Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model

In this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when R-0, the basic reproduction number, is less than unity. When R-0 > 1 and under some conditions, then our system has a unique positive omega-periodic solution that is globally asymptotically stable. Applying two controls, vaccination and treatment, to our model forces the system to be non-periodic, and all fractions of infected populations settle on a very low level.