# Robust Inverse Reconstruction of Time-Varying Transmission Rates Across Model Structures and Incidence Forms

## TL;DR

This paper shows that estimates of changing transmission rates are reliable even when using different disease models and assumptions about how diseases spread.

## Contribution

The study demonstrates robustness of inverse transmission rate reconstructions across various model structures and incidence forms.

## Key findings

- Transmission rate reconstructions for influenza show consistent timing and amplitude shifts across models.
- Measles transmission rates under saturated incidence preserve the rise-and-fall patterns seen with mass action.
- Inverse reconstructions are robust to typical structural and incidence choices in disease modeling.

## Abstract

Accurate, decision-ready estimates of time-varying transmission rates are critical, yet thought to be sensitive to model specification. We test this sensitivity by applying a continuous inverse method to weekly influenza and measles data, comparing reconstructions across eight common compartmental structures (SIS/SIR/SEIS/SEIR and vaccinated variants) and across five incidence forms (mass action vs. saturated). Timing and ordering of peaks and troughs in the transmission rates are highly consistent across influenza models, with amplitude shifts matching mechanistic expectations (attenuation with vaccination; smoothing with latent periods). For measles, we show that the transmission rates under saturated incidence preserve the rise-and-fall ordering observed under mass action and provide a sufficient condition ensuring matched monotonicity. These results indicate inverse transmission rate reconstructions are robust to typical structural and incidence choices, supporting their routine use for interpreting transmission dynamics, short-term forecasting, and intervention assessment.