Forecasting Epidemics Through Nonparametric Estimation of Time-Dependent Transmission Rates Using the SEIR Model

Abstract

Deterministic and stochastic methods relying on early case incidence data for forecasting epidemic outbreaks have received increasing attention during the last few years. In mathematical terms, epidemic forecasting is an ill-posed problem due to instability of parameter identification and limited available data. While previous studies have largely estimated the time-dependent transmission rate by assuming specific functional forms (e.g., exponential decay) that depend on a few parameters, here we introduce a novel approach for the reconstruction of nonparametric time-dependent transmission rates by projecting onto a finite subspace spanned by Legendre polynomials. This approach enables us to effectively forecast future incidence cases, the clear advantage over recovering the transmission rate at finitely many grid points within the interval where the data are currently available. In our approach, we compare three regularization algorithms: variational (Tikhonov's) regularization, truncated singular value decomposition (TSVD), and modified TSVD in order to determine the stabilizing strategy that is most effective in terms of reliability of forecasting from limited data. We illustrate our methodology using simulated data as well as case incidence data for various epidemics including the 1918 influenza pandemic in San Francisco and the 2014-2015 Ebola epidemic in West Africa.

Phase-adjusted estimation of the number of Coronavirus Disease 2019 cases in Wuhan, China

“…We employed an infectious disease dynamics model (SEIR model) for the purpose of modeling and predicting the number of COVID-19 cases in Wuhan, China. The model is a classic epidemic method to analyze the infectious disease, which has a definite latent period, and has proved to be predictive for a variety of acute infectious diseases in the past such as Ebola and SARS 22,[26][27][28][29][30][31] . Application of the mathematical model is of great guiding significance to assess the impact of isolation of symptomatic cases as well as observation of asymptomatic contact cases and to promote evidence-based decisions and policy.…”

Phase-adjusted estimation of the number of Coronavirus Disease 2019 cases in Wuhan, China

“…The model is a classic epidemic method to analyze the infectious disease which has a definite latent period, and has proved to be predictive for a variety of acute infectious diseases in the past such as Ebola and SARS. 22,[26][27][28][29][30][31] Application of the mathematical model is of great guiding significance to assess the impact of isolation of symptomatic cases as well as observation of asymptomatic contact cases and to promote evidence-based decisions and policy.…”

Quantifying the effect of quarantine control in Covid-19 infectious spread using machine learning

“…The classic SEIR epidemiological model has been employed in a number of prior studies, such as the SARS outbreak Fang et al (2006); Saito et al (2013); Smirnova et al (2019) as well as the Covid outbreak Read et al (2020); Tang et al (2020); Wu & Leung (2020). The entire population is divided into four sub-populations: susceptible S; exposed E; infected I; and recovered R. The sub-populations' evolution is governed by the following system of four coupled nonlinear ordinary differential equations (Smirnova et al 2019;Wang et al 2020)…”

“…We leverage this model to analyze and compare the role of quarantine control policies employed in Wuhan, Italy, South Korea and USA, in controlling the virus effective reproduction number R t Read et al 2020;Tang et al 2020;Li et al 2020a;Wu & Leung 2020;Kucharski et al 2020;Ferguson et al 2020). In the original model, known as SEIR (Fang et al 2006;Saito et al 2013;Smirnova et al 2019), the population is divided into the susceptible S, exposed E, infected I and recovered R groups, and their relative growths and competition are represented as a set of coupled ordinary differential equations. The simpler SIR model does not account for the exposed population E. These models cannot capture the largescale effects of more granular interactions, such as the population's response to social distancing and quarantine policies.…”