Modeling the impact of temperature and bird migration on the spread of West Nile virus

TL;DR

This study develops a spatial PDE model incorporating temperature effects, diffusion, and bird migration to understand and predict the spread of West Nile virus in Germany, aligning well with observed case data.

Contribution

The paper introduces a novel PDE-based spatial model that combines temperature-dependent parameters with diffusion and advection to simulate WNV spread.

Findings

Model accurately predicts WNV spread patterns in Germany.

Temperature and bird migration significantly influence virus distribution.

Advection is crucial for predicting hotspots in migratory bird pathways.

Abstract

West Nile virus (WNV) is a climate-sensitive mosquito-borne arbovirus circulating between mosquitoes of the genus Culex and birds, with a potential spillover to humans and other mammals. Recent trends in climatic change, characterized by early and/or prolonged summer seasons, increased temperatures, and above-average rainfall, probably facilitated the spread of WNV in Europe, including Germany. In this work, we formulate a spatial WNV model consisting of a system of parabolic partial differential equations (PDEs), using the concept of diffusion and advection in combination with temperature-dependent parameters, i.e., mosquito biting rate, extrinsic incubation, and mortality rate. Diffusion represents the random movement of both mosquitoes and hosts across space, while advection captures the directed movement of migratory birds. The model is first studied mathematically, and we show that it has non-negative, unique, and bounded solutions in time and space. Numerical simulations of the PDE model are performed using temperature data for Germany (2019 - 2024). Results obtained from the simulation showed a high agreement with the reported WNV cases among birds and equids in Germany. The observed spreading patterns from the year 2018 to 2022 and the year 2024 were mainly driven by temperature in combination with diffusion processes of hosts and vectors. Only during the year 2023, the additional inclusion of advection for migratory birds was important to correctly predict new hotspots in new locations in Germany.