Analysis of a malaria model with mosquito host choice and bed-net control (1311.3209v1)

Abstract: A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticide-treated bed nets usage. The occurrence of a backward bifurcation at R_0=1 is shown to be possible, which implies that multiple endemic equilibria co-exist with a stable disease-free equilibrium when the basic reproduction number is less than unity. This phenomenon is found to be caused by disease-induced human mortality. The global asymptotic stability of the endemic equilibrium for R_0>1 is proved, by using the geometric approach to global stability. Therefore, the disease becomes endemic for $R_0>1$ regardless of the number of initial cases in both the human and vector populations. Finally, the impact of vector's host preferences and bed-net usage behavior on system dynamics is investigated.