Research On The Dynamics Of Two Multi-scale Epidemic Models On Complex Networks

The transmission of infectious diseases is a coupling process in which pathogens are expelled from infected individuals,and then invade into susceptible individuals through certain transmission routes,causing infection.Immuno-epidemiological dynamics model is an important tool to solve the pathogen evolution of within hosts and the diseases transmission of between hosts.Individual contact heterogeneity affects the patterns of infectious disease transmission.In this paper,two multiscale immuno-epidemiological models on complex networks are established to study the influence of virus evolution of within hosts and the topology of networks on the spread of infectious diseases.The specific contents are as follows:The first part introduces the research background and dynamics of immune-epidemiological models,and summarizes the research content,innovation points and preparatory knowledge of this subject.In the second part,considering the influence of network topology and virus evolution of within hosts on the spread of disease of between hosts,a class of immune-epidemiological model is constructed.First,the reproduction number of the within-host is obtained,and the existence and stability of equilibria of the within-host are studied.Second,the well-posedness of the solution to the between-host model is proved by using the contraction mapping principle,and the basic reproduction number of the between-host model is given.The stability of the disease-free equilibrium and the existence of the final size are obtained.Numerical results show that the reproduction number of the between-host is an increasing function of the reproduction number of the within-host system,while the final size is an increasing function of the reproduction number of the between-host system.Finally,we find that the topology of the networks affect the spread of disease of between hosts.In the third part,considering the non-Markovian feature of the recovery process,a class of immune-epidemiological model on complex networks is constructed by using the integral equation theory.The well-posedness of the model is proved by the contraction mapping principle,and the basic reproduction number of the between-host is given.The global stability of the disease-free equilibrium is proved by using the theory of linearization and comparison principle,the local stability of the endemic equilibrium is proved by using fixed-point theorem and eigenvalue analysis.Numerical results show that the prevalence is a non-monotonic function of the reproduction number of within hosts,and the exponential recovery process underestimates the spread of the disease.The fourth part summarizes the main work of this subject and the future prospects of the dynamics of multi-scale epidemic models on complex networks.