Stationary states and spatial patterning in the cellular automaton SEIS epidemiology model

We report computer simulation studies of the SEIS cellular automaton epidemiology model which takes into account explicitly the incubation period of the infection by considering separate fractions for the exposed E and infectious I individuals. The model is considered on a square lattice and the analysis is performed in various regimes covering cases of short and long incubation period at a range of contact rates. We found the critical curing rate to be independent on the incubation period, reflecting similarity between the SEIS model and the SI′S one, where I′=E+S. The stationary state of the lattice-based SEIS model compared to that of its compartment analogue indicates essential deviation between both at low contact rates. At long incubation period and high contact rates, the ratio between the values of E and I in a stationary state is found to depend strongly on the curing rate emphasizing the huge role of curing efficiency in this case. It was found that, upon approaching the critical curing rate, the time needed to reach a stationary state diverges, the effect reminiscent of critical slowing down. Visualization of the initial stage of the infection spread reveals porous clusters of infectious individuals with their surface decorated by exposed individuals.