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Target reproduction numbers for reaction-diffusion population models.

Xueying Wang1, Xiao-Qiang Zhao2

  • 1Department of Mathematics and Statistics, Washington State University, Pullman, WA, 99164, USA.

Journal of Mathematical Biology
|August 2, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces target reproduction numbers for reaction-diffusion population models. These numbers quantify control efforts, representing expected offspring within a target set for a primary newborn.

Keywords:
Population controlPositive operatorReaction-diffusion modelTarget reproduction number

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Area of Science:

  • Mathematical Biology
  • Population Dynamics
  • Epidemiology

Background:

  • The target reproduction number is a crucial metric for population control interventions.
  • Existing concepts generalize reproduction numbers for compartmental ordinary differential equation models.
  • There's a need to extend these concepts to more complex reaction-diffusion population models.

Purpose of the Study:

  • To investigate target reproduction numbers within compartmental reaction-diffusion population models.
  • To provide a computable characterization of these numbers for practical application.
  • To demonstrate the theoretical findings with relevant examples.

Main Methods:

  • Generalization of the target reproduction number concept to reaction-diffusion systems.
  • Reformulation of the target reproduction number as a basic reproduction number of a modified system.
  • Numerical characterization and computation strategies for reaction-diffusion models.

Main Results:

  • The target reproduction number for reaction-diffusion models is defined and characterized.
  • It is shown to be equivalent to the basic reproduction number of a modified system with specific newborn limitations.
  • A method for numerical computation of the target reproduction number is presented.

Conclusions:

  • The target reproduction number offers a valuable tool for assessing control strategies in reaction-diffusion population models.
  • The study provides a framework for understanding and calculating this metric in complex spatial-temporal models.
  • The findings facilitate the numerical evaluation of intervention effectiveness in ecological and epidemiological contexts.