Abstract
We use an agent-based computer simulation designed to model the spread of the 1918 influenza pandemic to address the question of whether, and if so, when disease-related mortality should be included in an epidemic model. Simulation outcomes from identical models that differ only in the inclusion or exclusion of disease-related mortality are compared. Results suggest that unless mortality is very high (above a case fatality rate of about 18 % for influenza), mortality has a minimal impact on simulation outcomes. High levels of mortality, however, lower the percentage infected at the epidemic peak and reduce the overall number of cases because epidemic chains are shortened overall, and so a smaller proportion of the population becomes infected. Analyses also indicate that high levels of mortality can increase the chance of oscillations in disease incidence. The decision about whether to include disease-related mortality in a model should, however, take into account the fact that diseases such as influenza, that sicken a high proportion of a population, may nonetheless lead to high numbers of deaths. These deaths can affect a real population’s perception of and response to an epidemic, even when objective measures suggest the impact of mortality on epidemic outcomes is relatively low. Thus, careful attention should be paid to the possibility of such responses when developing epidemic control strategies.
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Notes
- 1.
Note that the fundamental death parameter in the model is the per-tick probability of mortality, \(\upmu \). This parameter can be converted to a case fatality rate (cfr), but the estimate of the latter is dependent on the value of the infectious period. The cfr can be calculated from the equation cfr \(= 1 - (1 - \upmu )^\mathrm{i}\), where i is the length of the infectious period; \((1 - \upmu )^\mathrm{i}\) gives the probability that an individual survives through the entire infectious period assuming a constant probability of death. Thus, one minus this quantity gives the probability of dying while infected. If \(\upmu =\) 0.01 and the infectious period is 18 ticks (3 days), the estimate for the 1918 pandemic influenza, the corresponding cfr is 16.5Â %, a value substantially higher than that commonly observed during influenza pandemics. The cfr for \(\upmu =\) 0.01 jumps to 26.0Â % if the infectious period is 5 days (as used in the sensitivity analyses).
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Sattenspiel, L., Miller, E., Dimka, J., Orbann, C., Warren, A. (2016). Epidemic Models With and Without Mortality: When Does It Matter?. In: Chowell, G., Hyman, J. (eds) Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases. Springer, Cham. https://doi.org/10.1007/978-3-319-40413-4_19
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