Modeling the Seasonal Epidemic - Part 1
It’s fairly easy to recognize that influenza has a "season" - a time of year in which
transmission is exceptionally high, counterbalanced by the opposite time of year in
which incidence is low to almost-nil in a given location. This is the case with a wide
variety of diseases - vector-borne, food-borne, water-borne, respiratory, parasitic,
and so on. In general, these annual oscillations can be boiled down to two main causes:
behavioral and environmental.
In human communities, behavioral forces for seasonality can be associated with
significantly increased contact rates among children associated with school sessions,
clustering of people and activities indoors during inclement weather, increased travel
during holidays and vacations, contact with contaminated water bodies during summer
break, and so on.
Environmental causes for seasonality in disease transmission are generally
accounted for by weather conditions. Vector populations such as mosquitoes and ticks
require a certain range of temperature and moisture for reproduction. Certain pathogens
will not survive at temperature or humidity extremes, while others experience explosive
growth when the water temperature is just right.
The yearly seasonality described above is short-term - the variations occur
within a single year, and annual patterns in behavioral and environmental forcers can
be discerned fairly directly.
There are also, however, longer-term patterns that can be observed in the
transmission of many diseases. Measles, for example, shows larger oscillations
occurring on a 3-year scale, while pertussis (whooping cough) shows similar oscillations
over a 4-year period. Malaria has been known to show resurgence patterns that vary
depending on location, and cholera outbreaks have been observed to cycle over a 2-4 year
These longer term oscillations occurring over multiple years may be influenced by a
number of factors. The influenza virus, for example, is known to mutate significantly from
year to year, and thus some years will produce higher incidence than others. There may
also be a build-up of susceptible individuals in the host population - either a change
in birth rates, or a dramatic influx of immigrants, or even a decrease in vaccination
rates can increase the susceptible load. Some diseases also exhibit waning immunity,
either post-vaccination or following natural infection, so that previously protected
individuals get recycled back into the at-risk population. Regardless of the cause, a
significant increase in the number of susceptible individuals can easily result in
dramatic disease outbreaks following even the tiniest spark of transmission. After such
an outbreak acquired immunity in recovered or vaccinated individuals will provide
protection for a time, which will then wane and return these individuals to
susceptibility, and the cycle continues.
Protracted variations in disease transmission may also be traced to long term
climate fluctuations such as El Niño and La Niña, which impact local temperatures,
rainfall and humidity over multiple years, thus driving vector population growth and
pathogen survival in the environment.
When modeling disease transmission over simulation periods longer than a year,
it is important to address the presence of single- and multi-year periodicity in order
to capture the varying impact of the disease on the subject population. These
oscillations also provide opportunities - and obstacles - for disease control. Over the
next several issues we will continue covering seasonality in disease models, starting
next month with general model forms.
In the meantime, if your organization is struggling with modeling seasonal
epidemics and their control, give MathEcology a call - we’d be happy to help!
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