Abstract
Mathematical models have the potential to be useful to forecast the course of epidemics. In this chapter, a family of logistic patch models are preliminarily evaluated for use in disease modeling and forecasting. Here we also derive the logistic equation in an infectious disease transmission context based on population behavior and used it for forecasting the trajectories of the 2013–2015 Ebola epidemic in West Africa. The logistic model is then extended to include spatial population heterogeneity by using multi-patch models that incorporate migration between patches and logistic growth within each patch. Each model’s ability to forecast epidemic data was assessed by comparing model forecasting error, parameter distributions and parameter confidence intervals as functions of the number of data points used to calibrate the models. The patch models show an improvement over the logistic model in short-term forecasting, but naturally require the estimation of more parameters from limited data.
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Notes
- 1.
Results from Efron and Tibshirani [10] suggest that accurate results for confidence intervals can be obtained from 1000 bootstrap samples. For standard errors this number is reduced to 200.
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This work is partially supported by NSF grant DMS-1518529.
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Pell, B., Baez, J., Phan, T., Gao, D., Chowell, G., Kuang, Y. (2016). Patch Models of EVD Transmission Dynamics. 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_10
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DOI: https://doi.org/10.1007/978-3-319-40413-4_10
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