Dynamics Of Two Kinds Of Edge-Based Network Epidemic Models

At present,the epidemic of infectious diseases still poses a serious public health threat.It is of great practical significance to study the transmission mechanism and prevention strategies of infectious diseases.In recent years,researchers have found that many infectious diseases can be transmitted through multiple routes,and complex networks can more accurately simulate the contact between people in the real world.We construct two types of SEIR models based on edge on networks,study the stability of disease model equilibrium,optimal strategies for disease prevention and control,and verify and generalize the conclusions by numerical simulation in this thesis.In Chapter 1,the current situation and significance of using complex networks to study diseases and multi-channel transmission of diseases are introduced,and the preliminary knowledge related to this paper are listed.In Chapter 2,a edge-based sexually transmitted SEIR model on the contact network is introduced.The contact infection between the opposite sex and no infectivity during the latent period on bipartite networks are included.The basic reproduction number of the disease and the equations of the final epidemic size are derived.The dynamics of our model with arbitrary initial conditions are further studied.Sensitivity analysis on parameters and numerical results of the model are conducted.We show that the length of the latent period has an effect on arrival time and size of disease peak,but does not affect the basic reproduction number and the final epidemic size of the disease.In Chapter 3,a new edge-based SEIR model with sexual and non-sexual transmission routes is studied.The basic reproduction number and the final epidemic size of the disease are obtained.And the number of types of disease regeneration is also calculated,which can estimate the level of control required for the control work for a specific type of transmission.In addition,the obtained model is tested by numerical simulations,and its predictions for different epidemic situations of the disease are analyzed.The numerical simulation of the model is compared with the population average of the random simulation,and sensitivity analysis is also performed on several parameters.We conclude that the control of a particular transmission route is not only affected by the transmission rate on that route,but also by the transmission rate on other transmission route.In addition,both the initial infection and the length of the latent period affect the peak arrival time and the peak size of the epidemic.