In this paper, a non-linear mathematical model for computational dynamics and optimal control of Toxoplasmosis disease in human and cat populations is formulated and analysed. The steady states of the equilibrium points are determined and found to be locally asymptotically stable if the threshold parameter is less than unity and unstable if it is greater than unity. However the analysis shows that the endemic equilibrium point is globally asymptotically stable if the threshold parameter is greater than unity. The basic reproduction number of the model is determined. Two control measures: (vaccination and quarantine of infected humans) and (vaccination and quarantine of infected cats) are incorporated to the model and analysed in order to determine the optimal control. Numerical simulations of the model in the presence of control measures are finally performed. The results show that in the presence of optimal control, the Toxoplasmosis Disease can be eliminated in the Society.
