Hopf Bifurcation for a Susceptible-Infective Model with Infection-Age Structure |
| |
Authors: | Xiangming Zhang Zhihua Liu |
| |
Affiliation: | 1.School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China |
| |
Abstract: | An SIS model is investigated in which the infective individuals are assumed to have an infection-age structure. The model is formulated as an abstract non-densely defined Cauchy problem. We study some dynamical properties of the model by using the theory of integrated semigroups, the Hopf bifurcation theory and the normal form theory for semilinear equations with non-dense domain. Qualitative analysis indicates that there exist some parameter values such that this SIS model has a non-trivial periodic solution which bifurcates from the positive equilibrium. Furthermore, the explicit formulae are given to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions. Numerical simulations are also carried out to support our theoretical results. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|