The influence of climatic conditions on the transmission dynamics of the 2009 A/H1N1 influenza pandemic in Chile

Background The role of demographic factors, climatic conditions, school cycles, and connectivity patterns in shaping the spatio-temporal dynamics of pandemic influenza is not clearly understood. Here we analyzed the spatial, age and temporal evolution of the 2009 A/H1N1 influenza pandemic in Chile, a southern hemisphere country covering a long and narrow strip comprising latitudes 17°S to 56°S. Methods We analyzed the dissemination patterns of the 2009 A/H1N1 pandemic across 15 regions of Chile based on daily hospitalizations for severe acute respiratory disease and laboratory confirmed A/H1N1 influenza infection from 01-May to 31-December, 2009. We explored the association between timing of pandemic onset and peak pandemic activity and several geographical and demographic indicators, school vacations, climatic factors, and international passengers. We also estimated the reproduction number (R) based on the growth rate of the exponential pandemic phase by date of symptoms onset, estimated using maximum likelihood methods. Results While earlier pandemic onset was associated with larger population size, there was no association with connectivity, demographic, school or climatic factors. In contrast, there was a latitudinal gradient in peak pandemic timing, representing a 16-39-day lag in disease activity from the southern regions relative to the northernmost region (P < 0.001). Geographical differences in latitude of Chilean regions, maximum temperature and specific humidity explained 68.5% of the variability in peak timing (P = 0.01). In addition, there was a decreasing gradient in reproduction number from south to north Chile (P < 0.0001). The regional mean R estimates were 1.6-2.0, 1.3-1.5, and 1.2-1.3 for southern, central and northern regions, respectively, which were not affected by the winter vacation period. Conclusions There was a lag in the period of most intense 2009 pandemic influenza activity following a South to North traveling pattern across regions of Chile, significantly associated with geographical differences in minimum temperature and specific humidity. The latitudinal gradient in timing of pandemic activity was accompanied by a gradient in reproduction number (P < 0.0001). Intensified surveillance strategies in colder and drier southern regions could lead to earlier detection of pandemic influenza viruses and improved control outcomes.


Estimation of the reproduction number
In the early stages of an epidemic, when the effect of increasing incidence on the depletion of susceptibles is small, the growth of the epidemic is exponential in nature, with rate r[1]- [4]. Assuming the classical SEIR (susceptible-infectious-recovered) transmission model, the reproduction number, R 0 , is determined from where 1/κ and 1/γ are the latent and infectious periods, respectively.
Given M incidence measurements, y data i , at time points, t i , separated by ∆t (i = 1, ..., M ), the best fit exponential rise r is determined by minimizing the Poisson negative log likelihood [5]: where The s standard deviation upper and lower limits on r are determined from the values of r that yield where − log L min is the minimum value of − log L[5].

Determination of exponential growth phase
The standard deviation width of an epidemic curve consisting of N incidence measure- In this analysis we select the exponential rise portion of the epidemic curve by identifying incidence data points at the beginning of the epidemic that are sufficiently many standard deviations away from the time of peak incidence (denoted by t peak ) that a fit of an exponential curve to simulated data in that region provides unbiased estimates of the true exponential rise. The exponential rise region is thus the region where t i < (t peak − f σ t ).
In order to determine the optimal cut off value, f , we perform exponential rise fits to simulated data incidence curves from an SEIR (susceptible-exposed-infectiousrecovered) model as explained below. Then we choose the value of f that provides unbiased estimates of the true exponential rise.
We carry out a simulation study to generate synthetic data incidence curves from the SEIR transmission model. That is, to estimate the time variation of the incidence, y pred (t), we use a compartmental model that simulates the number of susceptible (S), exposed (E), infectious (I), and recovered (R) individuals in the population using the coupled deterministic ordinary non-linear differential equations ( [1]): where 1/κ and 1/γ are the average latent and infectious periods, respectively, β = R 0 γ is the transmission rate, and population size is given by N = S + E + I + R. We assume that 1/γ = 1.5 days and 1/κ = 1.5 days, which are within the range of mean estimates for the 2009 influenza pandemic [6,7,8,9].
We simulate the incidence curve, t y pred (t), under various R 0 hypotheses from 1.1 to 2.0 in steps of 0.1, and then scale t y pred (t) to simulate 1, 000 cases detected during the epidemic. We then obtain the simulated data epidemic incidence curve by random Poisson variation of the number of detected cases around the average within each time bin.
The exponential growth phase consists of data points at the beginning of the epidemic incidence curve that are at least f standard deviations away from the epidemic peak. Values of f between 0.5 to 2.0 in increments of 0.25 are examined, and the data simulation and fitting procedure is repeated 1000 times for each value of f . The optimal value of f is the one that is as low as possible, while still providing an unbiased estimate of the initial exponential growth rate, r. The estimated R 0 is determined from the r estimate using Equation 1.
We found that f >= 1.0 provides estimates of the true R 0 unbiased to within one standard deviation, and within 5% of the true R 0 .
In this analysis, we thus determine the exponential rise portion of the epidemic curve by selecting points that are at least 1.0 standard deviation from the epidemic peak.