The effect of using different types of periodic contact rate on the behaviour of infectious diseases: a simulation study

This paper studies the effect of using different types of seasonally varying contact rate on the behaviour of the seasonally varying infectious diseases for an SEIR epidemic model. Our target is to investigate the long term behaviour of the system in response to changes in beta(1), the amplitude parameter of the seasonal contact rate, which is our bifurcation parameter. This amplitude parameter is used as a filter to plot the length in years of the period of the stable endemic periodic solution of the SEIR model. Another main aim of this simulation study is to explain how can the type of the 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 [D. Greenhalgh, I.A. Moneim, SIRS epidemic model and simulations using different types of seasonal contact rate, Syst. Anal. Modelling Simul. 43(5) (2003) 573-600; I.A. Moneim, D. Greenhalgh, Threshold and stability results for an SIRS epidemic model with a general periodic vaccination strategy, J. Biol. Syst. 13(2) (2005), to appear].