The backward bifurcation of an age-structured cholera transmission model with saturation incidence

Zhiping Liu; Zhen Jin; Junyuan Yang; Juan Zhang; Zhiping Liu; Zhen Jin; Junyuan Yang; Juan Zhang

doi:10.3934/mbe.2022580

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 12427-12447. doi: 10.3934/mbe.2022580

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The backward bifurcation of an age-structured cholera transmission model with saturation incidence

1.
School of Data Science and Technology, North University of China, Taiyuan 030051, Shanxi, China
2.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
3.
Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006, China

Academic Editor: Petri Piiroinen

Received: 07 June 2022 Revised: 29 July 2022 Accepted: 07 August 2022 Published: 25 August 2022

In this paper, we consider an age-structured cholera model with saturation incidence, vaccination age of vaccinated individuals, infection age of infected individuals, and biological age of pathogens. First, the basic reproduction number is calculated. When the basic reproduction number is less than one, the disease-free equilibrium is locally stable. Further, the existence of backward bifurcation of the model is obtained. Numerically, we also compared the effects of various control measures, including basic control measures and vaccination, on the number of infected individuals.
- age-structured cholera model,
- saturation incidence,
- vaccination age,
- backward bifurcation,
- control measure
Citation: Zhiping Liu, Zhen Jin, Junyuan Yang, Juan Zhang. The backward bifurcation of an age-structured cholera transmission model with saturation incidence[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 12427-12447. doi: 10.3934/mbe.2022580

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Abstract

In this paper, we consider an age-structured cholera model with saturation incidence, vaccination age of vaccinated individuals, infection age of infected individuals, and biological age of pathogens. First, the basic reproduction number is calculated. When the basic reproduction number is less than one, the disease-free equilibrium is locally stable. Further, the existence of backward bifurcation of the model is obtained. Numerically, we also compared the effects of various control measures, including basic control measures and vaccination, on the number of infected individuals.

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