Dynamics analysis of a diffusional immunosuppressive infection model with Beddington-DeAngelis functional response

Yuan Xue; Jinli Xu; Yuting Ding; Yuan Xue; Jinli Xu; Yuting Ding

doi:10.3934/era.2023309

Electronic Research Archive

2023, Volume 31, Issue 10: 6071-6088. doi: 10.3934/era.2023309

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Theory article

Dynamics analysis of a diffusional immunosuppressive infection model with Beddington-DeAngelis functional response

College of Science, Northeast Forestry University, Harbin 150040, China

Received: 26 July 2023 Revised: 27 August 2023 Accepted: 04 September 2023 Published: 11 September 2023

This paper introduces diffusion into an immunosuppressive infection model with virus stimulation delay and Beddington-DeAngelis functional response. First, we study the stability of positive constant steady state solution and show that the Hopf bifurcation will exist under certain conditions. Second, we derive the normal form of the Hopf bifurcation for the model reduced on the center manifold by using the multiple time scales (MTS) method. Moreover, the direction and stability of the bifurcating periodic solution are investigated. Finally, we present numerical simulations to verify the results of theoretical analysis and provide corresponding biological explanations.
- immunosuppressive infection model,
- Beddington-DeAngelis functional response,
- delay,
- Hopf bifurcation,
- multiple time scales
Citation: Yuan Xue, Jinli Xu, Yuting Ding. Dynamics analysis of a diffusional immunosuppressive infection model with Beddington-DeAngelis functional response[J]. Electronic Research Archive, 2023, 31(10): 6071-6088. doi: 10.3934/era.2023309

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Abstract

This paper introduces diffusion into an immunosuppressive infection model with virus stimulation delay and Beddington-DeAngelis functional response. First, we study the stability of positive constant steady state solution and show that the Hopf bifurcation will exist under certain conditions. Second, we derive the normal form of the Hopf bifurcation for the model reduced on the center manifold by using the multiple time scales (MTS) method. Moreover, the direction and stability of the bifurcating periodic solution are investigated. Finally, we present numerical simulations to verify the results of theoretical analysis and provide corresponding biological explanations.

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