Spatio-temporal analysis of coinfection using wavefronts of Escherichia coli O157: H7 in a dairy cattle farm

This study proposes a new methodology to analyze the impacts of host and pathogen dispersal on coinfection dynamics using the example of Escherichia coli O157:H7 in a dairy farm. A multi-strain Susceptible–Infected–Susceptible model is extended to a Reaction–Diffusion (RD) coinfection model of E. coli O157:H7 transmission, which includes intermittent shedding and pathogen growth in the environment. Analysis of the new RD coinfection model consists of existence and stability of constant equilibria, calculation of the basic reproduction number, and existence of traveling and stationary wave solutions. A stationary wave solution of the RD model defines a nonconstant endemic equilibrium. Whereas a traveling wavefront represents an epidemic wave of infection passing through the farm with a specific speed, direction, and amplitude. The numerical simulations of the RD model demonstrate stable traveling and stationary wavefronts of the RD coinfection model. The stationary wavefront connects two constant coexistence equilibria and the traveling wavefront represents the gradual establishment of an endemic coexistence equilibrium in the dairy farm. The significance of this study lies in utilizing the nonlinear wave theory to analyze dynamics of coinfection in a dairy farm both with respect to location and time. Hence, in addition to Turing theory, the nonlinear wave theory can be used to determine the likelihood of acquiring the infection based on the location of cattle at each specific time.