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Dynamics analysis of a nonlocal diffusion dengue model.
Kangkang Chang1, Zhenyu Zhang2, Guizhen Liang3
1School of Mathematics and Statistics, Xinxiang University, Xinxiang, 453003, People's Republic of China. changkangkang86@sina.com.
Scientific Reports
|September 14, 2023
Summary
This study introduces a nonlocal diffusion model for dengue transmission, highlighting the importance of human movement in disease spread. Controlling dengue requires reducing virus transmission by infected humans and mosquitoes.
Area of Science:
- Epidemiology
- Mathematical Biology
- Diffusion Models
Background:
- Human movement patterns significantly influence disease transmission dynamics.
- Understanding spatial spread is crucial for effective public health interventions.
- Dengue fever remains a significant global health concern requiring advanced modeling approaches.
Purpose of the Study:
- To develop and analyze a nonlocal diffusion model for dengue spread.
- To investigate the impact of human mobility on disease dynamics.
- To establish conditions for the global stability and uniform persistence of the dengue model.
Main Methods:
- Utilized semigroup theory and continuously Fréchet differentiable functions.
- Employed eigenvalue analysis of the nonlocal diffusion term.
- Derived a Lyapunov function and applied the comparison principle.
- Performed numerical simulations to validate theoretical findings.
Main Results:
- Demonstrated the existence, uniqueness, positivity, and boundedness of the model's solution.
- Proved the global stability and uniform persistence of the dengue system.
- Numerical simulations confirmed the model's predictions.
- Identified key factors influencing disease containment.
Conclusions:
- Nonlocal diffusion is a critical factor in dengue transmission dynamics.
- Controlling dengue spread necessitates reducing transmission from infected humans and mosquitoes.
- The developed mathematical model provides a framework for understanding and managing dengue outbreaks.
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