Analysis on a Diffusive SI Epidemic Model with Logistic Source and Saturation Infection Mechanism.
Lingmin Dong1, Bo Li1, Guanghui Zhang2
1School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116 Jiangsu China.
Bulletin of the Malaysian Mathematical Sciences Society
|March 1, 2022
Summary
This study on epidemic modeling shows that enhancing the inhibitory effect on susceptible individuals, rather than reducing population movement, is key to controlling disease spread in SI models.
Area of Science:
- Epidemiology
- Mathematical Biology
- Reaction-Diffusion Systems
Background:
- Epidemic modeling is crucial for understanding disease transmission dynamics.
- Reaction-diffusion models incorporate spatial aspects into epidemic spread.
- Logistic growth and saturation infection mechanisms are key factors in disease transmission.
Purpose of the Study:
- To analyze an SI epidemic reaction-diffusion model with logistic source and saturation infection.
- To determine the conditions for disease extinction and persistence using the basic reproductive number.
- To investigate the global stability of equilibria in homogeneous and heterogeneous environments.
Main Methods:
- Establishing uniform boundedness of the disease.
- Analyzing the extinction and persistence criteria based on the basic reproductive number.
- Investigating global stability in homogeneous environments and asymptotic behavior in heterogeneous environments with small movement rates.
Main Results:
- The basic reproductive number determines disease extinction and persistence.
- Global stability of the endemic equilibrium is established for homogeneous environments.
- Asymptotic behavior of endemic equilibria is analyzed for heterogeneous environments with low population mobility.
Conclusions:
- Logistic growth, infection mechanisms, and population movement significantly influence disease transmission.
- Increasing the inhibitory effect on susceptible individuals is more effective for epidemic control than reducing population mobility in SI models.
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