A comprehensive spatial-temporal infection model

Motivated by analogies between the spread of infections and of chemical processes, we develop a model that accounts for infection and transport where infected populations correspond to chemical species. Areal densities emerge as the key variables, thus capturing the effect of spatial density. We derive expressions for the kinetics of the infection rates, and for the important parameter R 0 , that include areal density and its spatial distribution. We present results for a batch reactor, the chemical process equivalent of the SIR model, where we examine how the dependence of R 0 on process extent, the initial density of infected individuals, and fluctuations in population densities effect the progression of the disease. We then consider spatially distributed systems. Diffusion generates traveling waves that propagate at a constant speed, proportional to the square root of the diffusivity and R 0 . Preliminary analysis shows a similar behavior for the effect of stochastic advection.