Two-strain Epidemic Models On Complex Networks With Demographics

Many complex systems in nature and social contact networks can be described in complex network models.For example,research of infectious diseases on complex networks has been made great progress.But one of the research focus is modeling and analysis of infectious diseases on complex heterogeneous networks with demographics,which is one of the greatest challenges in complex network epidemiology.Additionally,there are a large number of infectious diseases with multi-strains and multi-virus in the real world.The heterogeneity and interactions between strains provide us a rich research area.Based on this,we will provide mathematical models to study the spread of two-strain epidemic diseases on heterogeneous networks with birth and death.In chapter 1,As the introduction,the practical significance on researching infectious diseases and the key role of the mathematical model used in researching infectious diseases on complex networks have been introduced.Additionally,research on epidemic models with multi-strains and some dynamical network models had considered the impact of demographics on infectious diseases are summarized.Then it introduces the research content and principle methods.In chapter 2,we develop a two-strain SI1I2 S epidemic model on complex networks with demographics.We calculate the basic reproduction number 0 of infection for the model by using the next generation matrix.We prove that if 0 < 1,the disease-free equilibrium is globally asymptotically stable.If 0 > 1,the conditions of the existence and global asymptotical stability of two boundary equilibria and the existence of endemic equilibria are established,respectively.we make some numerical simulations to verify the main results obtained in this chapter.In chapter 3,we study a two-strain SI1I2 R model on complex networks with demographics.We calculate the basic reproduction number 0 and prove that if 0 < 1,the disease-free equilibrium is globally asymptotically stable.If 0 > 1,the existence and global stability of two boundary equilibria are established,respectively.Numerical simulations are made to verify the main results.In Chapter 4,Summarize the main conclusion of this paper and do some expectation for future.