Delayed differential equations as a $\textit{Salmonella}$ biofilm model

Abstract

$\textit{Salmonella}$ is a widespread bacterial pathogen that is the primary cause of many foodborne illnesses worldwide. It gains significant strength against antibacterial treatments when it forms the biofilm structure, which can be considered a multicellular-like form where the pathogen is compartmentalized based on function in which each part communicates, further adding to the capabilities of resistance. To overcome this problem, it is important for practitioners to know how $\textit{Salmonella}$ biofilms will evolve through time under the presence of various carbon resources which are mostly present in food products. In this work, a mathematical model of $\textit{Salmonella}$ biofilm trajectories was made using Delayed Logistic Differential Equations after an experimental procedure which comprised treatments with seven carbon sources of six different concentrations. This model proved to be efficient for modeling $\textit{Salmonella}$ biofilm formation even without significant amount of data.

Keywords

• $\textit{Salmonella}$
• biofilm
• mathematical modeling
• carbon source

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