# Mapping Incidence and Prevalence Peak Data for SIR Modeling Applications

## TL;DR

This paper introduces a method to improve SIR model accuracy by incorporating peak hospital incidence data, enhancing epidemic forecasting.

## Contribution

A new method is proposed to integrate peak incidence data into SIR models using a system of equations for better parameter estimation.

## Key findings

- Using peak hospital incidence data stabilizes SIR model fits and improves forecasting accuracy.
- Misspecifying prevalence data as incidence leads to noticeable loss in model accuracy.
- The updated Dirichlet-Beta State Space framework shows practical improvements in accuracy and computation speed.

## 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.