Models and meta-models for interacting phenomena with social factors: a conceptual perspective

Abstract

We often introduce regulatory constraints or behavioral indications to control or avoid diffusion processes with nontrivial social interactions. Examples are a pandemic or circumstances dealing with construction and management of civil structures, such as energy-dissipation reduction or the design, use, and installation of new classes of sustainable materials. The application of regulatory constraints by individuals fluctuates in rigor, depending on cognitive aspects and a number of additional psychological factors that influence decision making processes. These fluctuations may affect even drastically the previsions made through mathematical models of the phenomena under scrutiny. A basic question is as follows: How can we include such (say) psychological factors – or at least some estimates of them – into mathematical models for phenomena interacting directly with the social structure? A cascade of ancillary questions emerge. Among them: Do we need to consider such psychological factors just as a source of noisy accumulation to a bound – a stochastic approach, indeed – or in appropriate circumstances can we have a variational view on them interpreting context-driven effects as the result of the balance of opposite events? May we accept an approximate deterministic picture of these fluctuations, based, e.g., on the introduction of continuous perturbations and/or memory effects? We indicate here a conceptual perspective to tackle such questions, and we formulate and discuss open problems.