Forecasting seasonal influenza with a state-space SIR model

Abstract

Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention’s influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are only partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.

An epidemiological forecast model and software assessing interventions on COVID-19 epidemic in China

“…Note that the explicit solution to the above system (4) of ordinary differential equations is unavailable. Following [23], we invoke the fourth-order Runge-Kutta(RK4) approximation, resulting in an approximate of f pθ t´1 , β, γq as follows:…”

Predication of Pandemic COVID-19 situation in Maharashtra, India

“…Previously there are several mathematical models reported [8]. The SIR model is simple and effective model which can give the prediction of different pandemic situation [9].…”

Evaluating the ALERT algorithm for local outbreak onset detection in seasonal infectious disease surveillance data

“…Many approaches have been used to detect and characterize transitions between endemic and epidemic incidence patterns. For the stochastic prediction of infectious disease spread between individuals, mechanistic models (such as agent‐based and compartmental susceptible‐infectious‐recovered, among others) are well developed and have been implemented as stand‐alone forecasting models . Autoregressive integrated moving average (ARIMA) or seasonal ARIMA (SARIMA) models are well‐known statistical approaches for modeling time‐series, such as infectious disease case counts, that correlate with past observations .…”

“…For the stochastic prediction of infectious disease spread between individuals, mechanistic models (such as agent-based 7 and compartmental susceptible-infectious-recovered, 8 among others) are well developed and have been implemented as stand-alone forecasting models. 9,10 Autoregressive integrated moving average (ARIMA) or seasonal ARIMA (SARIMA) models are well-known statistical approaches for modeling time-series, such as infectious disease case counts, that correlate with past observations. 11,12 Both statistical and mechanistic models have been used successfully in infectious disease forecasting.…”