Optimal Control of HIV/AIDS in the Workplace in the Presence of Careless Individuals

Seidu, Baba; Makinde, Oluwole Daniel

doi:10.1155/2014/831506

Cited by 37 publications

(30 citation statements)

References 22 publications

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“…We consider following optimal control parameters 1) 1 u is the control effort aimed at reducing the infection of susceptible individuals;…”

Section: S T Q I U I S D U S I T U Qmentioning

confidence: 99%

“…Mathematical models used extensively to study the dynamics of epidemics both from the cellular level to the population level by many researchers [1]- [6]. Early models concerned immigration of infective individuals are studied by many researchers [7]- [12].…”

Section: Introductionmentioning

confidence: 99%

“…The optimal control theory has been applied to quite a few HIV models (see [1] [4] [6]). Baba Seidu and Oluwole D. Makinde [1] stress their emphases on the optimally reducing the spread of the disease and the increasing productivity in workplace and show the positive effect of applying a multifaceted approach in the fight against HIV/AIDS.…”

Section: Introductionmentioning

confidence: 99%

“…Baba Seidu and Oluwole D. Makinde [1] stress their emphases on the optimally reducing the spread of the disease and the increasing productivity in workplace and show the positive effect of applying a multifaceted approach in the fight against HIV/AIDS. Tunde T. Yusuf and Francis Benyah [4] formulated an optimality system for controlling HIV/AIDS.…”

Section: Introductionmentioning

confidence: 99%

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

Mastahun¹,

Abdurahman²

2017

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In order to find out the effect of human (sexual) behavior change and immigration in spreading the HIV/AIDS, a deterministic model of HIV/AIDS with infective immigration is formulated. First, basic properties of the model, including non-negativity and boundedness of the solutions, existence of the endemic equilibrium and the basic reproduction number, 0  are analyzed. The geometrical approach is used to obtain the global asymptotic stability of endemic equilibrium. Then the basic model is extended to include several control efforts aimed at reducing infection and changing behavior. Pontryagin's maximum principle is used to derive the optimality system and solve the system numerically. Our numerical findings are illustrated through simulations using MATLAB, which shows reliability of our model from the practical point of view.

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“…We consider following optimal control parameters 1) 1 u is the control effort aimed at reducing the infection of susceptible individuals;…”

Section: S T Q I U I S D U S I T U Qmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Mastahun¹,

Abdurahman²

2017

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“…Some examples on the use of mathematical model for the analyzes of treatment and control of infectious disease can be found in ( Shah, N.H. and Gupta, J. 2013), (Seidu, B. and Makinde, O.D. (2014)., (Tripathi, A., et al 2007).…”

mentioning

confidence: 99%

Mathematical model for the control of infectious disease

Peter¹,

Akinduko²,

Oguntolu³

et al. 2018

Journal of Applied Sciences and Environmental Management

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ABSTRACT:We proposed a mathematical model of infectious disease dynamics. The model is a system of first order ordinary differential equations. The population is partitioned into three compartments of Susceptible ) (t S , Infected ) (t I and Recovered ) (t R . Two equilibria states exist: the disease-free equilibrium which is locally asymptotically stable if Ro < 1 and unstable if Ro > 1. Numerical simulation of the model shows that an increase in vaccination leads to low disease prevalence in a population.

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Mathematical Analysis of the Effects of HIV-Malaria Co-infection on Workplace Productivity

2015

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In this paper, a nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics and effects of HIV-malaria co-infection in the workplace. Basic reproduction numbers of sub-models are derived and are shown to have LAS disease-free equilibria when their respective basic reproduction numbers are less than unity. Conditions for existence of endemic equilibria of sub-models are also derived. Unlike the HIV-only model, the malaria-only model is shown to exhibit a backward bifurcation under certain conditions. Conditions for optimal control of the co-infection are derived using the Pontryagin's maximum principle. Numerical experimentation on the resulting optimality system is performed. Using the incremental cost-effectiveness ratio, it is observed that combining preventative measures for both diseases is the best strategy for optimal control of HIV-malaria co-infection at the workplace.

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Optimal Control of HIV/AIDS in the Workplace in the Presence of Careless Individuals

Cited by 37 publications

References 22 publications

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

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

Mathematical model for the control of infectious disease

Mathematical Analysis of the Effects of HIV-Malaria Co-infection on Workplace Productivity

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