[An analysis of the effect of measles vaccination program by a mathematical model]

The reported case rates of measles during 1967-1986 were analyzed and compared with rates predicted by a mathematical model for measles prevalence. In Japan, measles vaccination was introduced in October, 1978. Since data before and after the introduction were available, the effect of the vaccination program could be analyzed. The mathematical model was constructed by modifying the Kermack-McKendrick model. In the model, environmental virus density was involved as an additional variable and the 'death' (inactivation) rate of the virus was assumed to show seasonal variation. The strategy for prevention and eradication was also discussed. The main results were as follows: 1. The characteristics of measles prevalence were (1) seasonal (annual) variation which has a peak in May or June and a bottom in September or October, (2) bienniality (before the vaccination), i.e., higher prevalence and lower prevalence years alternate every other year, and (3) trienniality (after the vaccination), i.e., a higher prevalence year appears every three years. 2. The model could reproduce all these characteristics for a range of probable parameters. 3. According to the model, trienniality was a transient phase and the system finally reached a stationary state that showed neither bienniality nor trienniality. 4. The critical density of the susceptible population necessary for the survivability of the virus in the population, was also obtainable from the model.