A new mathematical model for co-infection of malaria and HIV

We propose a new model for malaria and HIV co-infection. The part of the model concerning malaria transmission was proposed by Chiyaka et al (Applied Mathematics and Computation, 2008). The HIV transmission dynamics is added to this model. We have computed the disease free equilibrium and the reproduction number. We have studied the dynamics of the model for variation of the personal protection parameters b and z. For increasing values of b, there is a decrease in the numbers of infectious humans with malaria, and infectious humans with both malaria and HIV. On the other hand, the number of infectious humans, with only HIV, increases. We obtain similar results for the variation of parameter z. Increasing values of the rate at which susceptible humans are infected with HIV, β_hiv, imply increasing values of infectious with malaria and HIV humans, and of infectious humans with HIV. Increasing the rate of recovery from malaria infection by individuals dually-infected with HIV and malaria, φ, is equivalent to a decrease in the number of infectious with malaria humans, and of infectious with malaria and HIV humans, and greater values of infectious humans with HIV. These results suggest that our model is mathematically and epidemiologically well-posed.