| Issue |
Math. Model. Nat. Phenom.
Volume 16, 2021
Mathematical Models and Methods in Epidemiology
|
|
|---|---|---|
| Article Number | 7 | |
| Number of page(s) | 17 | |
| DOI | https://doi.org/10.1051/mmnp/2021003 | |
| Published online | 03 March 2021 | |
Hopf bifurcation for an SIR model with age structure
1
Department of Mathematics, Shaanxi University of Science and Technology,
Xi’an,
710021, P.R. China.
2
School of Science, Nanjing University of Posts and Telecommunications,
Nanjing
210023, P.R. China.
3
School of Science, Xi’an University of Technology,
Xi’an
710054, P.R. China.
* Corresponding author: caohui@sust.edu.cn
Received:
18
September
2018
Accepted:
6
January
2021
This paper deals with an SIR model with age structure of infected individuals. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the existence of all the feasible equilibrium points of the system. The criteria for both stability and instability involving system parameters are obtained. Bifurcation analysis indicates that the system with age structure exhibits Hopf bifurcation which is the main result of this paper. Finally, some numerical examples are provided to illustrate our obtained results.
Mathematics Subject Classification: 92D30 / 34D20 / 47E05
Key words: Age-structured SIR model / C0-semigroup / Asymptotical stability / Hopf bifurcation
© The authors. Published by EDP Sciences, 2021
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