Abstract
In this work we consider a mathematical model based on a system of ordinary differential equations describing the evolution of population of dogs infected by leishmania diseases. By analyzing the corresponding characteristic equations, the local stability of infection free equilibrium point and infection equilibrium point are discussed. It is shown that if the basic reproduction number R 0 is less than one, the infection free equilibrium is locally asymptotically stable, whereas if the basic reproduction number R 0 is great than one the infection equilibrium point is locally asymptotically stable, and the infection free equilibrium is unstable.
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