Modeling the optimal control of computational dynamics of toxoplasmosis disease in human and cat populations

Toxoplasmosis continues to be a threatening disease in many parts of the world which is infecting almost one-third of the world population. In this work, a non-linear mathematical model is formulated and analysed to study the optimal control of computational dynamics of toxoplasmosis disease in human and cat populations. The model is subdivided into two sub populations; human population and vector (cat) population. The model is analysed qualitatively to determine the stability of equilibrium of the model. The steady states of the equilibrium are found to be locally asymptotically stable if the threshold parameter is less than unity and unstable if it is greater than unity. Also, the analysis shows that the existence of endemic equilibrium is globally asymptotically stable if the threshold parameter is greater than unity. The basic reproduction number and the sensitivity analysis of the model are calculated. Optimal control model was calculated and analysed with the aim of minimizing the transmission dynamics of toxoplasmosis disease in human and cat populations, which are done by introducing the control measure of human due to vaccination and quarantine of infected cat. However the combination of control strategies to both human and cat population will completely eradicate the infection from the community.