Dynamics Model Of Epidemic With Infection Age

The spread of epidemic has caused very serious harm to human beings,so the research on epidemic transmission has always been attached great importance by academic.Considering that the epidemic transmission is based on the contact of person,and the contact is uneven,so it is heterogeneous.Therefore,the study of epidemic transmission model on heterogeneous network has become a hot topic.In this paper,based on Volz network SIR model^[35],an SIR epidemic transmission model with infection age is established by introducing infection age.Moreover,in Chapter 3,we believe that the quarantine can effectively block the transmission of the epidemic,so an SIQR epidemic transmission model with quarantine is established.The detailed description is as follows:In Chapter 1,we introduce the research progress of epidemic spreading,the basic knowl-edge involved in the study and the main works.In Chapter 2,using the probability generating function method,we establish an SIR-epidemic model with infection age in heterogeneous networks,i.e.Then,the feasible solution region of the model is analyzed,and the basic reproduction number is obtained.Thirdly,the degree distribution of the network obeys the truncated Poisson distribution and the truncated Power-law distribution,and the accuracy of the main results in this paper are verified by numerical simulation and stochastic simulation.Finally,we discuss the impact of infection age on the spread of the disease by numerical simulation.In Chapter 3,we improve the model in Chapter 2.An SIQR-epidemic model of non-Markovian infection process and quarantine process in a heterogeneous complex network is established,in which the infection rate and the quarantine rate are related to infection age.Next,we analysis the initial conditions of the model.And we use the method of characteristics to transform the model into an integro-differential equation and derive the epidemic threshold of the model.Finally,we research the impact of three different infection or quarantine time distributions on the disease transmission by numerical simulation.