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 R₀, the basic reproduction number, is less than unity. When R₀ > 1 and under some conditions, then our system has a unique positive ω-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.