Optimal control of a multi-scale HIV-opioid model

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.