Modelling the temperature dependent extrinsic incubation period of West Nile Virus using Bayesian time delay models

West Nile Virus (WNV) is a mosquito-borne pathogen that primarily infects birds. Infections can spillover to humans and cause a spectrum of clinical symptoms, including WNV neuroinvasive disease. The extrinsic incubation period (EIP) is the time taken for a mosquito to become infectious following the ingestion of an infected blood meal. Characterising how the EIP varies with temperature is an essential part of predicting the impact and transmission dynamics of WNV. We re-analyse existing experimental data using Bayesian time delay models, allowing us to account for variation in how quickly individual mosquitoes developed disseminated WNV infections. In these experiments, cohorts of Culex pipiens mosquitoes were infected with WNV and kept under different temperature conditions, being checked for disseminated infection at defined timepoints. We find that EIPs are best described with a Weibull distribution and become shorter log-linearly with temperature. Under 18°C, less than 1% of infected Cx. pipiens had a disseminated infection after 5 days, compared to 9.73% (95% CrI: 7.97 to 11.54) at 25°C and 42.20% (95% CrI: 38.32 to 46.60) at 30°C. In the hottest experimental temperature treatment (32°C), the EIP₅₀ was estimated at 3.78 days (CrI: 3.42 to 4.15) compared to over 100 days in the coolest treatment (15°C). The variance of EIPs was found to be much larger at lower temperatures than higher temperatures, highlighting the importance of characterising the time delay distribution associated with the EIP. We additionally demonstrate a competitive advantage of WNV strain WN02 over NY99, where the former infects mosquitoes more quickly at colder temperatures than the latter. This research contributes crucial parameters to the WNV literature, providing essential insights for modellers and those planning interventions.