Abstract: A general model is presented for infectious diseases which have a latent stage of infection before the infected persons enter into acute phase. Patients may recover from acute stage or they enter into chronic phase. After recovery from acute or chronic phase they become susceptible again. For such a model a basic reproductive number R_0 is obtained. It is found that the disease-free equilibrium point is locally stable if R_0<1, whereas if R_0>1 the disease-present equilibrium point is locally stable and it is globally asymptotically stable when the rate of recovery is sufficiently large. Results of numerical simulation are also reported here.
Keywords: Dynamical system, endemic equilibrium, epidemic, global stability, non linear incidence.