# An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay

### Abstract

This paper presents a mathematical model with time delay for the transmission dynamics of zoonotic visceral leishmaniasis (ZVL which is caused by protozoan parasite leishmania infantum and transmitted by female sandflies). Qualitative analysis of the ODE version of the model reveals that the disease-free equilibrium of the model is globally asymptotically stable when the basic reproduction number, R_{0}, is less than unity. Using time delay as a bifurcation parameter in the delay-differential version of the model, it has been shown that the incubation period has a significant effect on the stability of the equilibria and we derived the condition for Hopf bifurcation to occur.

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