Dynamics Of Two Classes Of Heterogeneous Mumps Models With Vaccinated And Latency Delays

Mumps,as a vaccine-preventable respiratory infectious disease,has been experiencing a global resurgence among adolescents and young adults in recent years,and can induce various complications,threatening people's health seriously,especially for teenagers.Heterogeneity,asymptomatic infections and vaccination play important roles in the spread and prevalence of mumps,which should be incorporated into the propagation model for mumps.In this thesis,based on the relevant theoretical knowledge of the epidemic dynamical models,delay differential equations and nonstandard finite difference(NSFD)scheme,we developed a multi-group mumps model and its discrete version by the NSFD scheme.Furthermore,we established the global stability of the disease-free equilibrium and the endemic equilibrium of models,respectively.Finally,some specific numerical examples are provided to illustrate the validity of our theoretical results.The whole thesis has been divided into four chapters:The first chapter outlines the research backgrounds,research significances,research status as well as the main works that we have done in this thesis.In the second chapter,some notations in the thesis are presented,and some definitions,lemmas and inequalities are introduced.In the third chapter,a multi-group mumps dynamical model with infinite distribution of vaccination and latency,asymptomatic infection and nonlinear incidence rate is formulated and studied.Conditions for the global stability of the disease-free equilibrium and the endemic equilibrium of the model are established by suitable Lyapunov functionals,two special probability distributions of remaining in vaccinated and exposed classes are discussed.In the forth chapter,the discrete version of the multi-group mumps propagation model proposed with discrete delays in the third chapter is derived by using the NSFD scheme and studied.It is revealed that dynamic consistency(DC)in the original continuous model is preserved,including the non-negativity,boundedness for solutions,and the existence and stability conditions of equilibria.Finally,some specific numerical examples are provided to illustrate the validity of our theoretical results.