Probing bacterial predation with nonlinear population dynamics: a step towards antibacterial therapy

Abstract

Search for alternative antibacterial therapies has been intensified in last fifty years. This search has become inevitable because many of the well-known antibiotics of yesteryears are no longer effective againstthe resistant pathogens today Bdellovibrio and similar bacterial species (BLO; Bdellovibriolike organisms) capable of predating on other bacteria, specifically gram-negative pathogens arepromising candidates for anti-bacterial therapy. However, most experimental studies on predatory behavior of BLOs are carried out in simple lab simulated conditions and even their mathematical modelling also adopted similar simplifications. 

This paper proposes a set of nonlinear stage-structured differential equations under the influence of discreteconstant delay and white noise to describe predatory behavior of BLOs. It has been observed by previous authors that even in a simple liquid culture the mature BLO cell growth exhibit some delay and involve a so-called non-virulent phase. Our analysis revealed, when the BLOs are exposed to few tens of prey cells in a tissuethe delay parameter & white noise has a great role for dynamical behavior of theBLO population andlogistic growth rate of the prey.Further it represents microbial ecosystem dynamics together with the interactions between ecosystems and cellular as well as environmental noise. Here, the local and global stability analysisof the model with and without delay has been discussed. The stochastic perturbation analysiswas carried out and qualitatively compared with delay analysis. Finally, all three populations viz, mature and immature BLO plus the prey were studied as diffusive species to account