Database Reference
In-Depth Information
We assume that the rate at which mosquitoes bite humans (BITING RATE VEC-
TOR) is the product of the frequency with which a vector takes a blood meal (MEAL
VECTOR) and the proportion of these meals that are taken from humans—the “hu-
man blood index” (HBI in the model). Following,
1
values for HBI may lie in the
range from 0.005 to 0.63. By choosing alternative values for the converter REPEL-
LENTS, contact among vectors with humans, and thus the rate of transmission of
the disease, can be changed.
The MEAL VECTOR depends on temperature,
MEALVECTOR
=
D
/
(
TEMP
−
Tmin
)
,
(4.5)
where D is the number of the degree days required for the completion of develop-
ment (36.5 days), Tmin is a minimum temperature requirement for parasite devel-
opment (9.9 degrees C), and TEMP is average assumed temperature for the tropics.
1
Similarly, the length of incubation T of parasites in vectors, measured in days, is
a function of the temperature threshold Tmin, a minimum number of degree days
required for development, Dm, and average temperatures.
T
=
Dm
/
(
TEMP
−
Tm
)
.
(4.6)
Following
6
we assume that 105 degree days are needed for the development of the
parasite.
The female mosquito has to live long enough for the parasite to complete its de-
velopment if transmission is to occur. Longevity of the mosquito vector depends on
the species, humidity, and availability of hosts and temperature. Actual transmis-
sion intensity also depends on vector abundance, which is not modeled here. The
daily survival of vectors is calculated from the survival probability, Y, during one
gonothrophic cycle, and length of the cycle, X
(1
,
3)
as
X
∧
(
DAILYSURVIVALVEC
=
1
/
Y
)
(4.7)
The second module (Figure 4.3) focuses on the spread of the infection in the vectors.
To be infectious, an uninfected vector must get the parasite from a human host. The
development of the parasite in the vector requires certain temperatures included in
the model. Most of the steps followed in this module of vector birthing, hatching,
and dying are based on the insect life stages model developed in
7
.
The third module (Figure 4.4) uses, for illustrative purposes, population numbers
from Venezuela (U.S. Census Bureau) as well as data from the literature to simulate
the recovery rate of infected people and their loss of immunity. This module follows
the structure of the basic epidemic models developed in Chapter 2. Loss of immunity
is related to the transmission rate. If the transmission rate is high and humans are still
6
MacDonald, G. 1957. The epidemiology and control of malaria. Oxford University Press,
London, UK.
7
Hannon, B. and M. Ruth. 1997. Modeling dynamic biological systems. Springer-Verlag, New
Yo r k .
