Dynamics preserving nonstandard finite difference scheme for a microbial population model incorporating environmental stress

Abstract

Microbial populations depend on their environment, but can also modify it. 󠀼span style=󠀢color:black󠀢󠀾In addition to󠀼/span󠀾 breaking down complex nutrients for their growth, microbes can exhibit negative behavior by engineering the environment in ways that are detrimental to their proliferation. In this work, a deterministic mathematical model is formulated to include the environmental noise from the toxin-producing microbial population accounting for the switch of cells to dormancy at high concentrations. A dynamically consistent nonstandard finite difference scheme is designed. Theoretical and numerical investigation of the proposed model is presented to provide insight into the conditions that may lead to the extinction of the microbial population.