A comparative study of three mathematical approaches applied to the reversal of AMR

TL;DR

This paper compares three mathematical modeling approaches—ODEs, SDEs, and FDEs—to understand and analyze the reversal of antimicrobial resistance, supported by numerical experiments with E. coli data.

Contribution

It introduces a comparative analysis of different mathematical frameworks for modeling AMR reversal, highlighting their qualitative properties and applicability.

Findings

ODEs capture basic resistance dynamics.

SDEs incorporate stochastic variability.

FDEs model memory effects in resistance reversal.

Abstract

In this work, we study the qualitative properties of a simple mathematical model inspired by antimicrobial resistance (AMR), focusing on the reversal of resistance. In particular, we analyze the model from three perspectives: ordinary differential equations (ODEs), stochastic differential equations (SDEs) driven by Brownian motion, and fractional differential equations (FDEs) with Caputo temporal derivatives. Finally, we perform numerical experiments using data from Escherichia coli exposed to colistin to assess the validity of the qualitative properties of the model.