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Limiting the spread of disease through altered migration patterns.

R McVinish1, P K Pollett1, A Shausan1

  • 1School of Mathematics and Physics, University of Queensland, Australia.

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|January 23, 2016
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Summary

Susceptible individuals can collectively limit epidemic spread by optimizing their distribution to minimize disease growth rates during initial outbreaks. This strategy also minimizes the basic reproduction number, reducing extinction probability and epidemic size.

Keywords:
Basic reproduction numberBranching processExpected total sizeMinimax optimisation

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Population Dynamics

Background:

  • Epidemics spread within and between geographically distinct populations.
  • Disease transmission occurs via contact and infected individual migration.

Purpose of the Study:

  • To model epidemic spread in spatially structured populations.
  • To identify strategies for susceptible individuals to limit initial epidemic growth.
  • To minimize the basic reproduction number and overall epidemic impact.

Main Methods:

  • Developed a mathematical model for disease spread in distinct locations.
  • Analyzed the impact of susceptible individual distribution on epidemic growth rates.
  • Investigated strategies to minimize the basic reproduction number.

Main Results:

  • Identified a distribution for susceptible individuals that minimizes epidemic growth rate.
  • Demonstrated that this strategy also minimizes the basic reproduction number.
  • Showed optimality in terms of epidemic extinction probability and total size.

Conclusions:

  • Collective action by susceptible individuals can effectively control early epidemic spread.
  • Optimizing distribution is key to minimizing disease transmission and impact.
  • The proposed strategy offers a robust approach to epidemic mitigation.