Dynamics Analysis For Two-strain Pairwise Model With Infection Age

Infectious disease is a significant problem that are closely related to national economy and human?s Physical.Combining with regulation and characteristics of infectious diseases may build mathematical model to investigate the cause of the epidemic and key factors of epidemic and to predict development trend and final size of epidemic.For most real infectious diseases,infected with different strains have different infectious and recovery power for the same disease in the population.Therefore,it is necessary to take infection age into the model,in order to reflect effectively the influence power of individuals in their infectious period.In recent years,some researchers began to study widely the spread of infectious disease with non-Markovian process,which make the model more closer to the actual.In this paper,we consider two-strain network dynamic model with infection age and non-Markovian recovery process,and major discuss the two pairwise model of SI1I2R and SI1I2S respectively.In chapter 1,the basic knowledge of networks and some notations of network epidemic mod-eling are introduced,we also analysis research status at home and abroad for the network pairwise model with non-Markovian process and give some main description of notations.In chapter 2,we present and study a two-strain SI1I2R pairwise epidemic model with non-Markovian recovery process in which the recovery rate depends on infection age.For the two-strain pairwise model,the feasible solution region and the reproduction number with arbitrary recovery time distributions are obtained.We carry out rigorous analysis and obtain upper and lower estimates for the final epidemic size,we also give the final epidemic size relations of the general SI1I2Rmodel and the SI1I2R model with infection age at the mean time,and the effects of three commonly used recovery time distributions on the reproduction number are compared by numerical simulations.In chapter 3,we build a two-strain SI1I2S pairwise model with infection age and non-Markovian recovery process.The novel model can be transformed into a system of integro-differential equations by using the method of characteristics.Using the integrated semigroup formulation prove uniform persistence of system.We also derive the basic reproduction number by analysing the equilibria.In Chapter 4,making summary for the main conclusion of this paper and giving some expecta-tion for future.