 69: 1–21. https://doi.org/10.1002/star.201700019 doi: 10.1002/star.201700019
    [40] Li M-NN, Xie Y, Chen H-QQ, et al. (2019) Effects of heat-moisture treatment after citric acid esterification on structural properties and digestibility of wheat starch, A- and B-type starch granules. Food Chem 272: 523–529. https://doi.org/10.1016/j.foodchem.2018.08.079 doi: 10.1016/j.foodchem.2018.08.079
    [41] Pratiwi M, Faridah DN, Lioe HN (2018) Structural changes to starch after acid hydrolysis, debranching, autoclaving-cooling cycles, and heat moisture treatment (HMT): A review. Starch 70. https://doi.org/10.1002/star.201700028 doi: 10.1002/star.201700028
    [42] Duyen TTM, Huong NTM, Phi NTL, et al. (2020) Physicochemical properties and in vitro digestibility of mung-bean starches varying amylose contents under citric acid and hydrothermal treatments. Int J Biol Macromol 164: 651–658. https://doi.org/10.1016/j.ijbiomac.2020.07.187 doi: 10.1016/j.ijbiomac.2020.07.187
    [43] Hung P V, My NTH, Phi NTL (2014) Impact of acid and heat–moisture treatment combination on physicochemical characteristics and resistant starch contents of sweet potato and yam starches. Starch 66:1013-1021. https://doi.org/10.1002/star.201400104 doi: 10.1002/star.201400104
    [44] Chung H-JJ, Liu Q, Hoover R (2009) Impact of annealing and heat-moisture treatment on rapidly digestible, slowly digestible and resistant starch levels in native and gelatinized corn, pea and lentil starches. Carbohydr Polym 75: 436–447. https://doi.org/10.1016/j.carbpol.2008.08.006 doi: 10.1016/j.carbpol.2008.08.006
    [45] Gunaratne A, Hoover R (2002) Effect of heat-moisture treatment on the structure and physicochemical properties of tuber and root starches. Carbohydr Polym 49: 425–437. https://doi.org/10.1016/S0144-8617(01)00354-X doi: 10.1016/S0144-8617(01)00354-X
    [46] Wu T-Y, Tsai S-J, Sun N-N, et al. (2020) Enhanced thermal stability of green banana starch by heat-moisture treatment and its ability to reduce body fat accumulation and modulate gut microbiota. Int J Biol Macromol 160: 915–924. https://doi.org/10.1016/j.ijbiomac.2020.05.271 doi: 10.1016/j.ijbiomac.2020.05.271
    [47] Hung P Van, Vien NL, Lan Phi NT (2016) Resistant starch improvement of rice starches under a combination of acid and heat-moisture treatments. Food Chem 191: 67–73. https://doi.org/10.1016/j.foodchem.2015.02.002 doi: 10.1016/j.foodchem.2015.02.002
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    22. Du-Ri Kim, Ting-Fu Lai, Minji Sung, Minwoo Jang, Yeo-Kyung Shin, Young jin Ra, Yung Liao, Jong-Hwan Park, Myung-Jun Shin, Effect of information and communication technology-based smart care services for physical and cognitive functions in older adults living alone: A quasi-experimental study, 2024, 28, 12797707, 100318, 10.1016/j.jnha.2024.100318
    23. Daniel Jung, Jeong Ha (Steph) Choi, Kerstin Gerst Emerson, Discharge disposition for home health care patients with Alzheimer's disease and related dementia: The role of living arrangements and rural living, 2024, 0890-765X, 10.1111/jrh.12872
    24. Jiyoung Shin, Hun Kang, Seongmi Choi, JiYeon Choi, Exploring social activity patterns among community-dwelling older adults in South Korea: a latent class analysis, 2024, 24, 1471-2318, 10.1186/s12877-024-05287-5
    25. Abigail T. Stephan, Hye Won Chai, Ava McVey, Briana N. Sprague, Annamaria V. Wolf, Christine B. Phillips, Lesley A. Ross, Differential Longitudinal Associations Between Depressive Symptoms and Cognitive Status by Living Situation in Older Adults, 2024, 0733-4648, 10.1177/07334648241285602
    26. Meiqian Chen, Xiang Cao, Afeng Wang, Yi Zhu, Guanzhen Lu, Li Zhang, Lijuan Shen, A global perspective on risk factors for social isolation in community-dwelling older adults: A systematic review and meta-analysis, 2024, 116, 01674943, 105211, 10.1016/j.archger.2023.105211
    27. Julia Ortmann, Jette Möller, Yvonne Forsell, Yajun Liang, The Dual Trajectories of Depressive Symptoms and Social Support—A Population‐Based Cohort Study Among Swedish Adults Across 23 Years, 2024, 2575-5609, n/a, 10.1176/appi.prcp.20240063
    28. Youngmin Cho, Donruedee Kamkhoad, Natalie G. Regier, Lixin Song, Ruth A. Anderson, Bei Wu, Baiming Zou, Anna S. Beeber, Coping with cognitive decline in older adults with mild cognitive impairment or mild dementia: a scoping review, 2025, 1360-7863, 1, 10.1080/13607863.2025.2453819
    29. Ali Gökhan Gölçek, The Dynamics of Poverty Among Türkiye’s Aging: An Investigative Study of Determinants, 2025, 1874-7884, 10.1007/s12062-025-09482-z
    30. Kimia Ghasemi, Mahsa Fallahi, Mohamad Molaei Qelichi, Hiva Farmahini Farahani, Kasra Dolatkhahi, Factors contributing to urban isolation: A mixed-methods analysis of three new towns in Tehran, 2025, 161, 02642751, 105863, 10.1016/j.cities.2025.105863
    31. Jichao Zheng, Zeqiang Ni, Living arrangements, health outcomes, and the buffering role of social capital among older adults in China, 2025, 13, 2296-2565, 10.3389/fpubh.2025.1469914
    32. Siwei Sun, Xuechun Wang, Na Guo, Peipei Li, Ruoxi Ding, Dawei Zhu, Association between catastrophic health expenditure and mental health among elderly in China: the potential role of income and social activity, 2025, 25, 1471-2318, 10.1186/s12877-025-05887-9
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