Dynamics of Toxoplasmosis Disease in Cats population with vaccination

Abstract

We extend the deterministic model for the dynamics of toxoplasmosis proposed by Arenas et al. in 2010, by separating vaccinated and recovered classes. The model exhibits two equilibrium points, the disease-free and endemic steady states. These points are both locally and globally stable asymptotically when the threshold parameter R_v is less than and greater than unity, respectively. The sensitivity analysis of the model parameters reveals that the vaccination parameter $\pi$ is more sensitive to changes than any other parameter. Indeed, as expected the numerical simulations reveal that the higher the vaccination rate of susceptible individuals the smaller the value of the threshold R_v (i.e., increase in $\pi$ results in the decrease in R_v , leading to the eradication of toxoplasmosis in cats population.