Dynamic Analysis Of Infectious Disease Models Under The Influence Of Public Health Education

In recent years,infectious diseases,especially the emerging infectious diseases,outbreak in endlessly.How to contain infectious disease outbreaks and to alleviate the popularity of infectious diseases is imminent major issues facing the world today.Due to the occurrence of emergent infectious disease without any early warning signal,so that the public have few necessary psychological preparation about it,and they always be covered with panics and doubts.Hence,the government can carry out public health education activities for the masses,spreading disease related knowledge and protective measures to the public directly,which play a important role in guiding public opinion direction,disseminating correct knowledge,and soothing the the public mood,when we begin to deal with this kind of emergency.The way of public health education can be divided into two parts,mass communication and interpersonal communication.There are many achievements to study the impact of mass communication on the control of infectious disease until now,but rare has been found on interpersonal communication,of which the extent and scale is still largely unknown.This paper is based on the classical compartmental model to split the susceptible population S into two disjoint classes,S1 and S2,who have no idea or have a certain understanding about the disease,with the impact of public health education.First of all,aiming at some infectious diseases with lifelong immunity,by analyzing the dynamic behaviors of our model,we found two thresholding parameters R1 and R2 on which the disease persistence and extinction condition depend.Also we found that there is at most a endemic equilibrium for the model.The results showed that the endemic equilibrium,whenever it exists,is locally asymptotically stable.Furthermore,we analyzed the global stability,and ruled out the existence of periodic solution,thus it must be globally asymptotic stable when the system exists only one local stably equilibrium.In addition,we discussed the effect of increasing the input rate of public health education on the existence of endemic equilibrium.The results showed that the input rate of public health education becomes larger,the existence regionof endemic equilibrium becomes smaller,and the influence of interpersonal communication on it is greater than mass communication.Secondly,studying the transmission dynamics of the infectious disease with temporary immunity under the influence of public health education.There is only one endemic equilibrium for the model and it is globally asymptotic stable.By analyzing the model,we found that the endemic equilibrium may be degraded into the disease free equilibrium when R2 < 1 < R1,which means that the disease will be extinct;Although the endemic equilibrium always be existed when 1 < R2 < R1,the number of infected individuals will decrease with increasing the public health education activities,which also implies that the public health education should be able to slow down the spread of infectious disease.Finally,we established an SIR model with two patches and only one patch has migration.Using the qualitative and stability theory of differential equation to analyze the model,we found that there is at most a endemic equilibrium for the model.The results showed that the endemic equilibrium,whenever it exists,is locally asymptotically stable by using Hurwitz criterion to estimate the local stability of the equilibria.If we want to control the disease,we need to take corresponding measures,which combined with the actual situation,to In order to get effective control of the disease,it is necessary to take the corresponding preventive measures to make the existing condition of the endemic equilibrium does not exist,which also provide theoretical guidance for disease prevention and control in real life.