Database Reference
In-Depth Information
(LOSING IMMUNITY
+
BIRTHING
−
INFECTING
−
S DYING) * dt
INIT NUMBER SUSCEPTIBLE
=
97
INFLOWS:
LOSING IMMUNITY
=
NUMBER RECOVERED*IMMUNITY LOSS RATE
BIRTHING
=
BIRTH RATE * TOTAL POPULATION
OUTFLOWS:
INFECTING
=
NUMBER SUSCEPTIBLE * INFECTION RATE
S DYING
NUMBER SUSCEPTIBLE * DEATH RATE
BIRTH RATE
=
=
0.014
DEATH RATE
0.011
DZ MORTALITY RATE
=
=
0
IMMUNITY LOSS RATE
=
0
INFECTION RATE
PROPORTION INFECTED *
PROPORTION SUSCEPTIBLE * TRANSMISSION EFFICACY
PROPORTION INFECTED
=
=
NUMBER INFECTED/TOTAL POPULATION
PROPORTION RECOVERED
=
NUMBER RECOVERED/TOTAL POPULATION
PROPORTION SUSCEPTIBLE
=
NUMBER SUSCEPTIBLE/TOTAL POPULATION
RECOVERY RATE
1/8
TOTAL POPULATION
=
=
NUMBER SUSCEPTIBLE
+
NUMBER RECOVERED
NUMBER INFECTED
TRANSMISSION EFFICACY
+
=
1
12.3 Base WNV SIR Model with a Dynamic Vector Population
12.3.1 Base Model Structure and Behavior
With a few simple modifications, a population-dynamic SIR model can also be ap-
plied to diseases with indirect transmission through a vector
4
. Complexity certainly
increases when we consider dynamically changing host and vector population den-
sities, even as these populations interact with one another through disease transmis-
sion feedbacks. Further, the disease transmission cycle may negatively feedback on
population growth rates, reducing reproductive output of infected or even recovered
individuals. This is especially true for the host population if illness can result in per-
manent or slow-healing damages, such as chronic neurological deficits, which may
alter reproductive behaviors or physiology. In this chapter, we will make the sim-
plifying, but unrealistic assumption that neither the host nor the vector reproductive
4
Anderson, R.M. and R.M. May. Population biology of infectious diseases: Part II. Nature 1979b;
280: 455-461.
