Locally temperature - driven mathematical model of West Nile virus spread in Germany

West Nile virus (WNV) is an arthropod-borne virus (arbovirus) transmitted by the bites of infected mosquitoes. WNV can also infect horses and humans, where it may cause serious illness and can be fatal. Birds are the natural reservoir, and humans, equines and probably other mammals are dead-end hosts. In 2018, WNV occurred for the first time in Germany, affecting birds and horses. Seroconversion of an exposed veterinarian has also been reported. It is therefore of importance to evaluate the circumstances, under which WNV may establish in Germany as a whole or in particular favourable regions. In our current work, we formulate a dynamic model to describe the spreading process of West Nile virus in the presence of migratory birds. To investigate the possible role of migratory birds in the dissemination of WNV in Germany, we include the recurring presence of migratory birds through a mechanistic ordinary differential equations (ODE) model system. We also perform a sensitivity analysis of the infection curves. Seasonal impacts are also taken into consideration. As result, we present an analytical expression for the basic reproduction number R0. We find that after introducing WNV into Germany, R0 will be above the critical value in many regions of the country. Furthermore, we observe that in the south of Germany, the disease reoccurs in the following season after the introduction. We include a potential distribution map associated with WNV cases in Germany to illustrate our findings in a spatial scale.