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Invasion reproductive numbers for periodic epidemic models

Christopher Mitchell1, Christopher Kribs2

  • 1Department of Mathematics, Tarleton State University, Stephenville, TX 76402, USA.

Infectious Disease Modelling
|June 14, 2019
PubMed

Insights

This study introduces a method to determine if new infections can invade and persist alongside existing ones using invasion reproductive numbers (IRN). It extends these calculations to periodic systems, aiding in understanding disease dynamics and competition.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Infectious Disease Modeling

Background:

  • Infectious diseases often compete for persistence within a population.
  • Understanding invasion dynamics is crucial for public health interventions.

Purpose of the Study:

  • To extend methods for calculating invasion reproductive numbers (IRN) to periodic epidemiological systems.
  • To identify conditions for simplifying IRN calculations.
  • To analyze how seasonal variations impact pathogen persistence.

Main Methods:

  • Reinterpreting resident infections epidemiologically.
  • Extending IRN calculation methods to periodic systems.
  • Illustrating complex computations with examples.

Main Results:

  • Developed methods for calculating IRNs in periodic systems.
  • Identified conditions where a simple time-average suffices for IRN derivation.
  • Demonstrated how seasonal influenza affects bacterial respiratory infection persistence.

Conclusions:

  • The study provides a framework for analyzing multi-pathogen invasion in periodic environments.
  • Seasonal forcing can enable the year-round persistence of certain infections.
  • The methods offer insights into disease ecology and control strategies.
Keywords:
Basic reproductive numberMathematical epidemiologyPeriodic models

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