Mathematical Modeling of Antibiotic Resistance in Hospital with Dysbiosis

In this paper, we propose and study a transmission model among individuals in a hospital of antibiotic-resistant bacteria considering dysbiosis. The transmission of such bacteria in a hospital setting has been the focus of several previous researches. However, the aspect and contribution of antibioticinduced dysbiosis was not considered in the existing literature. Antibiotics impact the human intestinal microbiome for it unintentionally affects the needed gut microbiota diversity which are fundamental drivers of health and disease in humans. This unintentional destabilization of the healthy human microbiome results in microbial imbalance called dysbiosis. The goal of this paper is to analyze the dynamics of the proposed model in order to come up with insights and possible strategies to control antibiotic-resistant bacterial transmission among individuals in a hospital considering dysbiosis. Possible equilibria of the model system include the resistance-free equilibrium and the endemic equilibrium. The stability of the former means that the antibiotic resistance dies out, while the stability of the latter implies that the antibiotic resistance persists. We determined using sensitivity analysis that the most infl uential parameter is the drug 1 treatment rate. Moreover, we found a threshold value for this parameter, using numerical continuation, where the antibiotic resistance persists. These results provide insights on how to strategize to control the transmission of antibiotic-resistant bacteria in this setting.