Comments on Heterogeneity Aspects in Mathematical Epidemiology

To begin with I remark generally upon two important aspects of communication in mathematical epidemiology, nomenclature and interpretation of formulae (Sections 1 and 2), and then upon the tension between simple and sophisticated models (Section 3). Finally possible quantitative and qualitative effects of heterogeneity on the basic reproduction ratio in epidemic models are discussed (Section 4).

Nomenclature

Mathematical epidemiology is a scientific field where interdisciplinary collaboration is essential and, as part of this, communication between mathematicians and non-mathematicians (biologists, epidemiologists, etc.) is most important. One prerequisite for efficient and fruitful communication – in particular with people who are not specialists in mathematical epidemiology – is a joint nomenclature which tries to avoid using verbal expressions in ambiguous or misleading ways. But unfortunately there seems to persist some confusion about this, not only between persons who are specialists in different scientific fields, but occasionally even within fields.

One example of expressions in epidemiology which are quite misleading, but can be easily avoided, is random mixing and non-random mixing. Both terms assume that an infection is transmitted through contacts which are made at random (even if the mathematical model does not contain explicitly a stochastic formulation, but some deterministic counterpart). But whereas the first of these two terms intends to express that the population mixes homogeneously, and thus even contacts between individuals of distinct subpopulations are made uniformly, the latter particularly expresses that this is not the case. Since both types of mixing patterns involve random contacts, these two inappropriate verbal expressions should not be used.