Simple models of influenza progression within a heterogeneous population

The focus of this ‘OR framing paper’ is to introduce the operations research (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 nonhomogeneous 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 nonmedical 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.