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Analysis of Dynamics of Recurrent Epidemics: Periodic or Non-periodic
Hui Cao1, Dongxue Yan2, Suxia Zhang3
1Department of Mathematics, Shaanxi University of Science and Technology, Xi'an, 710021, People's Republic of China.
Abstract:
The periodic behaviors and non-periodic behaviors of recurrent epidemic are discussed by building an SIS model with disease age structure and infectious delay. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the existence of Hopf bifurcation under the condition where endemic equilibrium is unstable. It implies that the recurrent epidemics will switch between periodic behavior and non-periodic behavior as the parameter values changing when the disease persists in population. The numerical examples are provided to illustrate our theoretical results.
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