A random-walk based epidemiological model

Random walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic. We have found that a simple random-walk system generates nontrivial dynamics compared with traditional well-mixed models. Phase diagrams characterizing the long-term behaviors of the epidemics are calculated numerically. The phase boundary separating those sets of parameters leading to outbreaks dying out and those leading to indefinite growth is mapped out in detail. The functional dependence of the basic reproductive number R0 on the model9s defining parameters reveals the role of spatial fluctuations and leads to a novel expression for R0. Special attention is given to simulations of inter-regional transmission of the contagion. The attack rate and the (growing) radius of gyration of the affected zones are used as measures of the severity of the outbreaks, in cases where R0 is not sufficiently prescriptive to chart the epidemic dynamics.