A Generalized Mathematical Model of Toxoplasmosis with an Intermediate Host and the Definitive Cat Host

In this paper, we construct a generalized epidemiological mathematical model to study toxoplasmosis dynamics, taking into consideration both cat and mouse populations. The incorporates proportions for the congenital transmission in populations, along with oocysts available environment. We focus on determining conditions under which can be eradicated. conduct stability analysis order reveal dynamics of populations; moreover, compute basic reproduction number R0, is crucial long-term behavior disease these populations as well steady states related find that vertical population essential, affects R0. If full considered R0<1, all solutions converge limit set comprised by infinitely many toxoplasmosis-free-cat states, meaning would vanish from regardless initial conditions. On other hand, if R0>1, then there only one toxoplasmosis-endemic state. When not population, unique toxoplasmosis-free equilibrium exists eradicated This has important public health implications. Numerical simulations are carried out reinforce our theoretical observe repercussion some parameters dynamics.