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 $R_0$. If $R_0 \<= 1$ we prove that the disease free equilibrium is globally asymptotically stable on the nonnegative orthant. If $R_0$ > 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 $R_0$ > 1 for SP model.
Mathematics Subject Classification: 34D23, 34A34, 92D30.