We presented and analyzed a mass action model with vital dynamics. This type of model is suitable for many childhood diseases like Mumps, Rubella and other highly contagious diseases like influenza. We showed that the region in which the model makes biological sense is positively invariant, this means that any solution of the model with initial condition in this region remain in the region for all times. The model has two equilibria, the disease – free equilibrium (DFE) and the endemic equilibrium. Using the concept of R_0, we showed that the DFE is locally asymptotically stable provided R_0<1, we similarly proved the global stability of the DFE using a suitable Lyapunov function. Further
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