Emergence of Strange Spatial Pattern in a Spatial Epidemic Model

Pattern formation of a spatial epidemic model with nonlinear incidence rate kI²S/(1+αI²) is investigated. Our results show that strange spatial dynamics, i.e., filament-like pattern, can be obtained by both mathematical analysis and numerical simulation, which are different from the previous results in the spatial epidemic model such as stripe-like or spotted or coexistence of both pattern and so on. The obtained results well extend the finding of pattern formation in the epidemic model and may well explain the distribution of the infected of some epidemic.