Application of Stieltjes parabolic partial differential equations to the population dynamics of Vespa Velutina

Abstract

In this work, we present a mathematical model based on Stieltjes differential equations to analyze the spread of Vespa Velutina. To this end, we start by defining a zero-dimensional model, which we later generalize to a two-dimensional model with a diagonalizable spatial differential operator. The advantage of considering Stieltjes differential equations lies in the fact that they allow us to naturally handle reproductive impulses due to the hatching of individuals and periods of inactivity resulting from hibernation. Finally, we present some numerical results obtained using real nest position data.