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The basic reproductive number for disease systems with multiple coupled heterogeneities.

Alun L Lloyd1, Uriel Kitron2, T Alex Perkins3

  • 1Department of Mathematics and Biomathematics Graduate Program, North Carolina State University, Raleigh NC 27695, USA.

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|December 15, 2019
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Summary

Mathematical epidemiology reveals that with three or more coupled heterogeneities, the basic reproductive number (R₀) depends on distribution details. This contrasts with simpler models, showing R₀ can behave non-monotonically with increasing heterogeneity.

Keywords:
Basic reproductive numberCoupled heterogeneitiesDisease transmission modelHeterogeneity

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Area of Science:

  • Mathematical Epidemiology
  • Infectious Disease Modeling
  • Population Dynamics

Background:

  • Heterogeneity in susceptibility and infectiousness impacts disease spread.
  • A known formula quantifies this for one source of variation in each.
  • Extending this to multiple variation sources is a key question.

Purpose of the Study:

  • Investigate if analogous results apply for multiple coupled heterogeneities.
  • Develop explicit formulae for multivariate distributions.
  • Analyze the impact of complex heterogeneity on the basic reproductive number (R₀).

Main Methods:

  • Derived explicit formulae for multivariate normal and log-normal distributions.
  • Analyzed R₀ dependence on heterogeneity magnitudes and pairwise correlations.
  • Employed numerical illustrations to demonstrate results.

Main Results:

  • With ≥3 coupled heterogeneities, R₀ depends on distribution specifics, unlike simpler cases.
  • Formulae differ for multivariate normal and log-normal distributions.
  • R₀ can exhibit non-monotonic behavior with increasing heterogeneity in systems with three variations.

Conclusions:

  • No single formula universally applies for ≥3 coupled heterogeneities.
  • The impact of heterogeneity on R₀ is more complex than previously understood.
  • Understanding these complexities is crucial for accurate disease transmission modeling.