This paper presents a new modelling framework that uses within‑day human movement to redefine how we measure transmissibility during an outbreak. The authors start from first principles and build a network model that explicitly tracks where people spend time during the day. From that model they derive a family of instantaneous reproduction numbers R(t) — the usual measure of how many new infections a single infected person causes at a given time — but now defined for places, pairs of places, meeting points, and for the entire mobility network.

At a technical level the framework is described with partial differential equations and yields so‑called renewal equations. In plain terms, renewal equations say how past infections produce new infections over time. The new work plugs time‑varying movement into those equations so the model counts infection opportunities that arise when people move between locations or meet in the same place for part of a day. This is different from simpler approaches that treat each location as a closed, static population or that use coarse origin‑destination flows.

The authors show how to compute multiple, targeted indicators from the same model. Examples include inward and outward R(t) for a single location (how many infections are brought into or sent out from a place), R(t) for transmission corridors between locations, R(t) at meeting locations, and an overall network R(t). They apply the framework to simulated epidemics on different kinds of networks and to anonymised mobile phone GPS data streams (for example data sources like SafeGraph or Google mobility data) to illustrate how these outputs can guide decisions on where, when, and how strongly to intervene.

Why this matters: many widely used methods for estimating R(t) assume people mix evenly or treat locations independently. Those assumptions can mislead local policy because they ignore that people spend parts of their day in several places. By building movement into the core equations, the new measures give a more mechanistic and spatially precise picture of transmission. That can help design targeted control measures — specifying the strength, type, and duration of interventions at particular locations and times — rather than applying blunt, area‑wide rules.