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Discrete epidemic models with two time scales.

Rafael Bravo de la Parra1, Luis Sanz-Lorenzo2

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Summary
This summary is machine-generated.

This study introduces a two time scales discrete-time epidemic model. It demonstrates that strategic movements between spatial locations can eradicate locally endemic diseases globally.

Keywords:
Discrete-time epidemic modelDisease eradication or persistenceTime scales

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Area of Science:

  • Mathematical epidemiology
  • Discrete-time dynamical systems
  • Population dynamics

Background:

  • Epidemic models are crucial for understanding disease spread.
  • Analyzing disease dynamics across different time scales presents unique challenges.
  • Metapopulation models are essential for studying spatial disease transmission.

Purpose of the Study:

  • To develop a general class of two time scales discrete-time epidemic models.
  • To analyze the interplay between disease progression and other processes (e.g., spatial movement).
  • To investigate conditions for disease eradication in metapopulations.

Main Methods:

  • Construction of a discrete-time susceptible-exposed-infectious-recovered-susceptible (SEIRS) model.
  • Analysis of disease dynamics on a slower time scale compared to other processes.
  • Utilizing a reduced model to approximate the behavior of a full two time scales model.
  • Calculation of the basic reproduction number () for assessing disease endemicity.

Main Results:

  • The basic reproduction number () of the reduced system approximates that of the full system.
  • The model framework allows for the analysis of asymptotic behavior.
  • Demonstration that metapopulation dynamics can influence global disease eradication.

Conclusions:

  • A novel framework for two time scales discrete-time epidemic modeling is presented.
  • The study highlights the potential of inter-patch movement to control and eradicate diseases.
  • The findings have implications for public health strategies in spatially structured populations.