Analyzation On The Dynamic Model Of Mumps

Dynamics of infectious diseases is to study the development of disease , predict itsprevalence patterns and trends, analyze the causes and the key factors of epidemics ,andtherefore,to find out the optimal strategy of its prevention and control by using the dynamicmethod.In this paper, we mainly investigate the transmission dynamics of epidemic models formumps with individuals in the same region and two di?erent regions. By constructing ap-propriate Lyapunov functions, the global stabilities of the epidemic models are theoreticallyproved.In chapter 1, we give the significance of investigating epidemic models, development ofthis filed and the main work in this thesis.In chapter 2, we analyze and formulate the eco-epidemiological model with the diseasein the predators and the migration of prey, considering two time scales,one is the fast timescales with prey migration and infected predators;the other is the slow time scales with theinteractions on each patch,and reduce the system's dimension by the fast time scale.Andwe obtain locally asymptotically stable of the equilibrias by analyzing the Jacobian ma-trix,furthermore we analyze the global stability of the equilibrias by excluding the existenceof periodic orbit.In chapter 3, we model an outbreak of mumps with infectious force in the latent andinfected period, and the model includes susceptible individuals(S), exposed individuals withinfectious force(E), infected individuals(I), and vaccinated-treated individuals(V). we analyzethe global properties of the epidemic model for mumps by constructing proper Lyapunovfunctions. It is shown that the global dynamics are determined by the basic reproductivenumber R0. If R0 < 1, then the disease-free equilibrium P0 is globally asymptotically stableand the disease always dies out. If R0 > 1, a unique endemic equilibrium P? is globally asymptotically stable, and the disease persists at the endemic equilibrium.In chapter 4, we investigate the model for mumps with individuals in two di?erent re-gions. The model includes susceptible individuals(S), infected individuals(I), and vaccinated-treated individuals(V), we analyze and prove the global properties of the epidemic model formumps by constructing proper Lyapunov functions.