Modeling toxoplasmosis spread in cat populations under vaccination

In this paper we present an epidemiological model to study the transmission dynamics of toxoplasmosis in a cat population under a continuous vaccination schedule. We explore the dynamics of toxoplasmosis at the population level using a mathematical model that includes the effect of oocyst, since the probability of acquisition of Toxoplasma Gondii infection depends on the environmental load of the parasite. This model considers indirectly the infection of prey through the oocyst shedding by cats. We prove that the basic reproduction number R(0) is a threshold value that completely determines the global dynamics and the outcome of the disease. Numerical computer simulations are presented to investigate different scenarios. These simulations show the effectiveness of a constant vaccination program.