The chemostat with lateral gene transfer.

We investigate the standard chemostat model when lateral gene transfer is taken into account. We will show that when the different genotypes have growth rate functions that are sufficiently close to a common growth rate function, and when the yields of the genotypes are sufficiently close to a common value, then the population evolves to a globally stable steady state, at which all genotypes coexist. These results can explain why the antibiotic-resistant strains persist in the pathogen population.

Senescence and antibiotic resistance in an age-structured population model.

Different theories have been proposed to understand the growing problem of antibiotic resistance of microbial populations. Here we investigate a model that is based on the hypothesis that senescence is a possible explanation for the existence of so-called persister cells which are resistant to antibiotic treatment. We study a chemostat model with a microbial population which is age-structured and show that if the growth rates of cells in different age classes are sufficiently close to a scalar multiple of a common growth rate, then the population will globally stabilize at a coexistence steady state. This steady state persists under an antibiotic treatment if the level of antibiotics is below a certain threshold; if the level exceeds this threshold, the washout state becomes a globally attracting equilibrium.

Adaptive responses to antimicrobial agents in biofilms.

Bacterial biofilms demonstrate adaptive resistance in response to antimicrobial stress more effectively than corresponding planktonic populations. We propose here that, in biofilms, reaction-diffusion limited penetration may result in only low levels of antimicrobial exposure to deeper regions of the biofilm. Sheltered cells are then able to enter an adapted resistant state if the local time scale for adaptation is faster than that for disinfection. This mechanism is not available to a planktonic population. A mathematical model is presented to illustrate. Results indicate that, for a sufficiently thick biofilm, cells in the biofilm implement adaptive responses more effectively than do freely suspended cells. Effective disinfection requires applied biocide concentration that increases quadratically or exponentially with biofilm thickness.