Open AccessDynamic analysis of the recurrent epidemic model
Author(s) -
Hui Cao,
Dongxue Yan,
Ao Li
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019299
Subject(s) - hopf bifurcation , stability (learning theory) , epidemic model , mathematics , population , bifurcation , age structure , mathematical economics , population model , computer science , demography , physics , nonlinear system , sociology , quantum mechanics , machine learning
In this work, an SIRS model with age structure is proposed for recurrent infectious disease by incorporating temporary immunity and delay. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the global stability of disease free equilibrium, the local stability of endemic equilibrium, and the existence of Hopf bifurcation. Both non-periodic and periodic behaviors are possible when the disease persists in population, where time delay plays an important role. Numerical examples are provided to illustrate our theoretical results.