  The large reservoir of antibiotic resistant bacteria in raw and treated water
supplies is a matter of public health concern. Currently, the National
Antimicrobial Resistance Monitoring Systems, a collaborative effort of the
Centers for Disease Control, the US Department of Agriculture, and the US Food
and Drug Administration, does not monitor antimicrobial resistance in surface
waters. Given the serious nature of antibiotic resistance in clinical settings,
and the likelihood that antibiotic resistant bacteria can be transmitted to
humans from large environmental reservoirs via drinking water, explanations for
the distribution of antibiotic resistant bacteria and tools for studying this
distribution must be found. Here we focus on mathematical modeling of
cultivable bacteria in a river, which will be used to study the distribution of
antibiotic resistant bacteria in the environment. We consider both antibiotic
resistant and non-antibiotic resistant bacteria in the model, and, taking into
account the strong correlation between land use and antibiotic resistant
bacteria in rivers, we include a function for the influx of bacteria into the
river from the shore. We simulate the model for two different time scales and
show that if there is too many bacteria from the land entering the river, the
river entirely fills with antibiotic resistant bacteria, while less frequent
influxes allows time for the bacteria to lose the antibiotic resistant gene.
This mathematically verifies that reduction in antibiotic use near the banks of
rivers, will reduce the counts of antibiotic resistant bacteria in rivers.
