We present techniques that allow for the statistical identification of the infection front and for the microscopic control of macroscopic statistics in a simple stochastic lattice automata model for the spread of an infectious disease through a mobile host population. The individual based model consists of susceptible and infected individuals that are free to move about a regular lattice. These individuals interact with each other when located at the same node of the lattice, and susceptible individuals become infected with a probability of infection that is dependent on the number of infected individuals present. By using statistics from the healthy population alone, we present a method by which the spread of an infection in the model can be located spatially, even in a low-density population. A parameter which governs the local mobility rules of the model is shown to be functionally related to the non-dimensional statistical values of skewness and flatness for various macroscopic quantities. We show formal convergence to reaction-diffusion equations from the lattice Boltzmann equations of the model via a Hilbert expansion. The validity of both the lattice Boltzmann equations and the reaction-diffusion equations is shown in a low-density population regime.
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