Résumé:
The aim of this thesis is to study the dynamics model of the malaria parasite. The
mathematical model was developed based on the SEIR model for humans and the SI model
for mosquitoes. The basic reproduction number was calculated, and then the stability of the
disease-free equilibrium point was studied. If R0>1, it is unstable, but if R0<1, it is locally
asymptotically stable. This was proven using the Poincaré-Lyapunov theorem and globally
asymptotically stable. This was proven using the Lyapunov function. The existence and
uniqueness of the endemic equilibrium point were studied, and it was proven to be globally
asymptotically stable if R0>1, also using the Lyapunov function, and otherwise unstable.
