Abstract

With the goal to comprehend the biological responses of bacteria exposed to nano-drugs in a spatiotemporally organized biological system, this work presents a mathematical model that was developed quantitatively. Non-linear population dynamics, migration, spatiotemporal drug transport and degradation, and regulation based on treatment outcome are all considered in the formulation. This study investigates trajectory analysis, network analysis, equilibrium, and stability of parameters, in contrast to previous approaches that just assess the impact of therapy based on concentration data. The non-dimensional form is used to identify dominating factors influencing system evolution and to assess the conflict between biological and transport phenomena on the same scale. While the spatial method shows the variety in drug concentration and distribution, numerical trajectories show bounded population behaviors and changes in the community's structure throughout treatment. Stability analysis may be used to discover parameter areas that correlate to robust and stable communities, while sensitivity analysis can be used to establish which parameters have the biggest impact on treatment results. Therapy regimens may be compared from several angles using a composite indicator of therapeutic response. In order to analyze microbial composition, exposure, and dynamic stability, this work's most significant novelty is the integration of the dynamic character of ecology with spatial drug transport and network factors inside a single mathematical modeling framework. A mechanistically based model for treatment-induced community changes has been made possible by the findings.