Mathematical Modeling of Toxoplasmosis in Cats with Two Time Delays under Environmental Effects

In this paper, we construct a more realistic mathematical model to study toxoplasmosis dynamics. The considers two discrete time delays. first delay is related the latent phase, which lag between when susceptible cat has effective contact with an oocyst and it begins produce oocysts. second that elapses from oocysts become present in environment they are able infect. main aim paper find conditions under can disappear population whether delays affect qualitative properties of model. Thus, investigate impact combination on Using dynamical systems theory, basic reproduction number R0d determines global long-term dynamics toxoplasmosis. We prove that, if R0d<1, will be eradicated toxoplasmosis-free equilibrium globally stable. design Lyapunov function order stability equilibrium. also threshold parameter greater than one, then there only one toxoplasmosis-endemic point, but point not theoretically proven. However, obtained partial theoretical results performed numerical simulations suggest R0d>1, addition, other were help support results.