On Several Classes Of Fractional Order Epidemic Dynamical Models

The dynamic model of infectious diseases is a branch of biomathematics that has very important practical significance.Since the classic SIS and SIR infectious disease compartment model was put forward in 1927,it has been widely used by scholars to study the dynamics of infectious diseases.In recent years,with the continuous development of fractional differential equation theory,more and more fractional models have been applied to the study of infectious disease dynamics.This paper establishes several types of fractional-order epidemic models and studies their dynamic behaviors to obtain the final epidemic situation by judging the global stability of the equilibrium point.This article is structured as follows:In Chapter 1,the first section of the first chapter introduces the research background and research status of infectious disease dynamics.The second section briefly explains the main content of each part of this article.The third section is preparation for knowledge.In Chapter 2,we establish a class of fractional SIS model with bilinear incidence,and then determine the stability of disease-free equilibrium and endemic equilibrium.It is concluded that when ₀R?1,the disease-free balance point E⁰ is global asymptotic stability,and the number of infected people eventually tends to zero,implying that the disease will eventually disappear in the region;When ₀R?1,the endemic equilibrium point E^*is global asymptotic stability,and the number of infected people tends to be constant,which means that the disease will eventually develop endemic diseases in the area.Therefore,we should take appropriate measures to reduce the value of ₀R to control the epidemic.Finally,the corresponding numerical simulation results and model comparisons are given respectively.These simulation results help us understand the theoretical results more vividly.In Chapter 3,we study a class of fractional SIR models with bilinear incidence.WhenR₀?1,the disease eventually disappears;when ₀R?1,the endemic equilibrium point E^*is globally progressively stable,and the number of infected people tends to be a constant constant,which means that the disease will eventually develop endemic diseases in the area.Finally,the corresponding numerical simulation results and model comparisons are given respectively.These simulation results help us understand the theoretical results more vividly.In Chapter 4,we discusses a class of fractional SEI epidemic models with multiple stages of parallel transmission and concludes the final epidemic of the disease.When ₀R?1,the disease eventually disappears in the region;when ₀R?1,the endemic equilibrium point E^*is globally progressively stable,and the number of infected people tends to be a constant,meaning that the disease will eventually develop endemic diseases in the area.