A Cellular Automaton SIS Epidemiological Model with Spatially Clustered Recoveries

Abstract

A stochastic two-state epidemiological cellular automaton model is studied, where sites move between susceptible and infected states. Each time step has two phases: an infectious phase, followed by a treatment or recovery phase. During the infectious phase, each infected site stochastically infects its susceptible neighbors. During the recovery phase, contiguous blocks of sites are reset to the susceptible state, representing spatially clustered treatment or recovery. The spatially extended recovery events are coordinated events over groups of cells larger than standard local neighborhoods typically used in cellular automata models. This model, which exhibits complex spatial dynamics, is investigated using simulations, mean field approximations, and local structure theory, also known as pair approximation in the ecological literature. The spatial scale and geometry of recovery events affects the equilibrium distribution of the model, even when the probability of block recovery events is rescaled to maintain a constant per-site recovery probability per time step. Spatially clustered treatments reduce the equilibrium proportion of infected invididuals, compared to spatially more evenly distributed treatment efforts.