Estimating spatially adjusted temperature-dependent time-varying reproduction numbers for vector-borne diseases

Estimating the effective reproduction number is crucial for understanding and managing infectious disease outbreaks. For vector-borne diseases like dengue, transmission depends on environmental and spatial conditions: temperature affects the extrinsic incubation period in mosquitoes, altering transmission timing, while spatial proximity can lead to clusters of transmission. We integrated a temperature-dependent (TD) generation time (GT) distribution and a spatial decay function weighting transmission likelihood by distance into the Wallinga & Teunis estimation framework. Simulations compared scenarios where the true generation time for spatially adjusted disease cases were TD or temperature independent (TI), versus their corresponding model assumptions. Daily reproduction numbers (Rt) estimated were evaluated via percent error against true values. We found error to be predominantly driven by variance rather than bias, indicating that stochastic uncertainty in infector assignment was the primary driver of inaccuracies rather than systematic model miscalibration. Assuming a spatial weighting function assigning higher probabilities of transmission to geographically close infector-infectee pairs (Gaussian spatial decay) percent errors measuring deviation between estimated and true outperformed those of alternative spatial kernels. Mis-specifying temperature-dependence under a Gaussian spatial kernel yielded higher errors when the ground truth was TD (16-38% vs 36-58% deviation), and similar errors when it was TI (32-52% vs 35-56% deviation), indicating limited sensitivity to temperature dependence when it was not present in the underlying transmission process. Application to dengue case data in Singapore showed that spatially adjusted models produced more variable trajectories than time-series smoothing approaches, with Gaussian decay yielding more stable estimates than exponential decay and the TD model producing modest refinements, suggesting that explicitly modeling spatial heterogeneity and TD transmission dynamics increases responsiveness to even fluctuations in case counts. Our framework is robust across climates, shown by simulations using a broader temperature range, and suggests a useful application in retrospective analyses.