Study on the Threshold Conditions for Infection of Visceral Leishmaniasis

Abstract

In this work, we have focused on the transmission dynamics of visceral strains of leishmania, by using mathematical model that includes human, reservoir and vector population. Threshold conditions for persistence of infection are obtained using Routh-Hurwitz criteria and Next generation method. Both the thresholds conditions agree on the same parameters. The biological sense of threshold is discussed and found meaningful. At the end results of numerical simulation are given, which shows that the disease is eradicable and the infected classes are inter-dependent. Simulation also shows the effect of treatment.