Modeling And Research On The Immuno-epidemiological Coupling System With Coinfection

The results in the filed of mathematical modeling and researches in within-host virus infection systems（micro）and disease transmission systems（macro）are very plentiful.Since it has very closed relations between the virus carrying status within host and ability of disease transmission of this host,it is of great significance and realistic meaning to formulate and to investigate coupled systems between immunological systems and epidemiological systems to reveal the mechanism of disease transmission.In this paper,we establish and study the two strains immuno-epidemiological coupling system with coinfection and a simplified two-strain immuno-epidemiological coupling model.The first chapter introduces the background of the problem and the research status of immuno-epidemiological model and epidemiological model with coinfection at home and abroad.In the second chapter,we establish and study a two-strain immune model with coinfection.The expressions of basic reproduction numbers and invasion reproduction numbers of the model are given.The existence of infection-free equilibrium and strain dominance equilibriums are discussed.The local asymptotical stability of infection-free equilibrium and strain dominance equilibriums are proved by using Jacobian matrix and Hurwitz criterion.In the third chapter,we establish and study a two-strain immuno-epidemiological coupling system with coinfection,in which the disease transmission rate and mortality rate due to disease are functions of free virus load.The expressions of the basic reproduction numbers and invasion reproduction numbers of the two strains are given.We discuss the existence and local asymptotical stability of the disease-free equilibrium and the strain dominance equilibriums.And the existence condition of coexistence equilibrium is given.In the fourth chapter,a simplified two-strain immuno-epidemiological coupling model is established and studied.The expressions of basic reproduction numbers and invasion reproduction numbers are calculated.We discuss the existence and local asymptotical stability of disease-free equilibrium and strain dominance equilibriums.The global asymptotical stability of disease-free equilibrium is proved by constructing appropriate Lyapunov function.