Traveling Waves in a SIRH Model with Spatio-Temporal Delay and Nonlocal Dispersal
Lu Yang1, Yun-Rui Yang1, Xue Song1
1School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, 730070 China.
Acta Mathematica Scientia = Shu Xue Wu Li Xue Bao
|February 8, 2022
Summary
This study proves the existence and behavior of traveling waves in a SIRH model with delays and nonlocal dispersal. New methods overcome challenges posed by spatio-temporal delays, offering broader insights into disease spread dynamics.
Area of Science:
- Mathematical Biology
- Epidemiology
- Dynamical Systems
Background:
- Investigates a Susceptible-Infected-Recovered-Hemorrhagic (SIRH) model.
- Addresses challenges in modeling disease spread with nonlocal dispersal and spatio-temporal delays.
Purpose of the Study:
- To establish the existence and analyze the asymptotic behavior of traveling waves in a SIRH model.
- To generalize existing results for SIRH models lacking relapse and delay components.
- To develop novel analytical techniques for handling spatio-temporal delays in epidemiological models.
Main Methods:
- Application of Schauder's fixed-point theorem.
- Utilized advanced integral and analysis techniques to address spatio-temporal delays.
- Investigated the asymptotic behavior of wave propagation.
Main Results:
- Confirmed the existence of traveling waves in the SIRH model with spatio-temporal delay and nonlocal dispersal.
- Successfully analyzed the asymptotic behavior of these traveling waves, overcoming prior limitations.
- Established a more general nonexistence result for traveling waves under specific conditions.
Conclusions:
- The study provides a comprehensive framework for understanding traveling wave phenomena in complex epidemiological models.
- The developed methods offer new tools for analyzing models with spatio-temporal delays.
- Findings contribute to a deeper understanding of disease dynamics and wave propagation in populations.
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