Numerical study of discretization algorithms for stable estimation of disease parameters and epidemic forecasting

Aurelie Akossi; Gerardo Chowell-Puente; Alexandra Smirnova; Aurelie Akossi; Gerardo Chowell-Puente; Alexandra Smirnova

doi:10.3934/mbe.2019182

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 3674-3693. doi: 10.3934/mbe.2019182

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Numerical study of discretization algorithms for stable estimation of disease parameters and epidemic forecasting

1.
Department of Mathematics and Statistics, Georgia State University, Atlanta, USA
2.
Department of Population Health Sciences, Georgia State University, Atlanta, USA

Received: 20 February 2019 Accepted: 17 April 2019 Published: 25 April 2019

In this paper we investigate how various discretization schemes could be incorporated in regularization algorithms for stable parameter estimation and forecasting in epidemiology. Specifically, we compare parametric and nonparametric discretization tools in terms of their impact on the accuracy of recovered disease parameters as well as their impact on future projections of new incidence cases. Both synthetic and real data for 1918 ``Spanish Flu" pandemic in San Francisco are considered. The discrete approximation of a time dependent transmission rate is combined with the Levenberg-Marquardt algorithm used to solve the nonlinear least squares problem aimed at fitting the model to limited incidence data for an unfolding outbreak. Our simulation study highlights the crucial role of a priori information at the early stage of an epidemic in mitigating the lack of stability in over-parameterized models with insufficient data. Fortunately, our results suggest that a balanced combination of problem-oriented regularization techniques is one way in which scientists can still draw useful conclusions about system parameters and in turn generate reliable forecasts that policy makers could use to guide control interventions.
- disease forecasting,
- parameter estimation,
- regularization
Citation: Aurelie Akossi, Gerardo Chowell-Puente, Alexandra Smirnova. Numerical study of discretization algorithms for stable estimation of disease parameters and epidemic forecasting[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3674-3693. doi: 10.3934/mbe.2019182

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Abstract

In this paper we investigate how various discretization schemes could be incorporated in regularization algorithms for stable parameter estimation and forecasting in epidemiology. Specifically, we compare parametric and nonparametric discretization tools in terms of their impact on the accuracy of recovered disease parameters as well as their impact on future projections of new incidence cases. Both synthetic and real data for 1918 ``Spanish Flu" pandemic in San Francisco are considered. The discrete approximation of a time dependent transmission rate is combined with the Levenberg-Marquardt algorithm used to solve the nonlinear least squares problem aimed at fitting the model to limited incidence data for an unfolding outbreak. Our simulation study highlights the crucial role of a priori information at the early stage of an epidemic in mitigating the lack of stability in over-parameterized models with insufficient data. Fortunately, our results suggest that a balanced combination of problem-oriented regularization techniques is one way in which scientists can still draw useful conclusions about system parameters and in turn generate reliable forecasts that policy makers could use to guide control interventions.

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