Global Stability and Sensitivity Analysis of SIA Model for AIDS Disease

Ilahi, Fadilah; Nurhalimah,

doi:10.1088/1742-6596/1245/1/012047

Cited by 2 publications

(3 citation statements)

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“…In this study, a deterministic mathematical model is formulated to analyze the transmission dynamics of the human immunodeficiency virus through applying prevention and treatment control strategies. The current model is a modification of the SIA model of HIV discussed in [ 13 ]. A base model has three compartments of human population and did not explicitly show the effectiveness of ART that reduces the viral load in the blood to the undetectable level for ART users.…”

Section: Model Formulationmentioning

confidence: 99%

“…Sensitivity analysis is used to determine the sensitivity of the variable with respect to the parameters involved in it [ 8 , 13 , 28 ]. The normalized forward sensitivity index of a particular variable, R , with respect to a parameter, p , is defined as

…”

Section: Mathematical Analysis Of the Modelmentioning

confidence: 99%

“…Human immunodeficiency virus (HIV) is a virus causing HIV infection and results in economic and life devastating crisis if immediate action is not taken to halt further prevalence of the infection [1][2][3][4][5][6][7][8][9][10][11]. Moreover, this infection has no curing medication, but antiretroviral therapy (ART) or its combination is used for halting further progression of infection by inhibiting the virus in human blood, but if left untreated leads to a sever stage called acquired immunodeficiency syndrome (AIDS) [12][13][14][15][16][17][18][19][20][21][22][23]. HIV infection progress through stages as follows: (i) primary stage (asymptomatic stage): this stage faces human individual where the virus is in the blood cannot be diagnosed with medical instruments; (ii) asymptomatic stage: this stage is symptomless stage of HIV infection but diagnosable with medical test; (iii) symptomatic stage: in this stage, the symptom of HIV infection like tiredness, loss of weight, and extreme loss of water starts to manifest in the life of HIV infected individuals; and (iv) AIDS stage: this is advanced stage of HIV infection where it is difficult for treatment and leads to death soon if special care is not taken [24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control and Bifurcation Analysis of HIV Model

Cheneke

2023

Computational and Mathematical Methods in Medicine

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In this study, a very crucial stage of HIV extinction and invisibility stages are considered and a modified mathematical model is developed to describe the dynamics of infection. Moreover, the basic reproduction number R 0 is computed using the next-generation matrix method whereas the stability of disease-free equilibrium is investigated using the eigenvalue matrix stability theory. Furthermore, if R 0 ≤ 1 , the disease-free equilibrium is stable both locally and globally whereas if R 0 > 1 , based on the forward bifurcation behavior, the endemic equilibrium is locally and globally asymptotically stable. Particularly, at the critical point R 0 = 1 , the model exhibits forward bifurcation behavior. On the other hand, the optimal control problem is constructed and Pontryagin’s maximum principle is applied to form an optimality system. Further, forward fourth-order Runge–Kutta’s method is applied to obtain the solution of state variables whereas Runge–Kutta’s fourth-order backward sweep method is applied to obtain solution of adjoint variables. Finally, three control strategies are considered and a cost-effective analysis is performed to identify the better strategies for HIV transmission and progression. In advance, prevention control measure is identified to be the better strategy over treatment control if applied earlier and effectively. Additionally, MATLAB simulations were performed to describe the population’s dynamic behavior.

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Section: Model Formulationmentioning

confidence: 99%

…”

Section: Mathematical Analysis Of the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Control and Bifurcation Analysis of HIV Model

Cheneke

2023

Computational and Mathematical Methods in Medicine

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Bifurcation and Stabillity Analysis of HIV Transmission Model with Optimal Control

Cheneke

Koya

Edessa

2021

Journal of Mathematics

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A mathematical model of HIV transmission is built and studied in this paper. The system’s equilibrium is calculated. A next-generation matrix is used to calculate the reproduction number. The novel method is used to examine the developed model’s bifurcation and equilibrium stability. The stability analysis result shows that the disease-free equilibrium is locally asymptotically stable if 0 < R 0 < 1 but unstable if R 0 > 1 . However, the endemic equilibrium is locally and globally asymptotically stable if R 0 > 1 and unstable otherwise. The sensitivity analysis shows that the most sensitive parameter that contributes to increasing of the reproduction number is the transmission rate β 2 of HIV transmission from HIV individuals to susceptible individuals and the parameter that contributes to the decreasing of the reproduction number is identified as progression rate η of HIV-infected individuals to AIDS individuals. Furthermore, it is observed that as we change η from 0.1 to 1 , the reproduction number value decreases from 1.205 to 1.189, where the constant value of β 2 = 0.1 . On the other hand, as we change the value of β 2 from 0.1 to 1 , the value of the reproduction number increases from 0.205 to 1.347, where the constant value of η = 0.1 . Further, the developed model is extended to the optimal control model of HIV/AIDS transmission, and the cost-effectiveness of the control strategy is analyzed. Pontraygin’s Maximum Principle (PMP) is applied in the construction of the Hamiltonian function. Moreover, the optimal system is solved using forward and backward Runge–Kutta fourth-order methods. The numerical simulation depicts the number of newly infected HIV individuals and the number of individuals at the AIDS stage reduced as a result of taking control measures. The cost-effectiveness study demonstrates that when combined and used, the preventative and treatment control measures are effective. MATLAB is used to run numerical simulations.

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Global Stability and Sensitivity Analysis of SIA Model for AIDS Disease

Cited by 2 publications

References 5 publications

Optimal Control and Bifurcation Analysis of HIV Model

Optimal Control and Bifurcation Analysis of HIV Model

Bifurcation and Stabillity Analysis of HIV Transmission Model with Optimal Control

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