Degree-dependent and distance-dependent contact rates interpolate between explosive, exponential and polynomial epidemic growth

2026-04-29

AI Summary

Existing theoretical frameworks lack a unified explanation for the diverse growth patterns—super-exponential, exponential, and polynomial—observed in epidemic spreading over the same contact network. This work proposes an agent-based network model that, for the first time, integrates the dependence of contact rates on both individual degree and spatial distance. By combining data-driven and synthetic network simulations with a geometrically grounded theory of long-range heterogeneous first-passage percolation and multiscale analysis, we rigorously demonstrate that even weak dependencies on degree or distance can substantially slow transmission dynamics. The interplay among network geometry, weak ties, and superspreaders is shown to jointly regulate the spreading velocity. This mechanism provides a unified account of multiple growth regimes across both empirical and synthetic networks.

Abstract

It is a fundamental question in epidemiology to estimate, model and predict the growth rate of a pandemic. Analogously, analysing the diffusion of innovation, (fake) news, memes, and rumours is of key importance in the social sciences. The resulting epidemic growth curves can be classified according to their growth rates. These have been found to range from exponential to both faster super-exponential curves and slower subexponential or polynomial curves. Previous research has lacked a unified explanatory framework capable of accommodating super-exponential, (stretched) exponential, and polynomial growth patterns within the same contact network. In this paper we propose a simple agent-based network model that can capture all these phases. We provide such a framework by modelling how transmission rates depend on spatial distance and on individuals' numbers of contacts. By comparing the growth rate of spreading processes with or without degree-dependent and/or distance-dependent contact rates through data-driven and synthetic simulations on real and modelled networks with underlying geometry, we find evidence that even a 'sublinear presence' of these causes may cause a significant slow down of the growth rate on the same underlying network. We find that the growth rate is governed by a combination of three factors: geometry, the prevalence of weak ties, and superspreaders. We confirm our results with rigorous proofs in a theoretical model, using a spatial multiscale-argument in long-range heterogeneous first passage percolation. Our results give a plausible explanation of why the consecutive waves of a single pandemic can differ in their growth even if their spreading mechanisms are similar.

Problem

• epidemic growth
• contact network
• super-exponential
• polynomial growth
• spreading dynamics

Innovation

• degree-dependent contact rates
• distance-dependent transmission
• epidemic growth phases
• spatial network geometry
• first passage percolation