American Journal of Epidemiology · 1973 · 188 citations · 0 references
Veterinary MedicineInfectious Disease ControlInfectious DiseasesEpidemiologic MethodsEpidemiologyInfectious Disease EpidemiologyDisease SpreadDisease Transmission PathwaysEpidemic ForecastingIncidence StudiesInfectious Disease DynamicsTransmission DynamicsDisease Outbreak DynamicsInfectious Disease ModelsTime-varying Contact RatesTime-varying Force Of InfectionTransmission Dynamics Modeling
Recurrent outbreaks of measles, chickenpox and mumps in cities are studied with a mathematical model of ordinary differential delay equations. The model estimates monthly mean contact rates from 30–35 years of reported cases and incorporates them as seasonally varying parameters in ordinary differential delay equations. The model shows that winter contact rates are 1.7–2 times higher than summer rates, and that incorporating this seasonality reproduces the observed annual chickenpox/mumps and biennial measles outbreaks; the biennial measles pattern indicates an endemic disease that would cease if infectivity rose or incubation shortened, and its persistence in vaccinated populations suggests uneven vaccine coverage.
Recurrent outbreaks of measles, chickenpox and mumps in cities are studied with a mathematical model of ordinary differential delay equations. For each calendar month a mean contact rate (fraction of susceptibles contacted per day by an infective) is estimated from the monthly reported cases over a 30- to 35-year period. For each disease the mean monthly contact rate is 1.7 to 2 times higher in the winter months than in the summer months; the seasonal variation is attributed primarily to the gathering of children in school. Computer simulations that use the seasonally varying contact rates reproduce the observed pattern of undamped recurrent outbreaks: annual outbreaks of chickenpox and mumps and biennial outbreaks of measles. The two-year period of measles outbreaks is the signature of an endemic infectious disease that would exhaust itself and become nonendemic if there were a minor increase in infectivity or a decrease in the length of the incubation period. For populations in which most members are vaccinated, simulations show that the persistence of the biennial pattern of measles outbreaks implies that the vaccine is not being used uniformly throughout the population.