We investigate the disease’s dynamics of a reaction-diffusion epidemic model. We first give a priori estimates of upper and lower bounds for positive solutions to model and then give the conditions of the existence and nonexistence of the positive nonconstant steady states, which guarantees the existence of the stationary patterns.
"The Existence of Positive Nonconstant Steady States in a Reaction: Diffusion Epidemic Model." Abstr. Appl. Anal. 2013 (SI02) 1 - 7, 2013. https://doi.org/10.1155/2013/921401