Several Heterogeneous Age-structured Models And Their Application In The Transmission Of Mumps

In the classical infectious disease models,individuals are usually assumed to be evenly mixed,while the heterogeneity between populations(preferential contact,activity,etc.)is ignored.This assumption may lead to deviation in the basic reproduction number and mistakes in the formulation of intervention strategies.It is of great significance to study the heterogeneous model based on age structures to deeply understand the characteristics of disease transmission and epidemic mechanism.In this thesis,we establish several types of heterogeneous age-structured dynamical models,and analyze the threshold and stability of the models.The transmission characteristics of mumps are studied using the heterogeneous age-structured models.In general case,the uniqueness of the equilibrium state of endemic diseases and the basic reproduction number can only be given under the separable mixed case.Explicit formula of basic reproduction number of age-structured SIR(Susceptible-Infected-Recovered)and Mumps model(periodic and aperiodic)are defined under heterogeneous mixture.The uniqueness and local stability of endemic equilibrium states are solved,and the accuracy of theoretical results is verified by numerical simulation.The relationship between the basic reproduction number of various mixed modes is clarified,and the threshold effect of the basic reproduction number of the heterogeneous mixed age-structured model is revealed.This study is of great significance to deeply understand the dynamic behavior of age-structured models,and provides new methods and ideas for analyzing the dynamic behavior of age-structured models.Mumps is a highly infectious disease caused by mumps virus(RNA virus).It is mainly transmitted among students who are in direct contact with respiratory droplets.It is important to analyze the transmission characteristics of mumps with heterogeneous age-structured model.The history(2005-2019)of mumps in Jiangsu Province can be divided into three different stages:Ⅰ.No vaccine stage(2005-2008);Ⅱ.Effectively controled stage(2009-2014);Ⅲ.Resurgence stage(2015-2019).Using discrete and continuous heterogeneous age-structured dynamics models to compared the epidemic characteristics of mumps in three stages,the underline causes of recurrence of mumps are analyzed,such as vaccine failure,seasonal transmission mode and demographic changes.The results show that the transmission rate of mumps in stage Ⅲ is significantly higher in summer than that in phase I,and decreases in November.The change in population structure gives reasonable explain for why the mumps is prevalent in children around 10 years old in phase I and in children around 5 years old in phase Ⅲ.The results and models will help public health personnel to implement more preventive interventions during the high incidence period of mumps.