Modelling Large Scale Invasion of <i>Aedes aegypti </i>and <i>Aedes albopictus</i> Mosquitoes

Abstract

The principle aim of this work is to simulate the invasion of two invasive mosquito species Aedes aegypti and Aedes albopictus in central Europe at a landscape scale. The spatial-temporal dynamics of invasion is investigated in dependence of predation pressure, seasonal variation of ambient temperature as well as human population density. The introduction of temperature dependent entomological parameters enables the simulation of seasonal pattern of population dynamics. The influence of temperature, predation pressure and human population density on invasion is studied in one-dimensional cases. In two dimensions, georeferenced parameters such as annual mean temperature and human population density are prepared by a geographical information system and introduced into the finite element tool COMSOL Multiphysics. The results show that under the current temperature, central Europe cannot become a permanent breeding region for Aedes aegypti. However, southwest Germany especially the regions along the Upper Rhine Valley may provide suitable habitats for the permanent establishment of Aedes albopictus. An annual temperature rise of two degrees would lead to dramatic increase of invasion speed and extension range of Aedes albopictus.

Lie Symmetries and Solutions of Reaction Diffusion Systems Arising in Biomathematics

“…Motivated by several papers concerned with the mathematical models describing the dispersal dynamics of the Aedes Aegypt mosquitoes (main vector of dengue, xicungunia, zika, and other similar diseases) [1][2][3] as well as Anopheles [4], in two previous papers [5,6], the following parabolic reaction-diffusion-advection system has been considered    u t = ( f (u)u x ) x + g(u, v, u x ),…”

“…It is useful stressing that even though the symmetry approach provides a methodological way to derive exact solutions of non linear system, the symmetry classification with respect to arbitrary constitutive functions, that appear in (2), could suggest special forms of them of a certain interest for the phenomena under consideration. Even though in the last decades several studies have been devoted to reaction diffusion equations only few papers have been devoted to the symmetry classification of non-linear systems like (1) or (2) with advection (convection) terms. It is possible instead to find, as in [14], a complete description of Lie symmetries for a class of diffusion systems with convection terms in both equations.…”