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Towers, S., Vogt Geisse, K., Chia-Chun, T., Han, Q., & Feng, Z. L. (2012). The Impact Of School Closures On Pandemic Influenza: Assessing Potential Repercussions Using A Seasonal Sir Model. Math. Biosci. Eng., 9(2), 413–430.
Abstract: When a new pandemic influenza strain has been identified, mass-production of vaccines can take several months, and antiviral drugs are expensive and usually in short supply. Social distancing measures, such as school closures, thus seem an attractive means to mitigate disease spread. However, the transmission of influenza is seasonal in nature, and as has been noted in previous studies, a decrease in the average transmission rate in a seasonal disease model may result in a larger final size. In the studies presented here, we analyze a hypothetical pandemic using a SIR epidemic model with time- and age-dependent transmission rates; using this model we assess and quantify, for the first time, the the effect of the timing and length of widespread school closures on influenza pandemic final size and average peak time. We find that the effect on pandemic progression strongly depends on the timing of the start of the school closure. For instance, we determine that school closures during a late spring wave of an epidemic can cause a pandemic to become up to 20% larger, but have the advantage that the average time of the peak is shifted by up to two months, possibly allowing enough time for development of vaccines to mitigate the larger size of the epidemic. Our studies thus suggest that when heterogeneity in transmission is a significant factor, decisions of public health policy will be particularly important as to how control measures such as school closures should be implemented.
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Towers, S., Vogt Geisse, K., Zheng, Y., & Feng, Z. (2011). Antiviral treatment for pandemic influenza: Assessing potential repercussions using a seasonally forced SIR model. J. Theor. Biol., 289, 259–268.
Abstract: When resources are limited, measures to control an incipient influenza pandemic must be carefully considered. Because several months are needed to mass-produce vaccines once a new pandemic strain has been identified, antiviral drugs are often considered the first line of defense in a pandemic situation. Here we use an SIR disease model with periodic transmission rate to assess the efficacy of control strategies via antiviral drug treatment during an outbreak of pandemic influenza. We show that in some situations, and independent of drug-resistance effects, antiviral treatment can have a detrimental impact on the final size of the pandemic. Antiviral treatment also has the potential to increase the size of the major peak of the pandemic, and cause it to occur earlier than it would have if treatment were not used. Our studies suggest that when a disease exhibits periodic patterns in transmission, decisions of public health policy will be particularly important as to how control measures such as drug treatment should be implemented, and to what end (i.e.; towards immediate control of a current epidemic peak, or towards potential delay and/or reduction of an anticipated autumn peak). (C) 2011 Elsevier Ltd. All rights reserved.
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