Optimal Control of an HIV/AIDS Epidemic Model with Infective Immigration and Behavioral Change

Mastahun, Mamatjan; Abdurahman, Xamxinur

doi:10.4236/am.2017.81008

Cited by 8 publications

(10 citation statements)

References 15 publications

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“…Include a separate compartment (E) for individuals that fail the therapeutic treatment. This wasn't considered by Okosun et al [8], Hussaini et al [9] and Mastahun and Abdurahman [10]. To the best of our knowledge, it has not been considered before.…”

Section: Introductionmentioning

confidence: 92%

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Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment

2020

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In this paper, we develop a new disease-resistant mathematical model with a fraction of the susceptible class under imperfect vaccine and treatment of both the symptomatic and quarantine classes. With standard incidence when the associated reproduction threshold is less than unity, the model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium. It is then proved that this phenomenon vanishes either when the vaccine is assumed to be 100% potent and perfect or the Standard Incidence is replaced with a Mass Action Incidence in the model development. Furthermore, the model has a unique endemic and disease-free equilibria. Using a suitable Lyapunov function, the endemic equilibrium and disease free equilibrium are proved to be globally-asymptotically stable depending on whether the control reproduction number is less or greater than unity. Some numerical simulations are presented to validate the analytic results.

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Section: Introductionmentioning

confidence: 92%

“…Several researchers like [6,[8][9][10][11][12] and references therein have published commendable research output about transmission dynamics of infectious diseases. They have also studied control and prevention strategies of these notorious epidemic.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment

2020

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“…Let the value of γ is 0.85 . Figures 4 to 6 describe the effect of different values of condom use, u , in dynamics of the model for three different values of α .…”

Section: Numerical Implementationmentioning

confidence: 99%

“…Recently, several mathematical models have been introduced to describe how the disease is distributed and to explain epidemic illnesses related to AIDS . Various factors have been investigated in the spread of AIDS, and several methods have been proposed to control the epidemic of it.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, several mathematical models have been introduced to describe how the disease is distributed and to explain epidemic illnesses related to AIDS. [4][5][6][7][8][9][10][11][12][13][14][15][16][17] Various factors have been investigated in the spread of AIDS, and several methods have been proposed to control the epidemic of it. For instance, a model was proposed in Tripathi, Naresh, and Sharma's study 4 for the effect of screening of unaware infectives on the spread of the HIV infection.…”

Section: Introductionmentioning

confidence: 99%

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A fractional order HIV/AIDS model based on the effect of screening of unaware infectives

Babaei

Jafari

Ahmadi

2019

Math Methods in App Sciences

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In this paper, a fractional order model for the spread of human immunodeficiency virus (HIV) infection is proposed to study the effect of screening of unaware infected individuals on the spread of the HIV virus. For this purpose, local asymptotic stability analysis of the disease‐free equilibrium is investigated. In addition, the model is studied for different values of the fractional order to show the relation between the variations of the reproduction number and the order of the proposed model. Finally, numerical solutions are simulated by using a predictor‐corrector method to illustrate the dynamics between susceptible individuals and unaware infected individuals.

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Optimal Control Strategies and Sensitivity Analysis of an HIV/AIDS-Resistant Model with Behavior Change

2021

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Despite several research on HIV/AIDS, it is still incumbent to investigate more effective control measures to mitigate its infection level. Therefore, we introduce an HIV/AIDS-resistant model with behavior change and study its basic properties. In order to determine the most sensitive parameters that are responsible for disease transmission with respect to the basic reproduction number and those responsible for disease prevalence with respect to the endemic equilibrium, the sensitivity analysis was established and it was confirmed that the influx rate of people into the infected population and total abstinence from all risk practices and endemic areas are some of the most sensitive parameters for disease spread and disease eradication, respectively. Furthermore, by considering controls denoting the government’s intervention in promoting and encouraging behavior change, representing intake of balanced nutritional supplementation, and connoting antiretroviral therapy (ART), an optimal control problem was developed and analyzed. Before the establishment of the necessary conditions of the optimal control using Pontryagin’s Maximum Principle, we proved the existence of the optimal control triplet where is the control set at time t ,) which has been neglected by many researchers in recent years. Using the Runge–Kutta scheme, the optimal control problem was solved to understand the best combination of control strategies. Using the demographic and epidemiological data for South Africa on HIV/AIDS, a numerical simulation was carried out and results are presented on 3D surface plots. The obtained results suggested that the combination of all the considered control measures is the best method to ensure disease eradication.

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Optimal Control of an HIV/AIDS Epidemic Model with Infective Immigration and Behavioral Change

Cited by 8 publications

References 15 publications

Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment

Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment

A fractional order HIV/AIDS model based on the effect of screening of unaware infectives

Optimal Control Strategies and Sensitivity Analysis of an HIV/AIDS-Resistant Model with Behavior Change

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