An SIR epidemic model with vaccination in a patchy environment
Qianqian Cui1, Zhipeng Qiu1, Ling Ding1
1School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
Mathematical Biosciences and Engineering : MBE
|November 23, 2017
Summary
This study models infectious disease spread using an SIR patch model. Vaccination effectively controls outbreaks, while human mobility impacts disease dynamics across different regions.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- Understanding disease transmission dynamics is crucial for effective public health interventions.
- Mathematical models, such as the SIR (Susceptible-Infectious-Recovered) model, are vital tools for simulating disease spread.
- The influence of vaccination and human mobility on disease dynamics in interconnected populations requires further investigation.
Purpose of the Study:
- To formulate and analyze an SIR patch model incorporating vaccination strategies.
- To investigate the impact of vaccination coverage on disease control across multiple interconnected patches.
- To assess how human mobility patterns influence the spatial spread and outbreak size of infectious diseases.
Main Methods:
- Development of an SIR patch model with vaccination and migration parameters.
- Derivation and analysis of the control reproduction number (Rv) to determine disease-free equilibrium stability.
- Mathematical analysis of local stability for boundary equilibria and existence of equilibria for n=2 case.
- Numerical simulations to visualize the effects of vaccination and mobility on disease spread.
Main Results:
- The disease-free equilibrium is globally asymptotically stable when Rv < 1 and unstable when Rv > 1.
- Sufficient conditions for local stability of boundary equilibria and existence of equilibria were established for n=2.
- Vaccination was shown to effectively control and prevent disease outbreaks across all modeled patches.
- Human migration can exacerbate outbreaks in some patches while mitigating them in others.
Conclusions:
- Vaccination is a potent tool for controlling and preventing infectious disease outbreaks in a multi-patch system.
- Human mobility introduces complex spatial dynamics, potentially leading to heterogeneous impacts on disease spread across different regions.
- The SIR patch model provides valuable insights into the interplay between vaccination, mobility, and disease transmission, informing public health strategies.
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