Optimal control strategies for mitigating antibiotic resistance: Integrating virus dynamics for enhanced intervention design

Given the global increase in antibiotic resistance, new effective strategies must be developed to treat bacteria that do not respond to first or second line antibiotics. One novel method uses bacterial phage therapy to control bacterial populations. Phage viruses replicate and infect bacterial cells and are regarded as the most prevalent biological agent on earth. This paper presents a comprehensive model capturing the dynamics of wild-type bacteria $\left(S\right)$, antibiotic-resistant bacteria $\left(R\right)$, and virus-infected ($I$) bacteria population, incorporating virus inclusion. Our model integrates biologically relevant parameters governing bacterial birth rates, death rates, mutation probabilities and incorporates infection dynamics via contact with a virus. We employ an optimal control approach to study the influence of virus inclusion on bacterial population dynamics. Through numerical simulations, we establish insights into the stability of various system equilibria and bacterial population responses to varying infection rates. By examining the equilibria, we reveal the impact of virus inclusion on population trajectories, describe a medical intervention for antibiotic-resistant bacterial infections through the lense of optimal control theory, and discuss how to implement it in a clinical setting. Our findings underscore the necessity of considering virus inclusion in antibiotic resistance studies, shedding light on subtle yet influential dynamics in bacterial ecosystems.