Two Kinds Of Epidemic Models With Heterogeneity

Based on the difference of space and strain,two kinds of epidemic models with heterogeneity are established.One is a population dispersal model with transport-related infection and spatial heterogeneity,and the other is a three-strains of influenza model with superinfection and virulent heterogeneity.The dynamics and biological significance of the two models are analyzed by using the basic theories and methods of dynamic system and stability theory,asymptotic autonomous system theory,and uniform persistence theory.In the first chapter,the research background and significance of heterogeneous epidemic model are introduced,and the research progress of two related dynamic model are briefly described.One is population dispersal model with spatial heterogeneity,the other is influenza model with virulent heterogeneity.Moreover,the main work of this thesis is outlined.In the second chapter,a class of transport-related epidemic model which takes into account the spatial heterogeneity are established and analyzed.The next generation matrix method is used to obtain the threshold R₀.If R₀< 1,it is obtained the infectionfree equilibrium is globally asymptotically stable by using the theory of asymptotically autonomous system.If R₀ > 1,it is proved that there is an endemic equilibrium point and the system is consistent and persistent by using uniform persistence theory.The effects of population dispersal on infectious disease outbreaks in heterogeneous space are analyzed from theoretical analysis and numerical simulation.In the third chapter,a class of three-strains influenza model with heterogeneous virulent and immunization and superinfection is constructed and studied.The basic reproductive number R₀ of the system and the invasion reproductive number R_i^j?i,j?{1,2,3},i?j?of each strain are calculated,the existence of the repulsive equilibrium point and the coexistence equilibrium point of each strain are discussed,and the dynamic behavior of the three-strains influenza model are analyzed by applying the Lyapunov stability theory.Morever,the effect of superinfection and immunization on the dynamic behavior of the system under heterogeneous virulent are revealed by numerical simulation.In the fourth chapter,the main work and conclusions of this thesis are summarized,and the practical value and biological significance of the research result is introduced.Meanwhile,the shortcomings of this work and further research direction are put forward.