Cyclic epidemics of Mycoplasma pneumoniae infections in England and Wales from 1975 to 2009: time-series analysis and mathematical modelling

Abstract

BackgroundRecurrent epidemics of Mycoplasma pneumoniae infection have been reported in several countries. Factors affecting epidemic frequency and persistence have received little attention in published work. We estimated transmission parameters of M pneumoniae infection and simulated its natural dynamics to explore factors that determine the persistence of epidemic cycles. MethodsFirst, using time-series methods, we analysed laboratory reports of M pneumoniae infections in England and Wales during 35 years, from 1975 to 2009. A linear regression model was fitted to the aggregated data to look for a long-term change in the mean number of reports. We investigated seasonal and non-seasonal cyclic variations by autocorrelation analysis; for this analysis, the time series was log-transformed to reduce the asymmetry between epidemic peaks, and long-term trends (which can dominate or hide other non-stationary parameters in the correlogram) were removed by subtracting the long-term best-fit straight line. We then used a catalytic model to estimate the basic reproduction number (R0; mean number of secondary infections from an infectious individual in a totally susceptible population). A reversible catalytic model describing the age-specific proportion of immune people was fitted to the age-specific IgG seroprevalence data by maximum likelihood to estimate the mean force of infection (rate at which susceptible people are infected) and the duration of immunity; these parameters were used to compute R0. R0 was included in a susceptible–preinfectious–infectious–recovered–(immune) susceptible model to simulate M pneumoniae natural dynamics in the population. The effect on the epidemic cycles of seasonal changes in transmissibility, chance of occurrence of events in individuals (demographic stochasticity), and randomness of environmental factors (environmental stochasticity) were explored. FindingsData from England and Wales showed cyclic epidemics with a mean duration of 18 months, recurring roughly every 4 years. This pattern was superimposed on annual seasonal fluctuations, with highest frequency in the winter and lowest during the summer. The basic reproduction number was estimated at 1·7 (95% CI 1·6–1·9), showing low transmissibility of M pneumoniae. Simulations of M pneumoniae intrinsic dynamics were qualitatively consistent with reported data, suggesting that epidemics would be expected to occur regularly, although the amplitude of epidemic peaks progressively lessened. Numerical experiments suggested that the persistence of epidemic cycles is partly explained by the interaction between the intrinsic dynamics of the infection and randomness in environmental factors that affects its transmissibility. The other factors explored did not affect the overall trend. InterpretationOur analyses propose estimates of M pneumoniae transmission parameters, and our model summarises and integrates present knowledge on its natural history. These simulations suggest that M pneumoniae epidemic cycles are intrinsic to its dynamic and are sustained by the interplay between its deterministic dynamics and randomness in environmental factors affecting its transmissibility. This study has limitations. We used laboratory reports, which are probably skewed to infected individuals with illness severe enough to need medical attention and laboratory testing; this factor underestimates the total number of infections but is unlikely to explain the pattern of recurrent epidemics. The model included simplifying assumptions and did not incorporate age-dependent mixing patterns. Quantitatively comparing model predictions with laboratory reports was also difficult because of large uncertainty around the infection-to-case ratio as well as the case-to-laboratory diagnosis ratio in the population. These factors might affect the magnitude of the simulated epidemics but are unlikely to substantially affect the general trends of epidemic cycles or the inter-epidemic interval. FundingPN-D was funded through a British Chevening Scholarship.