A generalised model for generalised transduction: the importance of co-evolution and stochasticity in phage mediated...

Antimicrobial resistance is a major global challenge. Of particular concern are mobilizable elements that can transfer resistance genes between bacteria, leading to pathogens with new combinations of resistance. To date, mathematical models have largely focussed on transfer of resistance by plasmids, with fewer studies on transfer by bacteriophages. We aim to understand how best to model transfer of resistance by transduction by lytic phages. We show that models of lytic bacteriophage infection with empirically derived realistic phage parameters lead to low numbers of bacteria, which, in low population or localised environments, lead to extinction of bacteria and phage. Models that include antagonistic co-evolution of phage and bacteria produce more realistic results. Furthermore, because of these low numbers, stochastic dynamics are shown to be important, especially to spread of resistance. When resistance is introduced, resistance can sometimes be fixed, and at other times die out, with the probability of each outcome sensitive to bacterial and phage parameters. Specifically, that outcome most strongly depends on the baseline death rate of bacteria, with phage-mediated spread favoured in benign environments with low mortality over more hostile environments. We conclude that larger-scale models should consider spatial compartmentalisation and heterogeneous microenviroments, while encompassing stochasticity and co-evolution.