Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate

Abstract EN

This paper is concerned with a delayed SEIS (Susceptible-Exposed-Infectious-Susceptible) epidemic model with a changing delitescence and nonlinear incidence rate.

First of all, local stability of the endemic equilibrium and the existence of a Hopf bifurcation are studied by choosing the time delay as the bifurcation parameter.

Directly afterwards, properties of the Hopf bifurcation are determined based on the normal form theory and the center manifold theorem.

At last, numerical simulations are carried out to illustrate the obtained theoretical results.