A Study Of Infectious Disease Models Influenced By Media Reports And Random Noise

The dynamic analysis of infectious diseases is an important part of the study of bio-logical mathematical model.With the development of mass media and social networking,information dissemination has more and more obvious influence on infectious diseases,and human's physical and environmental fluctuations will have an impact on infectious diseases,so this thesis based on previous studies,the epidemic model with media influence and made some improvements,constructed two types of infectious disease model:one is the delay SIS model with saturated media and a class of stochastic extinction of infectious disease model under the influence of media reports.Using the relevant theory,the partial dynamics of the two types of models are studied.First,a delay SIS model with the effect of media saturation is established.The infection rate with media saturation is used to characterize the impact of media on infectious diseases.First of all,there exists a unique endemic equilibrium to calculate the disease-free equilibrium and when R₀>1;Secondly,the stability of the disease-free equilibrium and the endemic equilibrium point.And when the parameters satisfy certain conditions,delay?exceeds the critical value of?₀,The equilibrium point of endemic disease is no longer stable and the Hopf-Bifurcation appears.Finally,the numerical simulation also validates the theoretical analysis,and get the number of infected rate can be reduced by adding most of the execution.Secondly,the random extermination of the infectious disease model affected by media coverage is analyzed.First of all,through the Liapunov analysis method to prove the positive solution,existence and uniqueness of the global stochastic system;secondly,using nonnegative semi-martingale convergence theorem,when R₀<1,the infectious diseases is stochasic extinction;Finally,theoretical analysis is supported by numerical simulation,and through the simulation can be seen when the noise intensity is large,there will be significant changes the solution of the stochastic model and its solution in a shorter time tends to be stable.In a word,people can take measures to reduce infection probability through the media's understanding of infectious diseases,and consider the effects of time lag and random noise in the media borne infectious disease model,which is more consistent with the reality of life.