A note on observation processes in epidemic models

TL;DR

This paper examines how different assumptions about reporting timing in epidemic models affect the estimation of key parameters, highlighting potential biases and inaccuracies in disease modeling.

Contribution

It compares two common reporting assumptions in a simple SIR model and demonstrates their impact on parameter estimation accuracy.

Findings

Incorrect reporting assumptions bias the basic reproduction number estimates.

Different observation assumptions lead to varying confidence interval widths.

Mis-specification of reporting processes can mislead epidemic analysis.

Abstract

Many disease models focus on characterizing the underlying transmission mechanism but make simple, possibly naive assumptions about how infections are reported. In this note, we use a simple deterministic Susceptible-Infected-Removed (SIR) model to compare two common assumptions about disease incidence reports: individuals can report their infection as soon as they become infected or as soon as they recover. We show that incorrect assumptions about the underlying observation processes can bias estimates of the basic reproduction number and lead to overly narrow confidence intervals.