Abstract
AbstractThis paper studies a two-age structured SIRS epidemic model with logistic growth of susceptible population and two-time delays. We simultaneously introduce two-time delays, i.e., the immunity and incubation periods, into this dynamic system and investigate their impact on different dynamic behaviors for the model. By means of the $C_{0}$
C
0
-semigroup theory, the model is transformed into a non-densely defined abstract Cauchy problem, and the condition of the existence and uniqueness of the endemic equilibrium is obtained. Following the spectral analysis, the characteristic equation technique, and the Hopf bifurcation theorem, we show that different combinations of the two delays perform a vital role in the instability/stability as well as the Hopf bifurcation results of equilibrium solutions. We numerically provide some graphical representations to check the main theoretical results and show the rich dynamics by varying the two delay parameters.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Province of China
The Natural Science Foundation of the Jiangsu Higher Education Institutions of China
Nanjing University of Posts and Telecommunications Science Foundation
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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