PNAS – Proceedings of the National Academy of Sciences of the United States of America
Timing and periodicity of influenza epidemics
Ottar N. Bjørnstad and Cecile Viboud
PNAS 2016 ; published ahead of print November 3, 2016, doi:10.1073/pnas.1616052113
Although the annual cycle of summers and winters is a long-resolved mystery of astronomy, the annual antipodal waxing and waning of influenza epidemics is still an unresolved question in epidemiology. In 1981, R. E. Hope-Simpson, an astute British physician who maintained and analyzed detailed records of his patients and their diseases for more than three decades, observed that “Influenza outbreaks are globally ubiquitous and epidemics move smoothly to and fro across the surface of the earth almost every year in a sinuous curve that runs parallel with the ‘midsummer’ curve of vertical solar radiation…” (1). In PNAS Deyle et al. (2) combine convergent cross-mapping with empirical dynamic modeling to elucidate the nonlinear roles of absolute humidity and temperature in explaining influenza’s “sinuous curve that runs parallel with the ‘midsummer’” across the globe (1).
Understanding interepidemic intervals and timing of outbreaks has been a focus of mathematical epidemiologists for more than 50 y (3, 4). Acute immunizing infections have internal cyclic clockworks determined by the overcompensatory predator/prey-like interaction that results from slow susceptible recruitment, through births and loss of immunity, and rapid susceptible depletion from transmission during epidemics. The internal clock depends on traits of both the pathogen and the host and determines the frequency of oscillations we expect to see in the presence of random perturbations to the disease dynamics (3). The “flu” is a recurrent menace—and sometime scourge—caused by cocirculating strains of influenza A and B viruses, which at the strain-aggregate level can be modeled using the “susceptible-infected-recovered-(re)suceptible” compartmental model (5). For influenza, the internal interepidemic period is usually in the 10- to 16-mo range depending on the infectious period and transmissibility (the basic reproductive ratio, R0) of each strain (Fig. 1A). The prediction is that, in the absence of extrinsic forcing, the flu peak would …