BOUGHRARA Assia2026-06-292025-06-03https://dspace.univ-tebessa.dz/handle/123456789/318The 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.enBasic Reproduction NumberGlobal and Local Asymptotic Stabilitiyand Disease-Free EquilibriumEndemic EquilibriumLyapunov FunctionSEIR and SI Model.Thesis