Stability Analysis of Mathematical Models of Toxoplasmosis Spread in Cat and Human Populations with Time Delay

Novandri Sitinjak (Jurusan Matematika, Universitas Negeri Medan)
Tri Andri Hutapea (Jurusan Matematika, Universitas Negeri Medan)

Formosa Journal of Science and Technology (FJST)
Vol. 2 No. 2 (2023): February 2023

Toxoplasmosis is caused by the parasite Toxoplasma gondii. In this study, model construction, determining the equilibrium point, stability analysis, and model simulation were carried out. The results showed that there were two equilibrium points, namely the disease-free equilibrium point, locally asymptotically stable if and disease endemic, locally asymptotically stable if. The simulation results show when the solution is stable towards the free equilibrium point, when the solution is stable towards the disease endemic equilibrium point without delay or with time delay. Giving a time delay will cause differences in the population dynamics of each class at the start, but then all solutions move towards a stable point.