Model answers or trivial pursuits? The role of mathematical models in influenza pandemic preparedness planning

Abstract

The panzootic of H5N1 influenza in birds has raised concerns that the virus will mutate to spread more readily in people, leading to a human pandemic. Mathematical models have been used to interpret past pandemics and outbreaks, and to thus model possible future pandemic scenarios and interventions. We review historical influenza outbreak and transmission data, and discuss the way in which modellers have used such sources to inform model structure and assumptions. We suggest that urban attack rates in the 1918-1919 pandemic were constrained by prior immunity, that R(0) for influenza is higher than often assumed, and that control of any future pandemic could be difficult in the absence of significant prior immunity. In future, modelling assumptions, parameter estimates and conclusions should be tested against as many relevant data sets as possible. To this end, we encourage researchers to access FluWeb, an on-line influenza database of historical pandemics and outbreaks.

Figure 1

The 1924 influenza epidemic at the Royal Naval School, Greenwich. The introduction of new classes of (susceptible) students led to recrudescence of the outbreak with both ‘new boys’ and ‘old boys’ affected. ³⁹

Figure 2

Incidence of influenza cases in Royal Air Force camps (black columns) and the city of Copenhagen (white columns) during the 1918–1919 pandemic. ¹⁹ Time‐line units are in weeks measured from the maximum of the initial peak. Both curves display multiple waves, consistent with hypotheses of waning immunity and/or antigenic drift. De‐mobilization at the conclusion of World War I could have prevented the third wave, visible for Copenhagen, from being registered in the Air Force camps.

Figure 3

Distribution of the serial interval during the 1920 influenza epidemic on Kelleys Island, Ohio, USA. Interval taken to be the time in days between the first and subsequent cases in a household, assuming that the first case is the source of infection for other household cases. ⁶⁰

Figure 4

Map showing the location of influenza cases on Kelleys Island, Ohio, USA, during the 1920 epidemic. ⁶⁰ In this small population, relatively isolated from the outside world, it was possible to reconstruct likely networks and hubs of disease transmission. Paths and arrows indicate a known contact between a first case in a family and a previous case. Note the large number of first cases having their only known exposure at the island's school (indicated).

Figure 5

Daily incidence of influenza cases on Kelleys Island, Ohio, USA, during the 1920 epidemic for (1) cases occurring in families having school attendees and (2) cases occurring in families having no schoolchildren. The peak incidence for (1) occurs 3 days before the peak for (2) showing the effect of mixing in school on earlier transmission to households. The island's school was closed on 31 January. ⁶⁰