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Environmental transmission of low pathogenicity avian influenza viruses and its implications for pathogen invasion

Edited by Andrew P. Dobson, Princeton University, Princeton, NJ, and accepted by the Editorial Board March 27, 2009 (received for review September 11, 2008)
Abstract
Understanding the transmission dynamics and persistence of avian influenza viruses (AIVs) in the wild is an important scientific and public health challenge because this system represents both a reservoir for recombination and a source of novel, potentially humanpathogenic strains. The current paradigm locates all important transmission events on the nearly direct fecal/oral birdtobird pathway. In this article, on the basis of overlooked evidence, we propose that an environmental virus reservoir gives rise to indirect transmission. This transmission mode could play an important epidemiological role. Using a stochastic model, we demonstrate how neglecting environmentally generated transmission chains could underestimate the explosiveness and duration of AIV epidemics. We show the important pathogen invasion implications of this phenomenon: the nonnegligible probability of outbreak even when direct transmission is absent, the longterm infectivity of locations of prior outbreaks, and the role of environmental heterogeneity in risk.
Avian influenza viruses (AIVs) are an important class of infectious agents, both as a model for the influenza viruses that infect millions of people each year and as a generator of the genetic variation that might give rise to a future pandemic strain (1, 2). In contrast to the dominant human strains (3–5), the dynamics, control, and management of transmission remain poorly understood even in historically prevalent low pathogenic avian influenza viruses (LPAIVs) (2, 6). Given the recent emergence of H5N1 highly pathogenic avian influenza virus (HPAIV) and its continued introduction into new territories with attendant impacts on domestic waterfowl, poultry, and human populations, a thorough understanding of influenza evolution and epidemiology takes on a new urgency (6, 7).
For many infectious diseases, transmission theory assumes that the majority of infections is caused by direct interactions between infectious and susceptible individuals (8, 9). The presence of additional transmission modes, particularly environmental transmission, gives rise to mechanisms that alter the conditions for pathogen invasion and persistence (10). Based on a number of lines of reasoning, we believe environmental transmission of LPAIVs occurs in natural populations:

Environmental persistence of LPAIVs. LPAIV persistence in incubations intended to mimic aquatic environments may last many months, depending on environmental conditions (Fig. 1; ref. 11). Importantly, infectivity of persistent viruses has been unambiguously demonstrated (12, 13). These experiments might explain the routine isolation of many AIV subtypes, including H5, from unconcentrated surface water (14), mud and soil swabs (15), and from aquatic environments where previous outbreaks have been documented (16).

Studies in poultry farms. Contaminated pond water and drinking water have been repeatedly implicated in farm outbreaks (17–19). Most tellingly, in one experiment, ducks reared under infectionfree conditions became infected when placed in pens positioned in contaminated Minnesota marshes (20, 21).

Natural history observations. The high incidence of infection among juvenile birds—even very early in the breeding season—is inconsistent with direct contact transmission, which would require high frequency of early interactions between ducklings and nonsiblings (1).

Epidemiological evidence. Roche et al. (22) have argued that neither density nor frequencydependent direct transmission captured the observed pattern of infections during an outbreak of LPAIV in the Rhône delta, France. By contrast, they considered the predictions of a model including waterborne transmission and the data in strong agreement.
For these reasons, environmental transmission could be important in AIV epidemiology (23). It is known that indirect transmission chains, which the standard susceptibles–infectives–removals (SIR) theory does not account for, alter the characteristic timescale of the transmission cycle and patterns of longterm persistence (24). To understand how, we introduce the following simplified model for the withinseason dynamics of a migratory waterfowl population and show that environmental transmission qualitatively changes the structure of an epidemic, with implications for invasion. In what follows, we study this model at parameterizations based on data from LPAIVs.
A Mixed Transmission Model
To simultaneously account for demographic stochasticity—crucial for understanding the probability of epidemic takeoff and extinction—and the large size of the environmental virus population, we adopt a hybrid dynamical system composed of a stochastic birth–death process for susceptible and infected birds, and an ordinary differential equation for virus kinetics. Denoting the number of susceptibles by S and infectives by I, we then define p_{(m,n)} as the probability of m susceptibles and n infectives at time t to arrive at the Kolmogorov forward equation:
where β gives the rate of any direct (fecal/oral) transmission, ρ is the per capita consumption rate and is scaled by the lake volume, L, and γ is the recovery rate of infectives. The constant host population is given by S + I + R = N, where R denotes the number of recovered birds. The environmental transmission term is the product of the consumption rate of lake water by susceptible birds
The stochastic dynamics of susceptibles and infectives are coupled to virus concentration (V) by using the following differential equation:
where ω is the rate at which infecteds shed virus and η is the decay rate of virus in water. Empirical estimates of all parameters are presented in Table 1. We obtain from the mean field equations for this model an expression for the basic reproductive ratio, R_{0} (see supporting information (SI) Appendix):
This expression separates the contributions of direct transmission (βSI) and environmental transmission
Results
Epidemic Curve.
By decomposing the infected class into indirectly and directly infected fractions, we show in Fig. 2 how the relative contributions of direct (darkblue line) and environmental (green dashdot line) transmission change over the course of an outbreak in the mean field model. We see the effects of environmental transmission are most pronounced during epidemic takeoff and the epidemic tail (Fig. 2 Insets). Specifically, when there are few infectious birds at the start of an epidemic
Thus, we conclude that AIV invasion success is substantially altered by the inclusion of environmental transmission.
Implications for Pathogen Invasion.
To assess the invasion consequences of environmental transmission, we study the probabilities of outbreak under a range of conditions. We solve the full hybrid model by using Gillespie's direct method (27) for Eq. 1, updating V after each event according to Eq. 2. In Fig. 3A, we show that when R_{0}^{direct} < 1, environmental transmission can boost R_{0}, resulting in successful AIV invasion. Within the deterministic direct transmission framework, β < γ would guarantee the failure of the pathogen to invade. Similarly, within a stochastic direct transmission setting, the likelihood of invasion in this region would be very small. Hence, the region of positive probability in Fig. 3A to the left of the black line is solely attributable to the effects of environmental transmission. We explore the mean length of environmental transmission chains in Fig. 3B, which demonstrates that when R_{0}^{direct} < 1, environmental transmission consistently gives rise to small outbreaks, typically with < 10 infected birds in our population. However, these sparks may spasmodically lead to much larger epidemics, amplified by direct transmission events (Fig. 3C).
Next, we ask how the persisting environmental pool of virus, which results in ongoing exposure of susceptibles to pathogens, affects outbreak probability after an epidemic. For instance, we envision an epidemic among arriving migrants sparked by the residual environmental reservoir. Accordingly, we study how the probability of a new outbreak changes in the ensuing months. This is equivalent to studying the early phases of the dynamics when the initial conditions are given by S(0) = N,I(0) = 0 and V(0) = V_{0} > 0.
Three findings emerge (Fig. 4A). (i) In small lakes, there is a noticeable chance of a large secondary outbreak, even in the absence of infected birds initially. (ii) Environmental transmission represents a lesser problem in large lakes because of dilution. (iii) Finally, distinguishing between likely (mean) and extreme (99th percentile) scenarios reveals a disparity of two orders of magnitude between the volume of lake at which secondary outbreaks are unexpected (the median) and where they occur with a small but meaningful (1%) probability.
To characterise the role of initial virus density (V_{0}) in this scenario, we plot probability contours of outbreaks that infect 10% or more of the population (Fig. 4B). These contours are flat with respect to V_{0}, implying that the environmental reservoir of virus may represent a longterm source of infections irrespective of the interval before migrants arrive. Despite the indifference of contours to V_{0} over many orders of magnitude, initial virus concentration determines the predicted distribution of epidemic sizes (see Fig. 4B Insets).
Discussion
Our work has shown that the mixture of direct and environmental transmission characteristic of avian influenza viruses gives rise to transmission chains that are unaccounted for in standard SIR theory. Although a subtle component of a primary outbreak, these environmental transmission chains could play a significant role in generating secondary outbreaks and in the persistence of LPAIV. A similar role for environmental transmission has been proposed for other systems. For example, outbreaks of the Nuclear Polyhedrosis Virus in forest defoliators such as the Gypsy Moth have been shown to be sparked by environmental contamination of egg masses (28). In cholera, the environmental reservoir is considered to affect mainly longterm persistence, with a limited transmission contribution during violent epidemics (29).
An interesting question raised by results shown in Fig. 3 is why the probability of outbreak observed in simulations is negligible in a large neighbourhood around the R_{0} = 1 isocline. We conjecture that this phenomeon is a manifestation of the J to U transition in the distribution of the final outbreak size of stochastic epidemics in finite populations, as has been previously demonstrated for the stochastic SIR epidemic by Ball and Nåsell (30). Consider a stochastic model with two processes, infection {S → S − 1, I → I + 1} at rate βSI and removal {I → I − 1} at rate γI, and initial conditions S_{0} and I_{0} = 1. Until an infection occurs, the expected number of infecteds is Thus, the expected number of locally derived (second generation) infections is approximately
Now consider an infection process {S → S − 1, I → I + 1} at rate (ρ/L)SV/(V + κ), where V satisfies Eq. 2, with initial conditions S_{0}, I_{0} = 0 and V_{0} (i.e.,the environmental component of our mixed transmission model). At all times before the first infection, the virus concentration is approximated by Hence, the expected number of infections is given by
Whereas the expected number of locally derived infections in the direct transmission process is linearly dependent on I_{0} (Eq. 4), there is only a logarithmic dependence on V_{0} in the environmental transmission model (see Eq. 5). The condition under which, on average, one susceptible is infected by the environmental transmission process can be obtained by setting Eq. 5 to 1 and solving for R_{0}^{env}. Using the empirically obtained parameters described in Table 1 (and V_{0} = 10^{4}), we obtain:
Altough environmental transmission events may be infrequent, as this argument shows, failure to account for them results in a superficial understanding of AIV epidemiology and, as shown in Fig. 4, in considerably underestimating outbreak probability. Further, in nature, virus persistence in the environment will be further complicated by local environmental conditions, such as temperature and salinity that degrade the infectious particle (31, 32), which will have implications for virulence evolution due to novel opportunities for selection (33, 34). In particular, virus persistence [or durability (33)] may trade off with traditional parameters such as the direct transmission rate (β) and the infectious period (γ) giving rise to new challenges in virulence management. For these reasons, we conclude that environmental transmission warrants serious consideration in the study of avian influenza ecology and evolution.
Acknowledgments
We thank Andrew Park, Benjamin Roche, Kristzian Magori, and three anonymous reviewers for helpful comments on this article. This work was supported by Centers for Disease Control and Prevention Grant 5U19Cl000401 and by the James S. McDonnell Foundation. P.R. was supported by the Research and Policy in Infectious Disease Dynamics program of the Science and Technology Directorate, Department of Homeland Security, and the Fogarty International Center, National Institutes of Health.
Footnotes
 ^{1}To whom correspondence should be addressed. Email: rohani{at}uga.edu

Author contributions: P.R., R.B., D.E.S., and J.M.D. designed research; P.R. and J.M.D. performed research; P.R. analyzed data; and P.R., R.B., D.E.S., and J.M.D. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. A.P.D. is a guest editor invited by the Editorial Board.

This article contains supporting information online at www.pnas.org/cgi/content/full/0809026106/DCSupplemental.

Freely available online through the PNAS open access option.
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