Abstract
Antimicrobial resistance (AMR) poses a major global public health challenge, with Escherichia
coli (E. coli) playing a central role due to its high prevalence and capacity to acquire resistance
through plasmid-mediated gene transfer. This study examined the temporal and spatial
dynamics of drug-sensitive and drug-resistant E. coli within the human gut and the external
environment, focusing on mechanisms that drive the persistence and spread of resistance. A
deterministic reaction-diffusion model was developed to capture key biological processes, including
bacterial growth and competition, resistance fitness costs, horizontal gene transfer via
plasmid conjugation, environmental shedding and ingestion, and spatial diffusion in both domains.
Mathematical analysis examined model positivity, boundedness and equilibrium behaviour,
while stability and Turing analyses were used to identify conditions under which diffusion
could destabilise homogeneous equilibria.
Numerical simulations, implemented using Crank–Nicolson and central difference schemes,
showed that sensitive and resistant E. coli populations can coexist in the gut and environment
through a feedback loop involving shedding and ingestion. Increased ingestion rates, representing
poor hygiene, accelerated resistant strain growth in the gut, whereas reduced ingestion
limited host colonisation but allowed environmental reservoirs to persist. The resistance fitness
cost was found to moderate the spread of resistance, promoting coexistence rather than
competitive exclusion, while plasmid-mediated gene transfer emerged as the dominant driver
of resistance proliferation. Spatial diffusion strongly influenced persistence and distribution,
with high diffusion promoting homogenisation and survival, and differential diffusion generating
spatial pattern formation. Overall, the results highlight that AMR dynamics are driven by
interacting spatial, biological and behavioural processes, underscoring the need for integrated
control strategies combining hygiene improvement, antimicrobial stewardship and disruption
of plasmid transfer mechanisms.