Infectious Disease Model With Delay In The Stability Study

Epidemic dynamical models is important part of mathematical models in biology. Re-cently,they have received much attention by a lot of scholars.In this paper, according to thestudy of systems both at home and abroad in recent years, we carefully studied the followingtwo dynamic models which are established to consider di?erent time delays.First, consider a class of distributed delay of the SEIR model of disease extinction bythe decision whether or not the basic reproduction number R0. When the basic reproductivenumber is greater than 1, the disease will be durable and lasting end gives the lower boundof the disease specific formulas. Finally, the use of the Liapunov functional method ofestablishing a disease-free equilibrium of the global stability and local stability of the endemicequilibrium and su?cient conditions.Second, the study of disease spread adult individuals with short-term immune stagestructure and time delay SIRS model stability, ie that individuals acquire immunity afterinfection after a short period of time will lose their immunity and enter the susceptible class.First discuss the local disease-free equilibrium and global stability are obtained when R0 < 1when the disease has been eradicated; Second, prove the existence of local equilibrium andlocal stability is obtained through analysis of the full Conditions; finally obtained by Lia-punov functional balance point where disease levels su?cient conditions for global stability,the numerical simulation.