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 period.

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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