A temperature-driven diffusion model of Usutu virus spread in Germany with spillover into neighbouring countries
Usutu virus (USUV) is a flavivirus of the Japanese encephalitis complex transmitted between \textit{Culex} mosquitoes and birds, a transmission pattern similar to that of the West Nile virus (WNV). In Germany, the first case of USUV was detected in 2010 in mosquitoes collected in the town of Weinheim, and by 2018 the virus had spread to almost the entire country. Interestingly, the infection front exhibited a clockwise rotational spread pattern throughout the years, a pattern completely different from that of the WNV. This clockwise progression corresponded closely with the spatial temperature gradient, suggesting that warmer regions probably facilitated faster viral amplification and onward transmission. Understanding the drivers that influence the spreading patterns of arboviruses is important as it guides surveillance and implementation of control strategies. In this study, we develop a reaction-diffusion partial differential equation (PDE) model to investigate the spatial spread of USUV in Germany within an extended domain that includes some neighbouring countries (Belgium, the Netherlands, and Luxembourg), thereby capturing cross-border transmission processes. Mosquito parameters, i.e., extrinsic incubation rate, mortality and biting rates, are temperature-driven, as temperature plays an important role in the activity of mosquitoes. Our model qualitatively reproduced the main spatial trends of USUV in Germany and surrounding countries. The heterogeneous spread pattern arises from the interplay of diffusion and spatially varying temperature, which together may influence determine regions with higher transmission potential.