A mathematical model for the propagation of infectious diseases has been discussed in this paper.  The model that has been examined is basically SIR model. The governing equations have been solved to the best possible solution.  The influence of critical parameters over the system has been discussed with the graphical illustrations. It  is observed that as the transmission (β) increases the sensitive population and, with the duration increasing, the vulnerable population diminishes and stays constant and is time-independent. Further, it is observed that as the rate of infection increases the susceptible population tens to zero. In addition to the above as R rate of recovered individual increases the susceptible population (S) decreases. The phenomena  is an agreement with the real life situation. In addition to the above as R rate of recovered individual increases the susceptible population (S) decreases. The phenomena  is an agreement with the real life situation.