DEPARTMENT OF MATHEMATICAL
& STATISTICAL SCIENCES
UNIVERSITY OF ALBERTA
MATHEMATICAL BIOLOGY SEMINAR
MONDAY, March 31, 2003
Dr. Marjorie Wonham
Department of Mathematical
& Statistical Sciences
Unviversity of Alberta
Invasion Model for West Nile Virus
The North American epidemic of the West Nile (WN) arbovirus was first detected
in New York State in 1999 (and Alberta in 2002) and has spread each subsequent
year. The virus is typically amplified in natural transmission cycles between
vector mosquitoes and host birds. The current epidemic has been particularly
damaging to corvids such as American crow. Infected horses, humans, and other
mammals may suffer mortality, but are generally considered incidental hosts.
We develop a model of WN cross-infection between birds and mosquitoes to explore the dynamics of disease transmission and control. We extend the basic SIR model for malaria transmission (Anderson and May 1991) to a system of differential equations for susceptible, infected, and recovered birds, and larval, susceptible, exposed, and infected mosquitoes.
We illustrate the WN transmission dynamics with numerical simulations parameterized using literature values for American crow, Corvus brachyrhynchos, and mosquitoes, Culex pipiens.
Using stability analysis of the disease-free equilibrium, we calculate the basic reproductive rate of the epidemic, R0. By setting R0 = 1, we obtain a simple formula for the critical susceptible mosquito population size, above which the virus will invade. We develop a crude approximation to mosquito seasonal dynamics and outline a graphical method to evaluate invasion conditions for WNV during a season where mosquito populations cycle.
Emerging WN control strategies include spraying after surveillance reports of WN-positive mosquitoes or birds, or after confirmed reports of WN infection in horses or humans. We use our model to examine the implications of these strategies, and discuss inter-annual and spatial extensions of the model.