Modelling a disease with a nonlinear incidence function

The present paper considers a disease model with nonlinear incidence function. It studies its bounded-ness. Since the real world is Boundedness of solutions is important for well-de ned model. We obtain free-disease and endemic equilibria both m = 0 and m > 0. We de ne the reproduction number by R0. The model has at least one and at most three positive equilibrium (endemic equilibria) provided R0 > 1. We show that free- disease equilibrium (0, 0, 0) is unstable. The disease free equilibrium (K, 0, 0) is globally asymptotically stable provided R0 < 1.

Keywords:

di erence scheme , Asymptotic stability , Epidemic models.