# Measuring real-time disease transmissibility with temperature-dependent generation intervals

## TL;DR

This paper introduces a new method to estimate disease transmissibility in real-time by adjusting for temperature effects, improving accuracy for diseases like dengue.

## Contribution

A novel temperature-dependent reproduction number (td-Rt) framework that dynamically updates generation intervals using real-time temperature data.

## Key findings

- td-Rt outperformed other methods in 54 of 72 simulation scenarios, especially in high temperature variability settings.
- td-Rt and the angular reproduction number (Ωt) showed 75% similarity when applied to Singapore dengue data.
- Incorporating temperature reduces bias in transmissibility estimates for climate-sensitive diseases.

## Abstract

Accurate real-time estimation of the effective reproduction number (Rt) is critical for infectious disease surveillance and response. In vector-borne diseases like dengue, temperature strongly influences disease transmission by affecting generation times. However, most existing Rt estimation methods assume a fixed generation interval, leading to biased estimates and unreliable assessments of transmission risk in settings with fluctuating temperatures. In this study, we proposed and evaluated a novel framework to estimate a temperature-dependent reproduction number (td-Rt) that dynamically updates the generation interval distribution based on observed temperature data. We obtained real-time estimates of td-Rt through an adapted Bayesian recursive filtering process. Using real and simulated data for a temperature-sensitive disease (dengue), we evaluated the performance of td-Rt against the typically used temperature-independent reproduction number (ti-Rt) and angular reproduction number (Ωt), which does not require specification of the generation interval. Simulated data was generated under varying patterns of underlying Rt and temperature datasets. Performance was evaluated by classification accuracy, defined by the proportion of instances where estimated Rt correctly identified whether the true Rt was above or below 1. We found that td-Rt generally outperformed ti-Rt and Ωt in classifying periods of epidemic growth. td-Rt achieved the highest classification accuracy in 54 of 72 simulation scenarios, with accuracy ranging from 37.1%–95.9%. td-Rt accuracy was highest in scenarios with greater temperature variability, surpassing other methods by up to 20%. With Singapore dengue case data, td-Rt and Ωt signals showed 75% similarity, highlighting Ωt’s potential as a complementary measure that is less sensitive to model assumptions. These findings highlight the importance of accounting for temperature in real-time transmissibility estimates, as temperature-driven variations in generation time can introduce model misspecification and bias. Incorporating temperature is especially crucial for climate-sensitive diseases like dengue. Future work could extend this framework to other pathogens and additional transmission-relevant covariates.

Many public health decisions rely on the effective reproduction number (Rt), the average number of new infections arising from a typical case at a given time. Standard estimators of Rt typically assume a fixed generation interval, which is the time between a primary and a secondary infection. For dengue, that interval shifts with temperature - warmer days shorten virus development inside mosquitoes and accelerate transmission. We developed a real-time estimator that updates the generation interval distribution daily using observed temperatures, then computes Rt from reported cases.

We evaluated this temperature-dependent estimator against two comparators: conventional estimator that holds the interval fixed and an interval-free statistic (the angular reproduction number). In simulations spanning temperature regimes, our method most often correctly classified transmission as growing or controlled (best in 54 of 72 scenarios), especially when temperatures varied widely. Applied to dengue in Singapore, the interval-free statistic showed potential as a complementary measure that is less sensitive to model assumptions.

By embedding temperature into estimation, we reduce bias from misspecified generation intervals and provide a practical, real-time tool for climate-sensitive infections. This framework can support timely and proportionate control decisions and is readily adaptable to other pathogens influenced by environmental conditions.