Moment Closure for a Birth-Death Model of Antimicrobial Heteroresistance

Developing predictive Antimicrobial Resistance (AMR) models supporting optimal treatment design to combat ”superbugs” poses a significant challenge for mathematical biology. Birth-Death (BD) processes constitute an intuitive and flexible approach for modelling biological systems’ stochastic dynamics that is regaining attention due to the advances in computational techniques. This work presents a multivariate BD model of antimicrobial heteroresistance, a phenotype in which a bacterial isolate contains many subpopulations with heterogeneous antimicrobial responses. The model includes Lotka-Volterra competition between subpopulations, leading to an infinite coupled system of equations for the moment dynamics of the BD process. Then, a moment closure is proposed by assuming a log-normal distribution for a univariate BD process approximating the total population behaviour. The results are compared with stochastic simulations of the multivariate BD process during a typical time-kill assay.