Fig 1.
Historical pandemics emerged at the tail-end of flu seasons.
Gray curves show the 1997-2015 flu seasons in the US, excluding the 2009 H1N1 pandemic, as estimated by the CDC’s ILINet surveillance system [29]. Vertical dashed lines indicate emergence week of historical pandemics in their source populations, defined as the first reported outbreak of severe influenza preceding the initial pandemic wave. These estimates were obtained from: 1889 [17], 1918 [18, 19], 1957 [20, 21], 1968 [22, 23], and 1977 [24]. To be consistent, we date the emergence of the 2009 pandemic according to the first significant outbreak preceding the initial wave, rather than the earlier outbreaks in rural Mexico that were identified only in retrospect [30].
Fig 2.
Seasonal epidemics produce a pandemic refractory period.
A: Actual 2008-2009 epidemic curve (solid black line) and 200 stochastic simulations of seasonal epidemics for each network (green for empirical; purple for homogeneous), assuming transmission parameters estimated from 2008-2009 data. B: The probability of pandemic emergence upon the introduction of a single infected individual, assuming that the pandemic virus has the same transmission rate as the seasonal virus. Probability is estimated as the proportion of introductions that subsequently infected at least 5% of the overall population out of the 5,000 simulations. Horizontal dashed lines indicate the emergence probabilities in a completely susceptible population calculated with Eq 2. The pandemic refractory periods (shaded regions) are expected to occur during and immediately following the seasonal epidemic peak. C: Underestimation of pandemic R0. Assuming that the emerging pandemic has an R0 = 2.5 in a naïve population (dashed horizontal line), we plot the median (points) and interquartile range of the measured Reff, for each introduction time and each network. For example, if a pandemic with R0 = 2.5 emerged in March of 2009 and we did not account for population immunity, we would interpret the Reff as the R0 and considerably underestimate the true transmission rate (R0 ≈ 2), regardless of our contact network assumptions.
Fig 3.
The evolving structure of the susceptible population as the flu season unfolds.
For purposes of illustration, we present caricatures of each model through time, assuming that the average degree is 〈k〉 = 6 and that we repeatedly observe the same subset of each population. Orange represents individuals susceptible to infection by the pandemic virus and the contacts between them; gray indicates individuals who are currently or recently infected by the seasonal virus, and thus immune to pandemic infection. The empirical (top) and homogeneous (bottom) networks experience different structural changes in pandemic susceptibility throughout the flu season. In January, prior to the onset of flu season, both networks are fully susceptible. Just following the seasonal epidemic peak (March), both networks are at the base of their refractory period, with many nodes resistant to the pandemic virus. Even with the same number of susceptible nodes, the empirical network is more disrupted than the homogeneous network. Highly connected (hub) nodes are more vulnerable to seasonal infection than less connected nodes and, once removed by immunity, critically disconnect the susceptible portion of network. After the seasonal epidemic has subsided (June), short-term immunity has largely waned in both models, leaving them vulnerable to pandemic invasion.
Fig 4.
Seasonal flu disconnects the susceptible portion of a population.
A: For a single (typical) seasonal epidemic simulation, the number of individuals susceptible to infection by a pandemic virus and the number of edges connecting two such individuals are plotted for each network (green for empirical; purple for homogeneous), with each point representing a single time point over the course of the epidemic. Arrows indicate temporal progression. For any given number of remaining susceptible individuals, the empirical model is always sparser than the homogeneous model (that is, it has fewer contacts remaining between susceptibles). B: The distribution of degrees (number of contacts) assumed for the empirical model. The homogeneous model assumes that all individuals have 16 contacts. C Snapshot of the susceptible portion of the empirical network at the base of the refractory period (at the time point indicated in panel A by the box labeled ‘C’). Points indicate the percent of the nodes that are immune to pandemic infection, across different levels of connectivity. (We bin degrees by 10; for example, the lowest bin includes individuals with 1 to 10 contacts). For comparison, the horizontal dashed line indicates the overall proportion of individuals immunized in the network at the base of the refractory period. In comparison to an individual with an average number of contacts, a highly connected individual will be more vulnerable to seasonal flu infection, and, once infected and immunized, cause greater epidemiological disruption.
Fig 5.
Seasonality further constrains pandemic emergence timing.
Probability density for pandemic emergence timing for pandemics that emerge during the seasonal influenza epidemic for the homogeneous (purple) and empirical (green) networks. Pandemic emergence timing, the time in which the simulated pandemic begins rapid spread, is defined as the day the pandemic strain incidence reaches five or more cases. Results are for a pandemic emerging during the 2008-2009 flu season with the same transmission rate as the seasonal epidemic. Vertical lines indicate the timing of historic pandemics, with the solid line indicating the timing of the 2009 pandemic and dashed lines indicating timing of others.