Analysis Of Infectious Disease Dynamics Model With Information Heterogeneous Feedback And Natural Growth

The spread of information has an important influence on the epidemic and control of diseases.Under the premise of considering the strong negative feedback of information,this paper establishes two kinds of infectious disease dynamic models according to different situations,and obtains some meaningful results through theoretical analysis and numerical simulation,which provides some valuable suggestions for the prevention and control of infectious diseases.In Chapter 1,we briefly introduce the background knowledge of infectious diseases and information feedback,including the generation and feedback of information in infectious diseases model,the application of optimal control theory in infectious diseases model and the research status of infectious diseases model including information feedback,and lists the related theoretical basic knowledge needed in this paper.In Chapter 2,we establish a dynamic model of infectious diseases considering the heterogeneity of information feedback and optimal control.Firstly,we prove the nonnegativity and boundedness of the solution of the model.Secondly,we discuss the existence and local stability of each equilibrium point and the global stability of the disease-free equilibrium point and the information-free equilibrium point,and obtain the conditions for the occurrence of Hopf bifurcation at the endemic equilibrium point.At the sametime,we establish the optimal control model,the optimal strategy to control the spread of disease is obtained by using the optimal control theory,and the relevant conclusions of this chapter are verified by numerical simulation.Finally,through the sensitivity analysis,we get the influence of different parameters on the number of infected people.The study find that when the disease broke out,if we can increase the propaganda in time,make more susceptible people quickly take protective measures to prevent themselves from being infected,and make more infected people hospitalized for treatment,then the disease may be controlled or even disappear.At the same time,it can effectively reduce the final number of infected people by increasing the dissemination of information to the public and encourage more infected people to be hospitalized.In Chapter 3,we establish a dynamic model of infectious diseases considering the logistic natural growth of information.Firstly,we prove the nonnegativity and boundedness of the solution of the model.Secondly,we analyze the existence and local stability of each equilibrium point,give the conditions for the existence of Hopf bifurcation at the endemic equilibrium point,and calculate the direction of Hopf bifurcation and the stability of periodic solution.Finally,The results of theoretical analysis are verified by numerical simulation and extended.And find that when the natural capacity of information is small or large,the endemic equilibrium point tends to be stable,while when the natural capacity of information is in the middle level,there is periodic oscillation,which shows that the daily accumulation of disease information plays an important role in controlling the spread of infectious diseases.In Chapter 4,we briefly summarize the conclusion of this paper,and point out the problems and directions for further study.