Pair-Approximation Modeling And Analysis In Terms Of Two Strains With Cross Infection

Up to now from the beginning of the human society,the infectious diseases accompany and affect public health and life.For one thing,in particular,the virus triggering the same disease are variable.For example,HIV virus resulting in AIDS includes type HIV-1 and type HIV-2.Additionally,as virus mutates,its species increasingly grow,such as the avian influenza with many variants.For another thing,the structure of the population disease spreads is complicated and variable.Both of these factors increase the difficulties that people explore the infectious diseases.Pair-approximation model is an effective method,which not only can model the disease spread of multiple strains on population but also capture the change of network topological structure.Noticeably,the study of applying pair-approximation model into multiple strains disease spread is paid little attention to.Therefore,the paper do next two works: 1)building an SIS pair-approximation model of two strains with cross infection on regular and static network and analyzing its equilibrium and dynamic behaviors;2)establishing an SIS pair-approximation model with demographics in terms of two strains with cross infection and analyzing its equilibrium and dynamic behaviors,as well as studying the effects demographics take on diseases threshold.The main content in paper is as follows:Chapter 1 emphasizes the significance of the disease spread on networks and introduces the basic concept and topological properties of network.Then,we introduce the latest developments about the static and dynamical network-based epidemic models.Finally,this section illustrates the significance and developments of pair-approximation models and epidemic models with multiple strains,further underlining the necessity and importance of integrating these two models.Chapter 2 develops an SIS pair-approximation model of two strains with cross infection on regular and static network,the influence of demographics on disease spread can be ignored.Then,applying the closure formula closes the models,and then analyzes the basic reproduction number and existence of equilibriums for the closed models.Finally,numerical simulation demonstrate the existence and stability of equilibriums.Chapter 3 develops an SIS pair-approximation model with demographics in terms of two strains with cross infection,the influence of demographics on disease spread can not be ignored.Then,applying the closure formula closes the models,and then analyzes the basic reproduction number and existence of equilibriums for the closed models.Additionally,numerical simulation demonstrate the existence and stability of equilibriums.Finally,we explore effects of demographics on disease threshold,finding that demographics lead to the decline of the basic reproduction number and further restrain the outbreak of disease.