West Nile virus is widespread in Africa, the Middle East, and Western Asia, where it is transmitted back and forth between bird hosts and mosquito vectors. In North America,
it is an emerging infectious disease. The first known North American epidemic was originally detected in New York State in 1999, when birds began to die in large numbers.

The cause of this bird mortality was initially unknown, but by December 1999 it had been identified as West Nile virus. In the following summers, West Nile virus spread across the continent. Crows and jays in particular suffered very
high mortality from West Nile virus: at the epicenter of the New York City outbreak, there was an approximately 67% decrease in the annual crow count from 1998 to 1999.

Other birds, such as sparrows, also contracted the virus but suffered lower mortality. Among mammals, horses appeared especially vulnerable, with a mortality rate of approximately 40%. Human cases were less common and less likely to
be fatal, but were a growing health concern nonetheless.

By the end of 2006, West Nile virus had been identified in 5 Canadian provinces and 48 U.S. states, and in at least 10 mosquito, 150 bird, and 17 other vertebrate species.

A model is a simplified representation of reality. Maps, for example, are visual models of places. Similarly, equations can be mathematical models of processes.

Different kinds of maps serve different purposes: road maps are useful for one kind of travel; topographic maps are useful for another. Different kinds of equations also serve different purposes. For example, a decreasing exponential
function can be used to model radioactive decay, while an increasing exponential function can be used to model the initial stages of bacterial growth.

All models, whether they are visual or mathematical, leave out considerable detail. A model, by definition, does not completely mirror reality – if it did, it would be reality, not a model. For a model to be useful, it must leave out
unimportant detail but keep important detail. The decision about what is important depends on the goal of the model.

In some cases, building a mathematical model can be as simple as fitting a curve – an equation – to data. In more complex instances, a mathematical model may consist of multiple equations that are linked together to represent a series
of connected processes. Our West Nile virus model is a system of six connected equations.

Abstract

Emerging infectious diseases are a concern for wildlife and human health. To understand, prevent, and control infectious diseases, it can be helpful to use mathematical models. West Nile is a new infectious disease in North America. The virus is transmitted back and forth continually between
mosquitoes and birds, and occasionally is transmitted from mosquitoes to humans. We developed a mathematical model to represent the West Nile virus outbreak in North America. We then used the model to determine whether it would
be more effective to remove mosquitoes or remove birds to prevent disease outbreaks. Our model showed that reducing mosquito abundances would help prevent an outbreak. Reducing bird abundances, however, would have the opposite
effect, increasing the chance of an outbreak.