Analysis of within-host mathematical models of toxoplasmosis in the presence of free parasites

Two mathematical toxoplasmosis transmission models that are found on differential equations and concentrate on the parasite dynamics within a host are examined in this study. The mathematical models encompass uninfected cells, tachyzoites, and bradyzoites. In the first model, we examined within-host dynamics assuming that free bradyzoites and free tachyzoites are in a steady state due to their slow dynamics. In the second model, we did consider explicitly the impact of free bradyzoites and free tachyzoites. We conducted a general stability analysis of the steady states for both of the within-host models which is suitable to obtain the long-term behavior. We found that the presence of free parasites affects the stability of the endemic equilibrium points. We obtained an expression for the basic reproduction number of each one of the models we studied and found conditions for the global stability of one of the endemic points of each of the models under some conditions. We performed numerical simulations to support the analytical conclusions and to validate the findings of the mathematical analysis performed in this study.