Mapping Incidence and Prevalence Peak Data for SIR Modeling Applications

Abstract

Infectious disease modeling and forecasting have played a key role in helping assess and respond to epidemics and pandemics. Recent work has leveraged data on disease peak infection and peak hospital incidence to fit compartmental models for the purpose of forecasting and describing the dynamics of a disease outbreak. Incorporating these data can greatly stabilize a compartmental model fit on early observations, where slight perturbations in the data may lead to model fits that forecast wildly unrealistic peak infection. We introduce a new method for incorporating historic data on the value and time of peak incidence of hospitalization into the fit for a Susceptible-Infectious-Recovered (SIR) model by formulating the relationship between an SIR model's starting parameters and peak incidence as a system of two equations that can be solved computationally. We demonstrate how to calculate SIR parameter estimates - which describe disease dynamics such as transmission and recovery rates - using this method, and determine that there is a noticeable loss in accuracy whenever prevalence data is misspecified as incidence data. To exhibit the modeling potential, we update the Dirichlet-Beta State Space modeling framework to use hospital incidence data, as this framework was previously formulated to incorporate only data on total infections. This approach is assessed for practicality in terms of accuracy and speed of computation via simulation.

Keywords: Compartmental Models; Disease Forecasting; Hospital Incidence; Prevalence.

Fig. 1

Three SIR models with incidence and starting values $S_0=0.9$ and $I_0=R_0=0.05$. While it is possible for incidence to be greater than prevalence, this is not of practical interest

Fig. 2

MAE of estimates on $\rho$ using (correctly) specified incidence data as incidence and using (incorrectly) specified prevalence data as incidence

Fig. 3

The DBSSM fit to the 2010 US nationwide influenza outbreak starting at week 13 (left column) and week 22 (right column). The dark grey regions correspond to the 95% credible regions of the posterior density while the light grey regions correspond to the 95% prediction intervals. The top plots reproduces the forecasting model of Osthus et al. (2017), which incorrectly treated incidence data as though it were prevalence data. The bottom plots fit the forecasting model described in Section 3, which correctly treats incidence data as incidence data. Earlier on in the outbreak, the model developed in this paper has a tighter prediction interval. The forecasts starting at week 22 are quite similar

Fig. 4

Infection rates, recovery rates, and reproductions numbers drawn from the Gibbs sampler used to fit the DBSSM using both specifications of incidence data. Using incidence data specified as prevalence leads to different estimates for these parameters. These values were calculated using the data up through timepoint 22 ($t^{\prime }=22$)

Fig. 5

The DBSSM fit to the 2014 US nationwide influenza outbreak starting at week 13 (left column) and week 22 (right column). The dark grey regions correspond to the 95% credible regions of the posterior density while the light grey regions correspond to the 95% prediction intervals. The top plots reproduces the forecasting model of Osthus et al. (2017), which incorrectly treated incidence data as though it were prevalence data. The bottom plots fit the forecasting model described in Section 3, which correctly treats incidence data as incidence data

Fig. 6

The DBSSM fit to the 2014 US nationwide influenza outbreak starting at weeks 8-12 compared against the model from Hickmann et al. (2015). The top plot visualizes predictions of PIV from each model; the bottom plot visualizes predictions of PIT

Fig. 7

The DBSSM fit to the 2010 US nationwide influenza outbreak starting at week 11 (left column) and week 14 (right column). The dark grey regions correspond to the 95% credible regions of the posterior density while the light grey regions correspond to the 95% prediction intervals. The top plots reproduces the forecasting model of Osthus et al. (2017), which incorrectly treated incidence data as though it were prevalence data. The bottom plots fit the forecasting model described in Section 3, which correctly treats incidence data as incidence data