WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
Global Dynamics of an SEIRS Epidemic Model with Constant Immigration and Immunity
Authors: , , ,
Abstract: An SEIRS model for disease transmission that includes immigration of the infective, susceptible, ex- posed, and recovered has been constructed and analyzed. For the reason that the immunity of the recovered is temporary, a proportion δ1 of recovered will come back to susceptible. We also consider vaccine injection to the susceptible with a proportion c. The model also incorporates a population size dependent contact rate and a disease- related death. As the infected fraction cannot be eliminated from the population, this kind of model has only one unique endemic equilibrium that is globally asymptotically stable. In a special case where the new members of immigration are all susceptible, the model shows a threshold phenomenon. In order to prove the global asymptot- ical stability of the endemic equilibrium, we change our system to a three-dimensional asymptotical autonomous system with limit equation. Finally, we discussed syphilis as a case to predict the development in China. Computer simulation shows that the model can reflect the dynamic and immigration behaviour for disease transmission.