Database Reference
In-Depth Information
9.2 Model Construction
The life cycle of the
T. gondii
parasite has three stages: cyst, oocyst, or tachyzoite.
A cat may eat cysts in infected rodents or birds, or other raw meat; then the organ-
isms will begin to multiply in the wall of the small intestine, producing the second
stage, oocysts. These are excreted in the feces for 2 to 3 weeks. Then they may
become spores and become infectious to other animals, including humans. Most
exposed cats shed oocysts during acute Toxoplasma infection, but not after. Oocysts
are very hardy and can survive in moist, shaded soil or sand for months. They can
be passed on directly to animals and humans, as well as indirectly to humans who
consume meat that is undercooked.
To capture the toxoplasmosis dynamics, we need information on the growth and
infection of the human population (by gender), the cat population, and the rat popu-
lation. Total human population on these farms was 174, (77% male). We begin our
model with knowledge that the mean prevalence of the disease in humans is a sur-
prising 31%. We assume the human birth rate is a normal distribution, centered on a
mean of 16 births per 1,000 residents. The natural human death rate is also a normal
distribution, centered on a mean of 0.85%. Infected humans have a higher death rate
of 2%. The infection rate for female humans is described by:
Human IR
=
(Percent Raw Food
∗
Pig Prev
∗
1
)+(
Inf Cat Density
∗
0
.
003
)
+(
Dirt Handling
∗
0
.
005
)
,
(9.1)
which shows the effects of eating raw or incompletely cooked pork, being around
infected cats, and handling dirt that could contain infective oocysts. The prevalence
in pigs, in turn, is dependent on the density of infected cats.
We assume that the percent of raw/undercooked food eaten by humans is 1%.
We also assume the infection rate four times higher for males than females. The
resulting human growth and infection model is given in Figure 9.1.
We assume the initial rat population is 200, with a 10% birth rate (Figure 9.2).
The initial value for the number of infected rats is based on a mean prevalence of
10%. The rat infection rate is 0.008 rats per year. Infected rats die at a rate that is de-
pendent on the cat population, with the infected rats dying at rate that is 20% higher.
We assume an initial cat population of 200 with a 10% birth rate. The cat
infection rate is dependent on both the number of infected cats and the number
of infected rats.
The relationship for the spread among cats is based on the law of mass action
so that the infection rate equals 1% of the product of infected and healthy cats plus
an additive effect from the presence of infected rats (0.01*Inf rat density). The cats
can then either become infected or become vaccinated. Infected cats stay contagious
for 2 years, after which they become immune, a process which is represented by a
conveyor. The infected cats die at a rate of 10%, while healthy cats die at a rate that
is dependent on the total cat population. The cat population and infection process
model is shown in Figure 9.3.
The small auxiliary models can be found in the model file.
