A MODEL OF THE TRANSMISSION DYNAMICS OF LEISHMANIASIS

Abstract

In this paper we present a susceptible–infectious–susceptible (SIS) model that describes the transmission dynamics of cutaneous Leishmaniasis. The model treats a vector population and several populations of different mammals. Members of the human population serve as the incidental hosts, and members of the various animals populations serve as reservoir hosts. We establish the basic reproduction number and the equilibrium conditions of the system. We use a generalization of the Lyapunov function approach to show that when the basic reproduction number is less than or equal to one, the diseases-free equilibrium is a global attractor, and that when it is greater than one the endemic equilibrium is a global attractor. We present numerical simulations that demonstrate the dynamics of the model for a system containing a human population and a single animal population.