The effects of population density and malnutrition on the dynamics of whooping cough

Liverpool, a seaport in NW England, suffered severely from lethal infectious diseases in the second half of the 19th century: the population was densely crowded and malnourished and life expectancy was low. Time-series analysis shows that the epidemics of whooping cough (i) had an interepidemic interval of 2.9 years, 1863-85, which lengthened to 3.4 years, 1885-1900 (ii) were strongly coherent with wheat prices (P < 0.001) and (iii) also correlated with cycles of seasonal weather conditions. It is suggested from mathematical modelling that the epidemics in this compromised population were maintained (i.e. the system was driven) by an oscillation of malnutrition and by seasonal weather conditions. A model that incorporates both the dynamics of whooping cough and the demographic characteristics of the population is presented. It has been shown to replicate the dynamics of the epidemics and has been used to predict the changes with time of (i) the force of the infection and (ii) the proportion of those infected with whooping cough who died.