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Optimal control of a multi-scale HIV-opioid model.

Eric Numfor1, Necibe Tuncer2, Maia Martcheva3

  • 1Department of Mathematics, Augusta University, Augusta, GA, USA.

Journal of Biological Dynamics
|February 19, 2024
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This study uses optimal control theory to model HIV and opioid epidemics. Combining risk reduction, opioid treatment, and antiviral therapies is the most effective strategy for managing both epidemics.

Keywords:
92D30Basic reproduction numberHIVmulti-scale modelopioid epidemicoptimal control

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Area of Science:

  • Mathematical modeling
  • Epidemiology
  • Optimal control theory

Background:

  • The co-occurrence of HIV and opioid use presents a complex public health challenge.
  • Understanding the interplay between these epidemics requires sophisticated modeling approaches.

Purpose of the Study:

  • To apply optimal control theory to an immuno-epidemiological model of HIV and opioid epidemics.
  • To identify and compare the effectiveness of different intervention strategies at both population and within-host levels.

Main Methods:

  • Development of a multi-scale immuno-epidemiological model.
  • Application of optimal control theory to determine the optimal combination of four control strategies.
  • Mathematical proof of the existence and uniqueness of an optimal control quadruple.

Main Results:

  • Reducing HIV risk behavior among opioid users showed a greater impact on the co-affected population than treating opioid use alone.
  • Within-host antiviral therapies affected both HIV-only infected and co-affected populations.
  • The combination of all four controls yielded the most effective management strategy.

Conclusions:

  • A comprehensive strategy integrating population-level (risk reduction, opioid treatment) and within-host-level (antiviral therapies) interventions is crucial.
  • Optimal control theory provides a framework for optimizing public health interventions for complex, co-occurring epidemics.
  • Synergistic effects of combined interventions are key to managing the dual HIV and opioid epidemics.