Abstract
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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Seidu, B., Makinde, O.D. & Seini, I.Y. Mathematical Analysis of the Effects of HIV-Malaria Co-infection on Workplace Productivity. Acta Biotheor 63, 151–182 (2015). https://doi.org/10.1007/s10441-015-9255-y
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DOI: https://doi.org/10.1007/s10441-015-9255-y