contact rate affect the behaviour of the disease dynamics. The simulation results have indicated that using different functional forms of seasonally varying contact rate generates different patterns of solutions for each disease parameter set and type of contact rate. So prediction of the type of disease outbreaks depends on the form of contact rate. Thus it is important to determine which type of contact rate is more likely to match the actual dynamics of each disease. Also these results have shown how the dynamics of the disease depend on the amplitude of the seasonally varying contact rate. Apart from some of the results for measles with a sinusoidal periodic function the simulation results are original and give a clear and a much broader insight into the features of the dynamics of these diseases