The role of environmental transmission in recurrent avian influenza epidemics

Abstract

Avian influenza virus (AIV) persists in North American wild waterfowl, exhibiting major outbreaks every 2-4 years. Attempts to explain the patterns of periodicity and persistence using simple direct transmission models are unsuccessful. Motivated by empirical evidence, we examine the contribution of an overlooked AIV transmission mode: environmental transmission. It is known that infectious birds shed large concentrations of virions in the environment, where virions may persist for a long time. We thus propose that, in addition to direct fecal/oral transmission, birds may become infected by ingesting virions that have long persisted in the environment. We design a new host-pathogen model that combines within-season transmission dynamics, between-season migration and reproduction, and environmental variation. Analysis of the model yields three major results. First, environmental transmission provides a persistence mechanism within small communities where epidemics cannot be sustained by direct transmission only (i.e., communities smaller than the critical community size). Second, environmental transmission offers a parsimonious explanation of the 2-4 year periodicity of avian influenza epidemics. Third, very low levels of environmental transmission (i.e., few cases per year) are sufficient for avian influenza to persist in populations where it would otherwise vanish.

Figure 1. Illustration of the model.

The decay curves of the virus during winter and summer are sketched in blue and red, respectively. The corresponding symbols of the viral persistence rates within each ground are also illustrated. The persistence rates of avian influenza strains in the breeding and wintering grounds are quite different because they increase strongly with the temperature of the environment. Since water temperatures where the ducks are present (i.e., breeding grounds in the summer and wintering grounds in the winter) may be similar, we chose the corresponding persistence rates to be similar, as well. The persistence rate is much reduced (i.e., the persistence time of the virus increases) in the breeding grounds during the winter as the temperature drops. Also, the persistence rate is significantly increased (i.e., the persistence time of the virus decreases) in the wintering grounds during the summer as the temperature increases.

Figure 2. Simulation results obtained using our deterministic model.

Panels A, B, and C show , and versus ; note the logarithmic scale for . The initial conditions are , , , and . The parameters are as in Table 1 with and . Panel D shows the Fourier power spectrum density of over a time interval of 25,000 years. Panels E and F show bifurcations diagrams of the model versus and , respectively. The orbits are sampled yearly, at the end of the wintering season. The dotted lines mark the positions of the orbit presented on the left within the corresponding bifurcation diagrams.

Figure 3. Simulation results obtained using our stochastic model.

Panels A, B, and C show , and versus ; note the logarithmic scale for . The initial conditions are , , , and . The parameters are as in Table 1 with and . The blue line in panel D shows the Fourier power spectrum density of over a time interval of 3,500 years. The yellow line represents the moving average of the spectrum density. Panels E and F show the global spectral decomposition in Difference-of-Gaussians (DoG) wavelets of stochastic orbits versus and , respectively. Each spectrum is an average over 100 wavelet transforms of individual stochastic realizations of the orbit over 3,300 years (this time interval gives 95% confidence to the peaks of each wavelet transform; the fluctuations are due to the stochasticity of the realizations of the model). The color map represents the power scale measured in . The dotted lines mark the positions of the stochastic realization presented on the left within the corresponding panels.

Figure 4. Color map of the time-average of the number of infected versus the direct transmissibility and the environmental infectiousness .

Each colored point is calculated by averaging the results of 100 stochastic realizations. For each realization, a transient of 100 years was discarded and the time average was performed over 200 years. The white line indicates the epidemic threshold of the mean-field model: for parameters in the circled area around the origin there are no epidemics, otherwise epidemics occur. In the Text S1, we present the results of extensive sensitivity analyses.

Figure 5. Direct versus environmental transmission.

Color maps versus the direct transmissibility and the environmental infectiousness of the time average of the A direct transmission rate; B environmental transmission rate and the average (over stochastic realizations) fraction of time when the C direct transmission is not zero; D environmental transmission is not zero. The simulation details are the same as for Figure 4.

Figure 6. Re-plot of data from Figure 5.

Direct and environmental transmission rates versus the direct transmissibility at environmental infectiousness .

Figure 7. Color map of the time-average of the environmental transmission rate when the epidemic is re-ignited versus the direct transmissibility and the environmental infectiousness .

The simulation details are the same as for Figure 4.