| The dissemination of information has an important influence on the epidemic and control of infectious diseases.Considering different information feedback mechanisms and saturated treatment,two kinds of epidemic models are established.Some interest-ing results are obtained through theoretical analysis and numerical simulation,which provide some valuable suggestions for the prevention and control of infectious diseases.In chapter 1,the influence of information feedback on the transmission and control of disease is introduced.We analyze the research status of the infectious disease dynam-ics model considering information feedback and saturation therapy.The main contents and basic theoretical knowledge of this paper are summarized.In chapter 2,a dynamic model of infectious disease considering weak negative feed-back of information and saturated treatment is established.By analyzing the existence of the model s equilibrium,we find that saturated treatment is a necessary condition leading to backward bifurcation in the system.With the introduction and increasing of the neg-ative feedback strength of disease information,the range of backward bifurcation will gradually decrease.When the intensity of negative feedback mechanism of disease infor-mation becomes strong enough,the backward bifurcation will disappear,which indicates that promoting the dissemination of information is conducive to controlling the disease.By analyzing the existence of the model s equilibrium,we find that the disease-free e-quilibrium is always locally asymptotically stable when the basic reproduction number is less than 1.When there are two endemic equilibria in the system,we prove that one of them must be saddle point and give the conditions for the local asymptotic stability of the other one.So we know that the system has bistability under certain conditions.Through numerical simulation,we find that the transmission of disease information may lead to periodic oscillation of the solutions by Hopf bifurcation.In chapter 3,a dynamics model of infectious diseases considering strong negative feedback of information and saturated treatment is established.Firstly,we prove the nonnegativity and dissipation of the solution of the model.Secondly,we analyze the existence and local stability of equilibrium points,and give the conditions for the exis-tence of backward bifurcation.Thirdly,we analyze the conditions for the appearance of Hopf bifurcation without considering saturation therapy,and then the bifurcation di-rection and stability are calculated by using the general theory of the central manifold.Finally,through numerical simulation,we find that when the information effect param-eter e is small,the solution of the system tends to a steady state with more patients;as the value of e increases,periodic oscillation may occur in the system;as the value of e increases further,the solution of the system finally tends to a steady state with fewer infected persons,which indicates that increased information dissemination may reduce the number of infected persons.In the last chapter,we briefly summarize the research results,analyze their biolog-ical significance and theoretical value.And we also point out the problems of further research. |
