Global Hopf bifurcation of a cholera model with media coverage

Jie He; Zhenguo Bai; Jie He; Zhenguo Bai

doi:10.3934/mbe.2023820

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18468-18490. doi: 10.3934/mbe.2023820

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Global Hopf bifurcation of a cholera model with media coverage

Jie He ,
Zhenguo Bai ^,

School of Mathematics and Statistics, Xidian University, Xi'an 710126, China

Academic Editor: Xiangsheng Wang

Received: 14 July 2023 Revised: 24 September 2023 Accepted: 25 September 2023 Published: 26 September 2023

We propose a model for cholera under the impact of delayed mass media, including human-to-human and environment-to-human transmission routes. First, we establish the extinction and uniform persistence of the disease with respect to the basic reproduction number. Then, we conduct a local and global Hopf bifurcation analysis by treating the delay as a bifurcation parameter. Finally, we carry out numerical simulations to demonstrate theoretical results. The impact of the media with the time delay is found to not influence the threshold dynamics of the model, but is a factor that induces periodic oscillations of the disease.
- cholera model,
- media coverage,
- threshold dynamics,
- basic reproduction number,
- global Hopf bifurcation
Citation: Jie He, Zhenguo Bai. Global Hopf bifurcation of a cholera model with media coverage[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18468-18490. doi: 10.3934/mbe.2023820

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Abstract

We propose a model for cholera under the impact of delayed mass media, including human-to-human and environment-to-human transmission routes. First, we establish the extinction and uniform persistence of the disease with respect to the basic reproduction number. Then, we conduct a local and global Hopf bifurcation analysis by treating the delay as a bifurcation parameter. Finally, we carry out numerical simulations to demonstrate theoretical results. The impact of the media with the time delay is found to not influence the threshold dynamics of the model, but is a factor that induces periodic oscillations of the disease.

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