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Reproductive numbers for nonautonomous spatially distributed periodic SIS models acting on two time scales
M Marvá1, R Bravo de la Parra, P Auger
1Dpto Matemáticas, Universidad de Alcalá, Madrid, Spain. marcos.marva@uah.es
Acta Biotheoretica
|December 8, 2011
Summary
Periodic migration rates in spatially distributed Susceptible-Infected-Susceptible (SIS) epidemic models can lead to global epidemic persistence or eradication. This contrasts with local outcomes where migration is absent, highlighting the impact of migration dynamics.
Area of Science:
- Mathematical Epidemiology
- Dynamical Systems
- Population Dynamics
Background:
- Spatially distributed epidemic models are crucial for understanding disease spread across populations.
- Periodic migration rates introduce complex dynamics not captured by static models.
- Two-time scale systems allow for simplified analysis of complex asymptotic behaviors.
Purpose of the Study:
- To derive global reproduction numbers for general spatially distributed periodic SIS epidemic models.
- To analyze the impact of time-dependent migration rates on epidemic persistence and eradication.
- To compare the behavior of spatially distributed models with their non-spatially distributed counterparts.
Main Methods:
- Development of a general class of spatially distributed periodic SIS epidemic models with two time scales.
- Utilizing an aggregated system to analyze the asymptotic behavior of the full system.
- Derivation of global reproduction numbers through the aggregated system, applied to mass action and frequency-dependent transmission laws.
Main Results:
- Global reproduction numbers were derived for the non-autonomous spatially distributed system.
- The study demonstrates that specific periodic migration rates can dictate global epidemic outcomes.
- Adequate migration can lead to global persistence or eradication, irrespective of local dynamics.
Conclusions:
- Periodic migration rates significantly influence the global dynamics of SIS epidemics.
- The derived global reproduction numbers provide a powerful tool for epidemic control strategies.
- Migration can override local conditions, enabling effective interventions for disease management.
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