We 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.
Keywords: 49J15; 92B05; Malaria-HIV co-infection; insecticide-treated nets; malaria control; optimalcontrol; treatment.