A 10-year prospectus for mathematical epidemiology

Abstract

There is little significant work at the intersection of mathematical and computational epidemiology and detailed psychological processes, representations, and mechanisms. This is true despite general agreement in the scientific community and the general public that human behavior in its seemingly infinite variation and heterogeneity, susceptibility to bias, context, and habit is an integral if not fundamental component of what drives the dynamics of infectious disease. The COVID-19 pandemic serves as a close and poignant reminder. We offer a 10-year prospectus of kinds that centers around an unprecedented scientific approach: the integration of detailed psychological models into rigorous mathematical and computational epidemiological frameworks in a way that pushes the boundaries of both psychological science and population models of behavior.

Keywords: cognitive modeling of human behavior; epidemiology; graph dynamical systems; mathematical modeling and simulation; psychology.

Figure 1

The 10-year prospectus imagined graphically shows the larger system graph illustrated on the left captured through coupled, co-evolving networks, possibly including mass media. Transfer functions (e.g., η₁ and η₂) govern how states associated to a different network layer (e.g., online) may influence dynamics in another network layer (e.g., physical contacts). A cognitive situation graph is illustrated in the top right, capturing dynamics at a compact level for the various agent classes present in the system network. Essential to this 10-year prospectus is the invocation of human cognitive architectures to realistically constrain mathematical models of system-level behavior.

Figure 2

A major component of our 10-year prospectus is to develop and design vertex functions for the GDS framework from cognitive first principles (i.e., derived from or constrained by a human cognitive architecture). The left portion above shows the development from cognitive architecture to cognitive model. The dotted-arrow represents an iterative process that is designed to vary the degree of abstraction (more abstraction means less fidelity) in the mathematical representation of an agent's cognitive model. Scaling criteria are considered in respect to the time and space complexity of computations on the graph; for large graphs with high-fidelity vertex functions, this may be a serious consideration. The mathematical frameworks for representing vertices are various and may be explored as part of the development of a GDS formalism.