Special issue on Erice 'MathCompEpi 2015' Proceedings.

The mathematical and computational modelling of the spread of infectious diseases is a research field in applied mathematics that in the same time was both able to give an impetum to various areas of the dynamical systems theory and mathematical analysis, and to give an important contribution to the biological and epidemiological understanding of the spread of these diseases. National as well as Inter-National health authorities adopt routinely in the practice methodologies and concept that were born in the field of Mathematical and Computational Epidemiology (MCE) for assisting public Health decisions and policies. A major example is provided by the huge advancement in modelling and prediction on pandemic threats, and related preparedness plans for disease containment/mitigation. This operative influence in biomedicine is unparalleled in any other fields of mathematical and computational biology, with the possible exception of intra-host virus dynamics, whose models partly derive from those of MCE.