Mathematical modeling of the influence of vertical transmission and mild infection on the dynamics of toxoplasmosis

In this article, a novel model for the dynamics of toxoplasmosis in human and cat populations with vertical transmission and contribution of oocysts to the environment from the mildly infected cats is constructed. The non-negative properties of the model’s solutions are proved. We demonstrate that a secondary quantity that affects the overall dynamics of T. gondii in human and cat populations is the reproductive ratio R◦. The impact of the contribution of oocysts from the mildly infected cats as well as the impact of vertical transmission and the impact of effective contact between cat and cat and cat and humans on the reproductive ratio are shown. The model’s endemic and disease-free equilibria are derived, and their local and global stabilities are proved. The bifurcation and sensitivity of the model’s parameters to T. gondii dynamics are studied. Finally, simulations are performed with the aid of the computer-in-built Runge-Kutta package implemented in the software Maple to illustrate the behavior of the model graphically. The results indicate that vertical transmission, contact with the infected cats and contribution of T. gondii from the mildly infected cats have a significant impact on the dynamics of toxoplasmosis.