Spreading dynamics of an SVIRS model
Guo Lin1, Jiantao Lin1, Shuxia Pan2
1School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People's Republic of China.
Mathematical Biosciences
|December 5, 2025
Summary
This study models disease spread using a Susceptible-Vaccinated-Infected-Recovered-Susceptible (SVIRS) system. Vaccination reduces spatial disease transmission, while immunity loss in recovered individuals affects prevalence but not spread.
Area of Science:
- Epidemiology
- Mathematical Biology
- Dynamical Systems
Background:
- Disease geographic spread is a critical public concern.
- Reaction-diffusion systems are used to model epidemic dynamics.
- The Susceptible-Vaccinated-Infected-Recovered-Susceptible (SVIRS) model captures population dynamics with vaccination and immunity loss.
Purpose of the Study:
- Investigate the spatial spreading properties of the SVIRS model.
- Analyze the impact of habitat expansion/contraction on disease transmission.
- Explore factors influencing disease spread, such as vaccination and immunity.
Main Methods:
- Utilized a reaction-diffusion system to model the SVIRS process.
- Studied initial value problems and traveling wave solutions.
- Incorporated a transmission capacity constant to analyze influencing factors.
Main Results:
- Vaccination rate and vaccine efficacy significantly reduce spatial disease transmission capacity.
- The proportion of recovered individuals losing immunity impacts disease prevalence scale, not spatial spreading ability.
- Traveling wave solutions effectively model the spatial expansion of diseases.
Conclusions:
- Vaccination is a key strategy for controlling the spatial spread of epidemics.
- Understanding immunity dynamics is crucial for managing disease prevalence.
- The SVIRS reaction-diffusion model provides insights into epidemic spatial dynamics and control.
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