This study is to discuss a spatial epidemic model through a reaction-diffusion SIS model. In this model, the diffusion terms represents the movement of the susceptible and infected in a spatial domain. The study focused on the spatial pattern formation of the model. The patterns were obtained as a result of the occurrence of Turing instability. By applying the Turing analysis, the Turing conditions corresponding to the model and the Turing space in the parameter domain were obtained. Finally, an extensive numerical simulation was carried out to reveal the patterns which is exhibited by the model by varying the parameter within the Turing space. The patterns showed the dynamics of a disease spread which depends on the time and spatial dependence from an SIS model.

Keywords: epidemic spatial model, SIS model, Turing instability, pattern formation.