Abstract
ABSTRACTWe propose and study a mathematical model for malaria-HIV co-infection transmission and control, in which malaria treatment and insecticide-treated nets are incorporated. The existence of a backward bifurcation is established analytically, and the occurrence of such backward bifurcation is influenced by disease-induced mortality, insecticide-treated bed-net coverage and malaria treatment parameters. To further assess the impact of malaria treatment and insecticide-treated bed-net coverage, we formulate an optimal control problem with malaria treatment and insecticide-treated nets as control functions. Using reasonable parameter values, numerical simulations of the optimal control suggest the possibility of eliminating malaria and reducing HIV prevalence significantly, within a short time horizon.
Highlights
Malaria and HIV are among the deadliest diseases of our time and they cause 4 million deaths a year [2]
We proposed a mathematical model for malaria-HIV co-infection transmission and control in which malaria treatment and insecticide-treated bed-net controls are incorporated
We derived an expression for the basic reproduction number, showed the existence of a unique HIV-only boundary equilibrium, and derived conditions for the existence of either a unique malaria-only boundary equilibrium or existence of two malaria-only boundary equilibria or no malaria-only boundary equilibrium
Summary
Malaria and HIV are among the deadliest diseases of our time and they cause 4 million deaths a year [2] Both malaria and HIV are endemic in sub-Saharan regions of Africa, in some parts of Asia and Latin America. Malaria and HIV overlap geographically in sub-Saharan Africa, South-east Asia and South America; both diseases are endemic and have devastating effects on people living in these endemic areas [2]. Cuadros et al [10] developed and analysed a stochastic, individual-based, co-infection model that incorporates the dynamics of HIV and the co-infection effect on the HIV transmission caused by other infectious diseases such as malaria, gonorrhea and syphilis. We propose and study a mathematical model for malaria-HIV co-infection transmission and control, in which insecticide-treated nets and malaria treatment are incorporated.
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