Abstract
Malaria and HIV are two of the most deadly diseases in Africa. Combined they account for 4 million deaths each year, and according to the Center for Disease Control and Prevention (CDC), there is an estimated 5 percent increase in malaria deaths in those who tested positive for HIV than those without HIV infection. Since the co-infections were recorded, malaria has seen a 28 percent increase in its incidence. These results raise the possibility that biological differences could alter the effect of co-infection and underscore the importance of identifying these factors for the implementation of control interventions focused on co-infection. Malaria associated death rates have nearly doubled for those with co-infections. The biological integrations between the malaria parasite and HIV are not fully understood, but it is conceivable that the parasite or viral load can increase by an order of magnitude due to coinfection. HIV-infected persons are at increased risk for clinical malaria; the risk is greatest when immune suppression is advanced. Malaria is associated with increases in HIV viral load that, while modest, may impact HIV progression or the risk of HIV transmission. We also showed that in the Full Model, total cause of deaths are from co-infection when the amplification factor , i ρ , i =1, 2, 3, 4, is larger than 25. We introduce a system of differential equations linking the host-vector system of malaria with co-infection with HIV. Data were collected from Sub-Saharan Africa for the global parameter estimates and we simulated for sensitivity analysis using data collected from Malawi. Finally, these simulations show that the HIV-induced increase in susceptibility to malaria infection has marginal effect on the new cases of HIV and malaria but increases the number of new cases of the dual HIV-malaria infection.
Highlights
The Sub-Saharan region of Africa has many endemic diseases including malaria and HIV, which are two of the deadliest diseases of our time [1]
In this study we propose a mathematical model for the joint dynamics of HIV and malaria co-infections
We started with a simple system of six equations which we reduced to four
Summary
The Sub-Saharan region of Africa has many endemic diseases including malaria and HIV, which are two of the deadliest diseases of our time [1]. The geographic overlap of these diseases (Figures 1 and 2) in Sub-Saharan Africa facilitates co-infections with HIV and malaria [2]. We assume the total vector population is constant, but since death is a major concern for people infected with HIV or malaria, we do include disease induced mortality for people. The HIV only model is a simple SI model obtained by setting the infectious malaria classes ( IM , IHM and IV ) to zero The dynamics of this model are known, the DFE is stable when R0H < 1 and there is a stable HIV only endemic equilibrium when R0H > 1 [9]. If R0 is dominated by R0M , we want to control βVM , βMV , or μV
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