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Optimal Multi-Drug Therapies for Antimicrobial Resistance with Horizontal Transfer.
Francesca Calà Campana1, Gian Paolo Incremona2, Franco Blanchini3
1Dipartimento di Ingegneria Industriale, Università degli Studi di Trento, Trento, Italy.
Journal of Optimization Theory and Applications
|May 25, 2026
Summary
This study models antimicrobial resistance (AMR) and proposes optimal multi-drug therapies. Computational experiments show adaptive treatment strategies can minimize bacterial populations and antibiotic use.
Area of Science:
- Mathematical Biology
- Computational Biology
- Pharmacology
Background:
- Antimicrobial resistance (AMR) poses a significant global health challenge.
- Effective multi-drug therapies are crucial for mitigating AMR.
- Bacterial resistance can emerge due to mutations and horizontal gene transfer during antibiotic treatment.
Purpose of the Study:
- To develop and analyze a mathematical model of host-pathogen dynamics under antibiotic pressure.
- To formulate an optimal control problem for minimizing bacterial load and antibiotic usage.
- To explore model predictive control (MPC) as an alternative treatment design strategy.
Main Methods:
- Mathematical modeling of bacterial populations (susceptible and resistant) and host immune response.
- Optimal control theory, including Pontryagin's minimum principle, to find treatment strategies.
- Numerical simulations using realistic biological parameters and various initial conditions.
Main Results:
- Existence and numerical computability of an optimal solution for minimizing bacterial populations and antibiotic use.
- Analysis of necessary conditions for optimality and singular controls.
- Demonstration of adaptive therapy strategies through computational experiments, showing dependence on initial conditions and cost functionals.
Conclusions:
- The developed framework provides a flexible approach to designing antimicrobial therapies.
- Optimal treatment strategies are highly dependent on the specific bacterial population dynamics and treatment goals.
- Model predictive control offers a viable alternative for dynamic treatment adaptation in the face of evolving antimicrobial resistance.
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