Optimal control and sensitivity analysis of HIV model with public health education campaign and antiretroviral therapy

Marsudi,; Hidayat, Noor; Wibowo, Ratno Bagus Edy

doi:10.1063/1.5062797

Cited by 5 publications

(3 citation statements)

References 16 publications

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“…In this section, we extend SWIUA model by considering control strategies. The optimal control analysis assists to identify the best control strategies to eradicate or control the disease in the community at a specified period of time [ 3 , 15 , 19 ]. In the optimal control problem, the following three control measures are used.…”

Section: Optimal Control Problemmentioning

confidence: 99%

“…However, in safe practice, the risk of HIV transmission can be reduced by using principle of abstinence–be faithful–use condom (ABC) [ 36 – 38 ]. Optimal control intervention through public health education, using of condom and treatment benefits a lot for continuing human life in safe [ 1 – 3 , 7 , 11 , 15 , 19 , 25 – 27 , 33 , 39 – 44 ].…”

Section: Introductionmentioning

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: Optimal Control Problemmentioning

confidence: 99%