A model describing the evolution of West Nile-like encephalitis in New York City

Encephalitis is a virus that is carried by mosquitoes and transmitted to humans and birds. Mosquitoes and birds do not show any signs of the virus and the main life cycle is carried between the two. Humans contract the virus from infected mosquitoes and the results can be deadly. In the Summer of 1999, New York City and the surrounding area were struck with a West Nile strain of encephalitis. We develop a difference equation model describing the evolution of the virus. The model incorporates a control variable that accounts for pesticide sprayed to influence mosquito populations in New York City. Using the theory of asymptotically autonomous difference equations, we arrive at parameter calculations that will eradicate the disease.