Mathematical Modelling of Bacterial Resistance to Anti-microbial Treatment by Bet-hedging Strategy

Infectious bacteria can be a major threat to humans, animals, and the environment, especially due to increasing levels of antimicrobial resistance (AMR), where certain bacteria are no longer significantly damaged by the antibiotic drug treatment. One example of AMR is through bacteria with a ‘bet-hedging’ strategy, where bacteria
may perform well in one environment by sacrificing fitness in another. In this research, we investigated the dynamics of bacterial populations in a varying environment using mathematical models. One strain of bacteria can ‘switch’ to specialize in each environment, while the other grows at the same rate in both. The death rates of the strain, and the antibiotic drug treatment which is held constant (fixed value) are also included in the model. The aim is to study the dynamical behaviors of these strains and the antibiotic drug administered at both constant and fluctuating rates, to find when each strain may be expected to dominate. We analyze the model using both mathematical analysis and computational simulations. We found a particularly interesting behavior by one strain
at early time points when there is a high density of the antibiotic drug concentration. Instead of the strain crashing out early, as would be seen in standard models, an initially high density of the antibiotic drug can allow this strain to stay at the equilibrium state for considerable time. These strain(s) can stay long past the time when the drug density has reduced, before finally being replaced by the ultimately stronger strain(s).