A fall in the incidence of both preventable and non-preventable or partly preventable infections with different modes of transmission has recently been documented in Russia and worldwide; it parallels marked changes in the demographic structure of the population. Simulation based on parasite-host mathematical models confirmed that demographic structure is a key factor responsible for the incidence of anthroponosis infections producing long-standing or lifelong immunity. It was shown that differences in the frequency of these diseases between countries may be due to different age structure of their populations. The lowered incidence of preventable and non-preventable infections in Russia appears to be associated with changes in the country's demographics. We have developed prognosis of further dynamics of anthroponosis diseases that predicts reversal of the mean morbidity rate toward that recorded in the 1980s and the shift of its higher values to senior age-groups.