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Global stability of an age-structured cholera model
Jianxin Yang1, Zhipeng Qiu, Xue-Zhi Li
1Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China. yjxin46501@sina.com.
Mathematical Biosciences and Engineering : MBE
|February 11, 2014
Summary
This study presents an age-structured epidemic model for cholera transmission, revealing that the basic reproduction number (R0) dictates disease persistence or extinction. The model analyzes infection-age-dependent infectivity and variable infectious periods.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- Cholera transmission is complex, influenced by factors like age structure and varying infectiousness.
- Existing models often simplify these dynamics, necessitating more comprehensive approaches.
Purpose of the Study:
- To formulate and analyze an age-structured partial differential equation (PDE) model for cholera transmission.
- To investigate the impact of infection-age-dependent infectivity and variable infectious periods on disease dynamics.
- To establish the global dynamics of the model and extend findings to general continuous age models.
Main Methods:
- Formulation of an age-structured PDE model incorporating direct and indirect transmission.
- Analysis using Lyapunov functions to determine model stability and global dynamics.
- Reduction of the PDE model to multi-stage models for comparison and extension.
Main Results:
- The global dynamics of cholera transmission are determined by the basic reproduction number (R0).
- If R0 < 1, cholera is predicted to die out.
- If R0 > 1, the disease is predicted to persist at an endemic equilibrium.
Conclusions:
- The developed age-structured PDE model provides a robust framework for understanding cholera transmission dynamics.
- The basic reproduction number (R0) is a critical threshold parameter for cholera control.
- The study extends existing findings on multi-stage models to a more general continuous age framework.
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