Modeling the Seasonal Epidemic - Part 3

In the first part of this series we discussed the existence of short- and long-term seasonality in epidemiology, and its impact on disease transmission; in the second part, we addressed ways in which to incorporate these seasonal effects into mathematical models. For this final installment well be looking into the implications of seasonality and longer-term periodicity for the control and eradication of infectious diseases.

From a public health perspective, an important - though often unattainable - goal is the eradication of a given infectious disease, that is, the local (or global) extinction of the pathogen at which point, barring re-introduction of the disease, transmission can no longer occur. Mathematically speaking there are two types of extinction: deterministic and stochastic. Deterministic extinction occurs when the species population (in this case, the virus itself) gradually and irretrievably approaches zero, due to the removal of some essential resource or when something lethal is introduced into the environment. In the case of infectious diseases, the "essential resource" may be represented by the susceptible host population, while routine vaccination or continuous vector control methods may represent the "lethal introduction".

Stochastic extinctions, on the other hand, are due to random variations that suddenly drive the infectious disease reservoir to zero. From the perspective of infectious diseases, these "random variations" may be vaccination campaigns, for example, or coordinated simultaneous mass insecticide applications over the entire affected area.

This second type of extinction becomes extremely important as transmission approaches very low levels due to gradual improvements in routine vaccination and other control measures - the proper combination of interventions timed just right with respect to short- and long-term disease fluctuations can be the tipping point which ends transmission.

Complications can arise when identifying the stochastic extinction of a disease, however, as what may have appeared to be eradication may simply have been a low point in normal longer-term fluctuations. The danger here is that interventions such as vaccination, vector control, etc. may be terminated too soon, and when the long-term periodicity cycles back around the susceptible population will have built back up again and a new outbreak will be inevitable. The implementation of a "certification period" can help prevent this catastrophe, by requiring the maintenance of zero transmission for multiple years in a row - longer than the anticipated long-term seasonality - in order to rule out regular fluctuations.

As we have seen, periodicity in disease transmission offers both opportunities and challenges in the implementation of interventions. Periods of very high transmission are when greatest media attention is on disease control - however this may be the most challenging time to implement interventions. For example, campaign vaccination during measles outbreaks can serve to create a "fire-break" around the majority of cases, however transmission will continue until it burns through all available susceptible populations due to the challenges in attaining 100% vaccination coverage (even assuming the vaccine is 100% effective immediately). From the perspective of vector-borne disease, during West Nile Virus high season is when most people think of mosquito control, however this same season also corresponds with the highest populations of adult mosquitoes and the greatest level of difficulty in controlling these populations. Nevertheless, challenging as these high transmission periods may be, implementing disease control efforts is still necessary to minimize morbidity and mortality during outbreaks.

In contrast, low transmission times may often be the best opportunity to make strides to eliminate disease transmission altogether. Taking advantage of the seasons when adult mosquito populations are near their minimum, and the bulk of the population is in egg or larva form, to employ campaigns to destroy breeding sites and apply larvicide and ovicide to risky areas can impact vector populations significantly enough that the following transmission season may show dramatic decreases in cases. Employing such controls over multiple consecutive years may be enough to drive transmission to zero provided sufficient protection is in place to prevent re-importation of the disease into the area.

Similarly, ramping up routine vaccination against direct-transmissible diseases such as measles during low periods has the potential to deprive incoming seasonal epidemics of sufficient susceptible populations to sustain transmission. Continuing this improvement in vaccination coverage while making efforts to immunize hard-to-reach populations, as with continued vector control efforts, can have the potential to eliminate local disease transmission altogether.

Of course, the challenge here is that the public may be less interested in disease interventions during the off-seasons when transmission is already low anyways - this is the case during regular seasonal lows, but also (and more significantly) when morbidity and mortality have already been driven down significantly by previous efforts. It is challenging to continue disease control in the absence of disease - which is why the eradication certification period is so essential. If transmission can be held down long enough to confirm elimination, at that point decisions can be made as the cost-benefit of easing up on interventions.

From this perspective mathematical modeling can be a marvelous tool to communicate the potential risks and benefits associated with various disease interventions and their appropriate timing. Of particular utility in this type of setting is a comparative analysis of the long-term transmission patterns when consistent interventions are applied or discontinued, and to evaluate the appropriate duration of the certification period. MathEcology has more than a decade of experience in this kind of modeling to assess short- and long-term transmission patterns and their implications for disease control. If your organization is assessing possible future policies for public health and infectious disease control, contact us - wed be happy to help!

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