Modelling dynamics of plasmid-gene mediated antimicrobial resistance in enteric bacteria using stochastic differential equations

The ubiquitous commensal bacteria harbour genes of antimicrobial resistance (AMR), often on conjugative plasmids. Antimicrobial use in food animals subjects their enteric commensals to antimicrobial pressure. A fraction of enteric Escherichia coli in cattle exhibit plasmid-gene mediated AMR to a third-generation cephalosporin ceftiofur. We adapted stochastic differential equations with diffusion approximation (a compartmental stochastic mathematical model) to research the sources and roles of stochasticity in the resistance dynamics, both during parenteral antimicrobial therapy and in its absence. The results demonstrated that demographic stochasticity among enteric E. coli in the occurrence of relevant events was important for the AMR dynamics only when bacterial numbers were depressed during therapy. However, stochasticity in the parameters of enteric E. coli ecology, whether externally or intrinsically driven, contributed to a wider distribution of the resistant E. coli fraction, both during therapy and in its absence, with stochasticities in individual parameters interacting in their contribution.