5. Mathematical equations
To use this
model to investigate our questions about West Nile virus control, we converted the flow chart diagram in 
FIGURE
3 into a system of mathematical equations. We chose
to use ordinary differential equations, which proves to be a natural way to write the instantaneous rate of change of the number of individuals
in each group of birds and mosquitoes. There is one equation for each group, or
variable.
The equation for the rate of change in the number of susceptible birds is:
. (Equation
1)
The equation for the rate of change in the number of infectious birds is:
. (Equation 2)
The equation for the rate of change in the number of susceptible mosquitoes is:
. (Equation 3)
The equation for the rate of change in the number of infectious mosquitoes is:
. (Equation 4)
To make it clear that this model considers only these four groups, we added two further equations that define the total bird population, for our purposes, as
, (Equation 5)
and the total mosquito population as
. (Equation 6)
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