Abstract: The existence and uniqueness of the solution of a reactiondiffusion system was studied by means of the method of upper and lower solutions. Existence and nonexistence results about the nonconstant steady states of the system were given. It was also proved that if the diffusion coefficient of the prey with epidemic disease is treated as bifurcation parameter, nonconstant positive steadystate solutions may bifurcate from the constant steadystate solution under some conditions.

Key words: ecoepidemiology, bifurcations, nonconstant positive steady solution, preypredator model