[Mathematical methods to judge the efficiency of protective vaccinations (author's transl)]

The effect, hazards and risk of vaccinations may be calculated by means of special formulas which determine the value for N, Q and D. The formula for N considers the question whether a vaccination is effective, necessary and valuable and may be recommended on epidemiological grounds. Q considers the individual risk (i. e. relation between total risk of unvaccinated and vaccinated persons) and D the yearly difference in risks between unvaccinated and vaccinated members of a community. If p stands for protection rate of a vaccination, t = time for which the vaccination effect is lasting, R = complications of disease under study in a community in which vaccinations against this disease are not in use and r = comparable complications of vaccination, the following formulas are applicable: (see article) A vaccination may be recommended if N and Q greater than 1 and the value for D is positiv. Application of these formulas to special vaccinations lead to the following conclusions: In case of BCG, measles and poliomyelitis (oral vaccination) the above mentioned values exceed at least 10(1)-10(2) (N), 4-5 (Q) or are highly positiv (D). These vaccinations-if performed correctly-are considered valuable and highly recommendable. Vaccination against pertussis is not recommendable beyond the second year of life. According to the present epidemiologic situation in Austria this vaccination is still rectified in children under 2 years. However, values for N, Q and D are near border-line and should be yearly evaluated. Smallpox vaccination in Europe is still recommendable. Similarly, continuous reevaluations are necessary due to low values of N, Q and D. On the other hand, vaccination against tetanus is available and vaccination against influenza may be recommended.