Characterizing spread of infection in cattle farms using wavefronts of a reaction-diffusion coinfection model

The present work studies the transmission dynamics of Escherichia coli O157:H7 in a dairy farm using a coinfection Reaction-Diffusion Susceptible-Infected-Susceptible model. Analysis of the model includes existence and stability of equilibria, and calculation of the basic reproduction number. Furthermore, it is numerically shown that the model exhibits stationary and traveling wavefronts. Existence of a stationary wavefront implies that the likelihood of infection transmission is a function of host's location. This is in contrast with recent studies that use Turing patterns to determine the likelihood of infection. In addition, formation of a one-hump traveling wavefront characterizes establishment of an endemic equilibrium in the entire spatial domain.