Global analysis and optimal control of a periodic visceral leishmaniasis model (Q1649077)

Summary: 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 \(\mathcal R_0\), the basic reproduction number, is less than unity. When \(\mathcal R_0 > 1\) 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.