The timing of outbreaks of both epidemic and pandemic influenza can be understood with reference to the effective reproductive number and its relation to the basic reproductive number and absolute humidity. To examine these issues, we further analyze results from model simulations of epidemic influenza, as presented by Shaman et al. (2
), for New York State, which experienced considerable spring and late summer/early autumn 2009 A/H1N1 transmission (5
). Although the real world is much more complex than these idealized simulations, these model representations of transmission provide insight into the dynamics underlying outbreak events.
The parameter combination used in this representative example is the 1972–2002 (31-year) best-fit simulation of epidemic influenza (). Given these parameter values and observed absolute humidity levels for New York State, R0(t) ranges seasonally on average from a summertime low of 1.24 to a wintertime high of 3.14. Susceptibility ranges from an average postoutbreak minimum of 0.34 to an average preoutbreak maximum of 0.52. In summer, when humidity is high, these susceptibilities imply an RE(t) ranging from 0.42 to 0.64. Thus, even at the highest population susceptibility level of 0.52, summertime RE(t) remains well below 1 and substantial outbreaks of influenza are not possible. However, during winter, when R0(t) is high, RE(t) rises well above 1 () and epidemics do occur. Thus, the seasonality of R0(t), which varies with absolute humidity, strongly favors wintertime epidemics in temperate regions. This finding, in which absolute humidity and susceptibility preclude epidemic transmission during summer, is also evident for other best-fitting model parameter combinations () and simulated susceptibilities (not shown).
For pandemic influenza, preoutbreak susceptibility is much higher than for epidemic influenza, particularly among younger individuals, including school-aged populations. Prior to the 2009 A/H1N1 pandemic, little immunity to this virus was measurable in individuals under 30 years of age, who are thought to be the main drivers of transmission of influenza and most other respiratory infections (9
). We can use absolute humidity conditions in New York City during 2009 to examine both R0
) and RE
) with respect to 2009 A/H1N1 (). The city was slightly more humid during late April and early May 2009 than normal (the 1948–2008 average) when the first pandemic wave developed (5
) is shown for several population susceptibility levels and reaches its nadir during August. In this simplified model, susceptibility above 80% permits epidemic growth even at the nadir of transmissibility in August, while transmissibility above about 60% permits epidemic growth in May–June, when the main epidemic occurred in New York City. After August, RE
) rises as humidity levels fall, and transmission of influenza becomes possible for even lower levels of susceptibility.
Figure 3. Time series of New York City observed specific humidity, estimated basic reproductive number, and estimated effective reproductive number for 1948–2008 and 2009. Top, plots of observed specific humidity, q(t), and estimated basic reproductive (more ...)
These numbers are not intended as precise estimates of R0
) or RE
) for New York City; moreover, RE
) is likely to increase after school opening (7
). Nonetheless, our model demonstrates the potential patterns of pandemic and epidemic influenza transmission facilitated by susceptibility and absolute humidity in temperate regions. High susceptibility (>60%–80% in this example) to a novel strain of influenza, such as 2009 A/H1N1, can support transmission even in the presence of high spring or summer absolute humidity, even in places where seasonal influenza could not spread. Sustained transmission of 2009 A/H1N1 did occur in many temperate locations, including New York City, during spring and summer (11
In temperate regions, typically, absolute humidity declines and R0
) rises beginning in September. At the same time, increased close contact, particularly between schoolchildren in classrooms and among college students in group residences, begins to occur. Both trends may have contributed to the autumn outbreaks of 2009 A/H1N1 observed in the United States (3
) and elsewhere.
In contrast, susceptibility is typically well below 60% for epidemic influenza that, in conjunction with high absolute humidity, precludes significant influenza transmission during summer and early fall (in this perfectly mixed model example). Only during late fall and winter, when absolute humidity is at its lowest, does RE(t) rise above 1 for epidemic influenza (). Population structure in human populations leads to more variability than this simple model would suggest. In temperate zones, epidemic influenza transmission does typically peak during winter; however, localized outbreaks during spring, summer, and autumn do occur. These out-of-season epidemic outbreaks occur where locally RE(t) has risen above 1. Real-world populations are clustered. This heterogeneity can group susceptible individuals together and create subpopulations in which the increased susceptibility to epidemic influenza, combined with high enough R0(t), as dictated by absolute humidity conditions, is sufficient to push RE(t) above 1.
Thus, although absolute humidity conditions determine the general phase organization of epidemic influenza transmission, such that the majority of temperate region infections occur during winter, absolute humidity conditions alone do not preclude out-of-season epidemic influenza transmission in select subpopulations. Rather, absolute humidity conditions must be evaluated in conjunction with local levels of susceptibility to determine whether RE(t) is >1 and transmission can be supported. The school environment is one such location where susceptible subpopulations cluster, and RE(t) may rise above 1 prior to winter.