Geodesic
Hopf bifurcation for an SIR model with age structure
Hui Cao1 ; Dongxue Yan2 ; Xiaxia Xu3
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.
Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 7.

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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.
DOI : 10.1051/mmnp/2021003

Hui Cao 1 ; Dongxue Yan 2 ; Xiaxia Xu 3

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. 
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Hui Cao; Dongxue Yan; Xiaxia Xu. Hopf bifurcation for an SIR model with age structure. Mathematical modelling of natural phenomena, Tome 16 (2021), article  no. 7. doi : 10.1051/mmnp/2021003. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2021003/

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