Dynamic Analysis Of A Epidemic Model In A Class Of Semi-Directed Networks

Infectious disease models are often used to study issues such as the speed,mode,range and dynamics of infectious diseases.Qualitative analysis of the dynamic nature of infectious disease models is of great significance for the control of infectious diseases.The combination of the propagation model and the complex network allows the propagation model with network characteristics to be described.At the same time,the network's own attributes,such as the directivity of the network,will also affect the disease transmission process.This article is based on complex network theory,qualitative theory of differential equations,considers the directional connection between nodes in the network,and considers the situation where some nodes cannot fully obtain immunity in the transmission of viruses,such as mobile phone virus transmission and other viruses.This article uses self-protection State instead of immune state,establish such infectious disease models under the conditions of scale-free network and semidirected network,and study their dynamic properties,including the model's basic regeneration number,equilibrium point calculation,equilibrium point Progressive stability judgment and numerical simulation.The full text is composed of five parts:The first chapter outlines the research background of this article,points out the significance of the study of infectious disease models under complex networks,and briefly describes the current research status and the research ideas of this article.The second chapter introduces the basic concepts of infectious disease models and complex networks,introduces the basic principles and common methods of differential equation models,and specifies the important applications of infectious disease models in the study of complex network propagation.Chapter 3 establishes a class of infectious disease models under scale-free networks and applies them to study disturbance propagation in ecosystems,from the model's basic regeneration number,equilibrium point expression,equilibrium point stability judgment and numerical simulation,etc.Research and demonstrate the nature of the model.In the fourth chapter,this paper generalizes the infectious disease model in scale-free networks to semi-directed networks,and focuses on the study of such semi-directed network models.Determine the stability and verify the conclusion through numerical simulation.Chapter 5 systematically summarizes the content of this article and looks forward to the future work direction.