Evaluating the connectivity, continuity and distance norm in mathematical models for community ecology, epidemiology and multicellular pathway prediction

Abstract

Abstract The main global threats of the biosphere on our planet, such as a global biodiversity impairment, global health issues in the developing countries, associated with an environmental decay, unnoticed in previous eras, the rise of greenhouse gasses and global warming, urge for a new evaluation of the applicability of mathematical modelling in the physical sciences and its benefits for society. In this paper, we embark on a historical review of the mathematical models developed in the previous century, that were devoted to the study of the geographical spread of biological infections. The basic notions of connectivity, continuity and distance norm as applied by successive bio-mathematicians, starting with the names of Volterra, Turing and Kendall, are highlighted in order to demonstrate their usefulness in several new areas of bio-mathematical research. These new areas include the well-known fields of community ecology and epidemiology, but also the less well-known field of multicellular pathway prediction. The biological interpretation of these abstract mathematical notions, as well as the methodological criteria for these interpretative schemes and their corroboration with empirical evidence are discussed. In particular, we will focus on the boundedness norm in polynomial Lyapunov functions and its application in Markovian models for community assembly and in models for cellular pathways in multicellular systems. Finally, the usefulness of hybrid mathematical modelling in miscellaneous biological, environmental and public health issues will be discussed. .