We consider models with a general structure which, for example, encompasses the so-called DI, SP or DISP models with mass action incidence. We give a very simple formule for the basic reproduction ratio R0. If R0 \leq 1, we prove that the disease free equilibrium is globally asymptotically stable on the nonnegative orthant. If R0 > 1, we prove the existence of a unique endemic equilibrium in the positive orthant and give an explicit formula. We prove the global asymptotic stability of the endemic equilibrium, when R0 > 1 for SP model.