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pump, and the epidemic soon
ended. This showed that cholera
was a waterborne disease that
humans contracted through
contaminated food and drink. A
decade later, Louis Pasteur’s “germ
theory” proposed that diseases, as
well as general rotting and decay,
were the work of microorganisms.Disease model
In their 1970s studies, Anderson
and May focused first on building
a mathematical model to show
how a microorganism could affect
a population. This led to a set of
equations that they hoped would
help explain the real-life impact of
different kinds of pathogens, from
bacteria and viruses to parasitic
worms and insect larvae.
In their model, a number of mice
were divided into three groups:
susceptible (uninfected) mice,
infected mice, and mice that had
survived infection and were now
immune. Unlike many earlier
epidemiological models, the total
population was not a fixed number;
mice could be added either by
reproduction or by additions from
other populations. Mice also died
from natural causes. In the absenceECOLOGICAL EPIDEMIOLOGY
A ravaged tree in North Yorkshire,
UK, shows the effects of Dutch elm
disease, a fungus spread by elm bark
beetles accidentally introduced to
Europe and America from Asia.of disease, the total would remain
more or less the same, with the
rate of added mice balancing that
at which other mice died.
For simplicity, the model
assumed that the diseases were
transmitted by contact between
infected and uninfected mice. Not
all infected mice would die, so the
model also included a recovery rate.
Mice that recovered would be
immune, at least initially. Immunity
to viruses is more or less lifelong,
but it is possible to become
susceptible again to the same
bacterial infection as time passes.
Therefore, the calculations also
included a rate of loss of immunity.
Putting all this together,
Anderson and May produced a
set of equations to predict the rate
of population change in the three
initial groups of uninfected but
susceptible mice, infected mice,
and the immune survivors. These
equations could be added together
to give the rate of change for the
total mouse population.The role of drought
in plant diseasesLike other disease-causing
agents, a plant pathogen
(disease-causing agent)
needs a supply of susceptible
individuals to infect. Periods
of drought slow the rate of
plant reproduction and
growth, thereby reducing the
prevalence of disease.
Aridity, however, also
weakens plants and makes
them susceptible to pathogens
that thrive in dry conditions.
These include various forms
of fungi that attack the leaves
of grain crops, legumes, and
fruits. These fungi are adapted
to survive in a dormant state
as hardened microscopic
bodies in soil. They can exist
for many years in dry soil, but
when the soil becomes wet,
the fungi must find a host
within a few weeks or die.
They do not necessarily kill
their host. Recent research
into chickpeas suggests that
although infections from such
fungi do increase during a dry
spell, the mortality rate of the
affected plants goes down
during a drought.A summer drought produces
only sparse growth of young barley
plants. Lack of moisture and too
much heat reduce their resistance
to fungi that attack their roots.Sensibly used,
mathematical models are
no more and no less than
tools for thinking about
things in a precise way.
Roy Anderson and
Robert MayUS_068-071_Ecological_Epidemiology.indd 70 12/11/18 6:24 PM