Stability Analysis of a Vector-Borne Disease with Variable Human Population

Abstract

A mathematical model of a vector-borne disease involving variable human population is analyzed. The varying population size includes a term for disease-related deaths. Equilibria and stability are determined for the system of ordinary differential equations. If $R_0\le 1$, the disease-“free” equilibrium is globally asymptotically stable and the disease always dies out. If $R_0>1$, a unique “endemic” equilibrium is globally asymptotically stable in the interior of feasible region and the disease persists at the “endemic” level. Our theoretical results are sustained by numerical simulations.