Analysis Of SI Epidemic Dynamics Model Based On Media Coverage

Infectious disease is one of the important factors that affect human health and social development.Therefore,the research on the prevention and treatment of infectious diseases is becoming more and more important.Some diseases can be prevented through immunization,but this method is expensive.On the other hand,media reports and other means of publicity and education can raise public awareness of disease prevention,and then influence their behavior habit.In this paper,based on the scale-free network,we build a SI model with birth and death to study the effect of two kinds of media reports on the spread of disease in the form of constant growth and the number of infected individuals which is positively related to growth.In the first chapter,we mainly introduce the historical background of the influence of media coverage on the spread of the disease and the basic ideas and research methods of the infectious disease model.In the second chapter,we give some preliminary knowledge about the research needs of this paper.In the third chapter,we consider the epidemic model of the media coverage in the case of constant growth,and study its dynamic behavior.Firstly,the local asymptotic stability of the disease-free equilibrium is analyzed by the eigenvalue method,and the sufficient condition for the local asymptotic stability is obtained;Secondly,by constructing the Lyapunov function and using the limit system theory,the global stability of the disease-free equilibrium point is further proved,and the sufficient condition for the global stability is given;Again,the continuity of the disease is discussed by using the relevant theorems;At last,our main results are verified by numerical simulation.In the fourth chapter,infectious disease model of media reported growth in direct proportion to the number of the infected is under consideration,and to study its dynamics.Firstly,the local asymptotic stability of the disease-free equilibrium is analyzed by the eigenvalue method,and the sufficient condition for the local asymptotic stability is obtained;Secondly,by constructing the Lyapunov function,the global stability of the disease-free equilibrium point is further proved,and the sufficient condition for the global stability is given;Again,the continuity of the disease is discussed by using the related theorems;At last,the numerical simulation is given by Matlab software to verify the results in this chapter.