Simple Models of Influenza Progression within a Heterogeneous Population June 15, 2007
Posted by Michael Trick in : Influenza 2007 , comments closedIn the May-June, 2007, issue of Operations Research, Professor Richard C. Larson looks at the role that operations research can place in one of the most pressing issues of our time: handling a possible influenza pandemic. In his abstract, he outlines his goals:
The focus of this ‘OR framing paper’ is to introduce the OR community to the need for new mathematical modeling of an influenza pandemic and its control. By reviewing relevant history and literature, one key concern that emerges relates to how a population’s heterogeneity may affect disease progression. Another is to explore within a modeling framework ‘social distancing’ as a disease progression control method, where social distancing refers to steps aimed at reducing the frequency and intensity of daily human to human contacts. To depict social contact behavior of a heterogeneous population susceptible to infection, a non-homogeneous probabilistic mixing model is developed. Partitioning the population of susceptibles into subgroups, based on frequency of daily human contacts and infection propensities, a stylistic difference equation model is then developed depicting the day-to-day evolution of the disease. This simple model is then used to develop a preliminary set of results. Two key findings are (1) early exponential growth of the disease may be dominated by susceptibles with high human contact frequencies and may not be indicative of the general population’s susceptibility to the disease; and (2) social distancing may be an effective non-medical way to limit and perhaps even eradicate the disease. Much more decision-focused research needs to be done before any of these preliminary findings may be used in practice.
In the paper, Prof. Larson provides a number of simple, yet plausible, difference equations and uses them to model influenza spread in and environment with a population that is heterogeneous in the amount of social interaction made. In his conclusions, Prof. Larson describes his view of the rationale and importance of this research:
No one knows how or when the next pandemic influenza will emerge and what its intrinsic properties will be. If history can be a guide, the next influenza will have ‘emergent properties,’ meaning that it will mutate during the course of the epidemic and its intrinsic properties will evolve accordingly. Any mathematical model of the disease and its control is bound to be incorrect. But we are not seeking multi-decimal numerical accuracy but rather insights on how to limit the spread of the disease. We firmly believe that fresh eyes from the OR community can play a significant role in this quest.
You can read the full paper here along with its online companion.
The editors of this journal have invited three individuals and groups to comment on Prof. Larson’s paper.
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