|Revista Colombiana de Matemáticas|
Abstract. The problem of the existence of periodic positive solutions for general parabolic systems is studied by means of the Kolesov theorem and the monotone scheme. The special case of an epidemic model wich involves difussion and a predator-prey problem is also examined.Palabras claves. Parabolic and elliptic systems, supersolutions, subsolutions, monotone scheme, periodic solutions, Kolesov theorems, predator-prey models, epidemic models, difussion equations.