Avian Influenza Dynamics Under Periodic Environmental Conditions

Since wild birds are the major natural reservoir for all known influenza A viruses, understanding the ecology of avian influenza (AI) viruses circulating in wild birds is critical to predicting disease risk in wild and domestic birds and preventing transmission to humans. AI virus which is shed by infected birds into aquatic environments plays a pivotal role in the sustained transmission of AI. Recent laboratory experiments, however, show that viral persistence in water is highly sensitive to environmental conditions such as temperature, which varies seasonally and geographically. Here, we develop mathematical models to study the effects of time-varying environmental conditions on AI dynamics, deriving the effects of temperature on the basic reproductive number (R0), the final outbreak size, and the effective reproductive number (Re). For periodic environmental temperatures, we derive a mathematical formulation of an AI invasion threshold (Ri) and conclude that apart from the mean temperature, the amplitude of the periodic temperature profile plays a significant role in the invasion of wild bird populations by AI. In particular, both higher means and higher amplitudes (warmer and more variable temperatures) reduce the likelihood of AI invasion. We also analyze the global dynamics of the model proving that AI is uniformly persistent in the wild bird population if Ri > 1. In numerical work, we fit the model to recent experimental data and field survey data from Northern Europe. Two important and robust quantitative conclusions emerge: that direct transmission is negligible compared to indirect and that immunity wanes within about 4 weeks. The latter conclusion is of particular interest since many previous models assume lifetime immunity. We also demonstrate that time-varying temperature may be the underlying cause of several features of AI dynamics which are observed in real data. In particular, AI prevalence is observed to peak in spring and fall but to wane in summer; this behavior naturally emerges from our model under a wide range of conditions.