Preface

Abstract

In the preface, we present a short overview of the papers included in the issue of Mathematical Modelling of Natural Phenomena 'Modelling in Ecology, Epidemiology and Evolution'.Mathematical Modelling in Ecology, Epidemiology and Evolution is a rapidly growing area of research, which takes advantage of recently developed mathematical and computational techniques as well as novel methods of data analysis. Interestingly, some classical fundamental notions, which have been included into almost all standard student textbooks on mathematical biology (e.g. population fitness, net reproductive number, role of the shape of functional responses in stability of food webs, etc.), are currently being revisited. This special Issue of the Journal is focused on few such topics. In particular, the contributions to the Issue address recent advances in our understanding of the net reproduction function in structured populations, stability of tri-trophic food webs, evolutionary fitness, models of co-infection in epidemiology and economic-demographic models. We should stress, however, that most of the contributions here are not restricted to only one of the mentioned topics but combine several of them, so it may be hard to assign a particular article to a single topic.In his work [10], Farkas revisits the fundamental notion of the net reproduction function in population models in the case the population is structured. Construction of a net reproduction function in physiologically and agestructured populations is crucial for understanding stability of their stationary states [11][12][13]. The idea of [10] consists in converting the initial non-linear structured population model into a family of linear ones, where each linear model describes population dynamics in a constant environment. Mathematically, the theory is based on the recently discovered link between the spectral bound of an unbounded operator and the spectral radius of a corresponding bounded operator.In their work, Zincenko et al. explore possible scenarios of the current growth of the human population across continents which is coupled with dynamics of family wealth and immigration rates [25]. This approach is known as economic-demographic modelling and it is currently increasing its popularity due to the need to explain and predict the observed population decline in some parts of the World such as, for example, Western Europe. The model is described by a system of two ODEs and it is an extension of the previous work by the same co-authors