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Optimal control analysis of hepatitis C virus with acute and chronic stages in the presence of treatment and infected immigrants

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International Journal of Biomathematics 2014年第2期7卷 141-163页

作者： kazeem oare okosun Oluwole Daniel Makinde Department of Mathematics University of TechnologyPrivate Bag X021 Vanderbijlpark 1900 South Africa Faculty of Military ScienceSteUenbosch University Private Bag X2 Saldanha 7395 South Africa

In this paper, we consider a deterministic hepatitis C virus （HCV） model and study the impact of optimal control on the screening of immigrants and treatment of HCV on the transmission dynamics of the disease in a homogeneous population with constant immigration of susceptibles. First, we derived the condition in which disease-free equilibrium is locally asymptotically stable and established that a stable disease-free equilibrium can only be achieved in the absence of infective immigrants. Second we investigated the impact of each control mechanism individually and the combinations of these strategies in the control of HCV. The costs associated with each of these strategies are also investigated by formulating the costs function problem as an optimal control problem, and we then use the Pontryagin＇s Maximum Principle to solve the optimal control problems. From the numerical simulations we found that the optimal combination of treatment of acute-infected and chronic-infected individuals control strategy produced the same results as the combination of the three strategies （combination of screening of immigrants, treatment of acute-infected and chronic-infected individuals）. By our model and these results, we suggest the treatment of acute-infected and chronic-infected individuals control strategy should be optimized where resources are scarce, because the implementation of the three strategies （combination of screening of immigrants, treatment of acute-infected and chronic-infected individuals） would imply additional cost.

关键词： Hepatitis C virus stability optimal control

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A MODEL FOR CONTROL OF HIV/AIDS WITH PARENTAL CARE

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International Journal of Biomathematics 2013年第2期6卷 131-145页

作者： GBENGA JACOB ABIODUN NIZAR MARCUS kazeem oare okosun PETER JOSEPH WITBOOI Department of Mathematics and Applied Mathematics University of the Western Cape Private Bag X17 Bellville 7535 South Africa Department of Mathematics Vaal University of Technology Private Bag X021 Vanderbijlpark 1900 South Africa Department oJ Mathematzcs and Applied Mathematzes University of the Western Cape Private Bag X17 BeUviUe 7535 South Africa

In this study we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyze a mathematical model that describes the dynamics of HIV infection among the immigrant youths and how parental care can minimize or prevent the spread of the disease in the population. We analyze the model with both screening control and parental care, then investigate its stability and sensitivity behavior. We also conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is globally asymptotically stable. We establish optimal strategies for the control of the disease with screening and parental care, and provide numerical simulations to illustrate the analytic results.

关键词： HIV/AIDS infected immigrants basic reproduction number disease-freeequilibrium endemic equilibrium parental care.

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Modeling and analyzing the impact of temperature and rainfall on mosquito population dynamics over Kwazulu-Natal, South Africa

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International Journal of Biomathematics 2017年第4期10卷 211-233页

作者： Gbenga J. Abiodun Peter Witbooi kazeem O. okosun Department of Mathematics and Applied Mathematics University of the Western Cape Private Bag X17 Bellville 7535 Republic of South Africa Department of Mathematics Vaal University of Technology Private Bag X021 Vanderbijlpark Andries Potgieter Blvrd-1900 Republic of South Africa

Malaria parasites are strongly dependent on Anopheles mosquitoes for transmission; for this reason, mosquito population dynamics are a crucial determinant of malaria risk. However, temperature and rainfall play a significant role in both aquatic and adult stages of the Anopheles. Consequently, it is important to understand the bio- logy of malaria vector mosquitoes in the study of malaria transmission. In this study, we develop a climate-based, ordinary-differential-equation model to analyze how rain- fall and temperature determine mosquito population size. In the model, we consider in detail the influence of ambient temperature on gonotrophic and sporogonic cycles over Amajuba District, Kwazulu-Natal Province, South Africa. In particular, we further use the model to simulate the spatial distribution of the mosquito biting rate over the study region. Our results reflect high seasonality of the population of An. gambiae over the region and also demonstrate the influence of climatic factors on the mosquito population dynamics.

关键词： Anopheles mosquito climate basic reproduction number.

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