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Measles dynamics on network models with optimal control strategies.

Yuyi Xue1, Xiaoe Ruan1, Yanni Xiao1

  • 1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, P.R. China.

Advances in Difference Equations
|March 8, 2021
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Summary

Waning immunity increases measles spread, especially in high-activity networks. Early, targeted interventions are crucial for effective measles control, prioritizing highly connected groups.

Keywords:
Basic reproduction numberMeaslesNetwork modelOptimal controlThreshold dynamics

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Area of Science:

  • Epidemiology
  • Network Science
  • Mathematical Biology

Background:

  • Measles transmission dynamics are influenced by population heterogeneity and immunity duration.
  • Understanding these factors is key to effective disease control strategies.

Purpose of the Study:

  • To investigate how population heterogeneity and waning immunity affect measles transmission.
  • To determine optimal control strategies for measles outbreaks in complex networks.

Main Methods:

  • Formulation of a network model with periodic transmission rates.
  • Theoretical examination of threshold dynamics.
  • Numerical analysis of an optimal control problem for heterogeneous models.

Main Results:

  • Waning immunity can increase the basic reproduction number and infected individual density.
  • Scale-free networks show faster increases in the basic reproduction number above a critical average degree compared to random networks.
  • Early implementation of control measures is vital, with higher intensity for highly connected subpopulations.

Conclusions:

  • Heterogeneity and waning immunity significantly impact measles transmission dynamics.
  • Timely and targeted interventions, considering network structure and contact patterns, are essential for controlling measles outbreaks.
  • Resource allocation should align with population contact patterns for maximum intervention effectiveness.