Stability Analysis Of An Infectious Disease Model With Media Coverage

In order to effectively prevent and control diseases,a reasonable model of infectious diseases was established by reading a lot of literatures.The paper was divided into two parts.First,an SIRS epidemic model with logistic population changes influenced by media reports was established,and the nature of the model equilibriums were proved and verified by Matlab software.Second,it was considered on the basis of the first part,it combined with latency and recurrence period two time delays to set up an SEIRS epidemic model affected by media reports.The model equilibriums were proved and verified by the Matlab software.Some meaningful conclusions were found by numerical simulation.An SIRS epidemic model with logistic population changes influenced by media reports was mainly established by K-M thoughts and the articles of professor Huaiping Zhu et al..The equilibriums of the model were calculated by the function's intermediate value theorem.According to the modified regeneration number and Hurwitz identification method,the sufficient conditions for the stability of the disease-free equilibrium and the local disease equilibrium were received.Finally,the validity of conclusion was verified by numerical simulation,and the new conclusion that the larger the population volume,the lower the proportion of infected people in the total population,and it would be tended to a fixed value was found.And the section is further enriching and expanding the conclusion of the Linda Q and Herbert W's "Disease transmission models with density dependent demographics".Then,in oder to consider the latency and recurrence period of some diseases,the population was divided into four categories: susceptible,lurker,infected and relapsed.First,the equilibriums of the model were received.Secondly,the sufficient conditions of the disease-free and the local disease equilibrium's stability were obtained by modifying the regeneration number and constructing appropriate Liapunov function.Finally,the validity of the conclusion was verified by numerical simulation,and the global asymptotic stability of local disease equilibrium was found by computer simulation.The section is enriching the conclusion and the model of the Lianwen Wang's article "Dynamics analysis of an epidemion logical model with media impact and two delays".