Abstract

This study presents a simple mathematical model with deterministic equations addressing antimicrobial resistance (AMR), in which sensitive and resistant bacteria interact in the environment, and mobile genetic elements (MGEs) are functions that depend on resistant bacteria. We studied analytical conditions for the existence and stability of equilibrium states and propose an optimal control problem in which avoiding mutations and horizontal gene transfer (HGT) are the primary control strategies. Our results showed that bacterial population dynamics are influenced by factors such as geographical area, immune system strength, and antibiotic usage, with oscillations occurring because of antibiotic frequency and immune response. Control strategies targeting mutations and MGEs reduced bacterial populations, but did not eliminate them, indicating the need for stronger interventions to fully manage bacterial adaptability. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024.