Mathematical modeling of HIV/AIDS with optimal control: A case study in Ethiopia

Ayele, Tigabu Kasia; Goufo, Emile Franc Doungmo; Mugisha, Stella

doi:10.1016/j.rinp.2021.104263

Cited by 38 publications

(20 citation statements)

References 29 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%

“…The expressions 0.5 w 1 u 1 2 , 0.5 w 2 u 2 2 , and 0.5 w 3 u 3 2 are costs associated with controls. The form of cost is quadratic because we assumed it to be nonlinear in nature [ 3 ]. Our goal is to minimize the population size of W ( t ), I ( t ), and A ( t ) through intervention with control measures u 1 ( t ), and u 2 ( t ) along with the costs associated with them.…”

Section: Optimal Control Problemmentioning

confidence: 99%

“…To show the existence of optimal control, we use the approach used in [ 3 ]. We have already proved that the HIV model ( 2 ) is bounded, so this result can be used to prove the existence of optimal control over finite time interval as applied in [ 3 , 52 ]. To ensure the existence of optimal control, we need to check if the following conditions are satisfied: The set of controls and state variables be nonempty The control set U is convex and closed The right hand side of the state system is bounded by a linear function in the state and control variables The integrand of objective functional is convex on U The integrand of objective functional is bounded below by k 2 − k 1 (| u 1 | 2 + | u 2 | 2 ) k /2 .…”

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%

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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%

Section: Optimal Control Problemmentioning

confidence: 99%

Section: Optimal Control Problemmentioning

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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“…Mathematical models have been created to investigate the dynamic properties of cell populations using parameters including latent reservoirs, immunological responses, total carrying capacity, and time-delayed fractional differential operators based on literature reviews (see [1][2][3][4][5]). Immature infected cells also known as latent stage are those that have been infected but are not yet infectious, which is considered in the present study.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis of Posttreatment HIV‐1 Infection Model

et al. 2022

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This paper aims to explore the dynamic characteristics of the post treatment human immunodeficiency virus (HIV) type-1 model by proposing the theoretical frameworks. Distinct from the previous works, this study explores the effect of effector cells, loss of functional effector cells, and two types of anti-retroviral therapies such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs) and also the effect of intracellular time delay. Based on the Routh—Hurwitz criterion and eigenvalue analysis, the stability of the proposed HIV-1 model is analyzed. To reveal the significance of time delay, the Hopf-type bifurcation analysis is performed. The optimal control algorithm is designed by choosing the antiviral therapies such as RTI and PI as control parameters. Numerical simulations are performed to validate the effectiveness of the proposed theoretical frameworks.

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