title: Decreasing stochasticity through enhanced seasonality in measles epidemics.
abstract: Seasonal changes in the environment are known to be important drivers of population dynamics, giving rise to sustained population cycles. However, it is often difficult to measure the strength and shape of seasonal forces affecting populations. In recent years, statistical time-series methods have been applied to the incidence records of childhood infectious diseases in an attempt to estimate seasonal variation in transmission rates, as driven by the pattern of school terms. In turn, school-term forcing was used to show how susceptible influx rates affect the interepidemic period. In this paper, we document the response of measles dynamics to distinct shifts in the parameter regime using previously unexplored records of measles mortality from the early decades of the twentieth century. We describe temporal patterns of measles epidemics using spectral analysis techniques, and point out a marked decrease in birth rates over time. Changes in host demography alone do not, however, suffice to explain epidemiological transitions. By fitting the time-series susceptible-infected-recovered model to measles mortality data, we obtain estimates of seasonal transmission in different eras, and find that seasonality increased over time. This analysis supports theoretical work linking complex population dynamics and the balance between stochastic and deterministic forces as determined by the strength of seasonality.
authors.affiliation: Centro de Ciencias de la Complejidad (C3), Universidad Nacional Autónoma de México, México, D.F. México. nmantilla@cantab.net
authors.forename: N B
authors.initials: NB
authors.lastname: Mantilla-Beniers
authors.forename: O N
authors.initials: ON
authors.lastname: Bjørnstad
authors.forename: B T
authors.initials: BT
authors.lastname: Grenfell
authors.forename: P
authors.initials: P
authors.lastname: Rohani
mesh_terms: D000818:Animals; D001723:Birth Rate; D003710:Demography; D004196:Disease Outbreaks; D006801:Humans; D008457:Measles / Q000453:epidemiology* / Q000503:physiopathology*; D015233:Models, Statistical; D008962:Models, Theoretical; D011157:Population Dynamics; D012621:Seasons; D013269:Stochastic Processes; D013997:Time Factors