Global behavior of a multi-group SEIR epidemic model with age structure and spatial diffusion
1College of Mathematics, Sichuan University, Chengdu, Sichuan 610065, China.
Mathematical Biosciences and Engineering : MBE
|December 31, 2020
Summary
This study introduces a new multi-group SEIR model incorporating age structure and spatial diffusion to understand disease spread. The model confirms disease-free states are stable and demonstrates conditions for persistent infectious disease outbreaks.
Area of Science:
- Epidemiology
- Mathematical Biology
- Dynamical Systems
Background:
- Existing epidemic models often lack integrated analysis of multi-group, age structure, and spatial diffusion.
- A comprehensive model is needed to accurately capture complex infectious disease transmission dynamics.
Purpose of the Study:
- To develop and analyze a novel multi-group SEIR epidemic model that incorporates both age structure and spatial diffusion.
- To investigate the theoretical properties of the model, including solution existence, uniqueness, and stability of steady states.
Main Methods:
- Analytical investigation of model properties: positivity, boundedness, and global attractors.
- Application of Lyapunov functionals and LaSalle's invariance principle to prove global asymptotic stability of the disease-free steady state.
- Utilizing Perron-Frobenius theorem and graph-theoretical results to establish the existence and stability of the endemic steady state.
Main Results:
- The model demonstrates the existence and uniqueness of solutions, along with a compact global attractor.
- The disease-free steady state is proven to be globally asymptotically stable under specific parameter assumptions.
- Conditions for the existence and global stability of the endemic steady state are established.
Conclusions:
- The novel multi-group SEIR model provides a robust framework for studying infectious disease transmission with age structure and spatial diffusion.
- Theoretical results are validated through numerical examples, highlighting the model's practical applicability in public health.
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