Modelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special Issue

Abstract

Mathematical modelling in ecology, epidemiology and eco-epidemiology is a vast and constantly growing research field. This is perhaps unsurprising since mathematical models can provide a wide-ranging exploration of the biological problem without a need for experiments which are usually expensive and can be potentially dangerous to ecosystems. The current Special Issue of MMNP presents recent findings and developments in the following areas of theoretical ecology and epidemiology: (i) revealing the biological processes behind observed complex patterns; (iii) modelling the role of dispersal and spatial heterogeneity in species persistence; (ii) applications of bifurcation theory in population dynamics and epidemiology; (iv) the role of selection in self-replicating biological and ecological systems; (v) sensitivity, predictability and control of biological models in a noisy environment. It is important to emphasize that many of the contributions to this issue are not limited to one of the above topics, but rather lie at the interface of several of them.The work of D. Ahmed and S. Petrovskii [1] studies the movement of insects whose spatial dispersal is a random variable and is described by a certain probability distribution. Understanding the mechanisms of insects movement behaviour is a highly relevant problem from the practical point of view, since it can help us to correctly interpret the results of insect trapping, which is the basis of many current pest monitoring programs [17]. There is a lively ongoing debate in the literature regarding the possibility of Lévy-type movement behaviour by animals, as opposed to the Brownian motion, and various mechanisms have been proposed to explain the observed patterns [3,16,24]. Ahmed and Petrovskii provide an alternative description of Levy-type movement by introducing time-dependent diffusivity. In particular, the authors claim that the trap counts of insects whose dynamics is given by an example of a Lévy-type distribution -a Cauchy type random walk -can be successfully modelled via a different movement pattern: classical Brownian motion with a time-dependent diffusion coefficient. Thus, the authors provide an excellent example of how two completely different mechanisms can describe the same pattern of field observations.Among the central topics in theoretical ecology is the understanding of the role of space in population dynamics and species persistence across different time scales [6,7,11,12]. In this issue, three contributions [2,4,20] directly focus on the role of space in population dynamics.Modelling the mechanisms of biological aggregation and patchiness is a pertinent topic in theoretical ecology, with various models suggested [6,14,19]. In their work, R. Eftimie and A. Coulier [4] explore the effects of communication between organisms on the formation and structure of large biological agc EDP Sciences, 2015 Article published by EDP Sciences and available at