Dynamics of a model of Toxoplasmosis disease in human and cat populations

A mathematical model for the transmission of Toxoplasmosis disease in human and cat populations is proposed and analyzed. We explore the dynamics of the Toxoplasmosis disease at the population level using an epidemiological type model. Discussion of the basic concepts of the Toxoplasmosis transmission dynamics on human and cat populations are presented. The cats in this model plays a role of infectious agents and host of the protozoan Toxoplasma Gondii parasite. Qualitative dynamics of the model is determined by the basic reproduction number, R0R0. If the threshold parameter R0<1R0<1, then the solution converges to the disease free equilibrium point. On the other hand if R0>1R0>1 the convergence is to the endemic equilibrium point. Numerical simulations of the model illustrates several different dynamics depending on the threshold parameter R0R0 and show the importance of this parameter.