Figure 1. Flow-chart of the model of the dynamics of ceftiofur-sensitive and resistant commensal E. coli in the cattle large intestine.

Bacterial growth is density-dependent with fractional net growth rate r; fitness cost for cells with blaCMY-2-carrying plasmids manifests as a reduction α in r. Resistant cells transfer blaCMY-2 to the progeny during cell division. Horizontally, blaCMY-2 is transferred to the sensitive cells at rate β; the transmission is frequency-dependent with the total of β*N_r*N_s/N. There is fractional in-flow and out-flow of E. coli at rate γ; fraction υ of in-flowing E. coli are ceftiofur-resistant. Antimicrobial action of ceftiofur metabolites, depending on their concentration, results in either reduced growth or decay in number of E. coli.