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Branching process approach for epidemics in dynamic partnership network.

Abid Ali Lashari1, Pieter Trapman2

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This study models infectious disease spread on dynamic sexual networks using branching processes. Ignoring dependencies can lead to inaccurate predictions of outbreak probability and size.

Keywords:
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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Network Science

Background:

  • Sexually transmitted infections (STIs) and other infectious diseases spread through complex social networks.
  • Dynamic networks, characterized by changing partnerships and population demographics, pose unique challenges for modeling disease transmission.
  • Branching process approximations offer a mathematical framework for analyzing early-stage epidemic dynamics.

Purpose of the Study:

  • To investigate the spread of infectious diseases on dynamic sexual networks using branching process approximations.
  • To evaluate the impact of ignoring dependencies between infected individuals on epidemic modeling.
  • To compare the accuracy of different branching process models under varying network conditions.

Main Methods:

  • Developed two branching process approximations to model initial STI outbreak stages.
  • Calculated the offspring mean for the first approximation and related it to the basic reproduction number.
  • Analyzed an asymptotically exact branching process for networks where individuals have at most one partner.
  • Investigated the impact of dependencies by comparing extinction probabilities of the two models.
  • Examined the first approximation for unbounded networks as population size increases.

Main Results:

  • Ignoring dependencies in epidemic models can lead to incorrect predictions of outbreak probability.
  • The two branching process approximations yield different extinction probabilities when dependencies are present (i.e., individuals with at most one partner).
  • The first branching process approximation becomes asymptotically exact for large, unbounded networks.

Conclusions:

  • Dependencies between infected individuals significantly influence epidemic modeling outcomes.
  • Accurate modeling of dynamic sexual networks requires careful consideration of partnership structures and dependencies.
  • Branching process approximations provide valuable insights into infectious disease dynamics, with accuracy dependent on model assumptions.