From localized to well-mixed: How commuter interactions shape disease spread

Aaron Winn; Adam Konkol; Eleni Katifori

Home/Archive/arXiv

arXiv · 2303.04490

From localized to well-mixed: How commuter interactions shape disease spread

Aaron Winn·Adam Konkol·Eleni Katifori

View original source ↗Read source document ↗Export metadata ↓

Abstract

Interactions between commuting individuals can lead to large-scale spreading of rumors, ideas, or disease, even though the commuters have no net displacement. The emergent dynamics depend crucially on the commuting distribution of a population, that is how the probability to travel to a destination decays with distance from home. Applying this idea to epidemics, we will demonstrate the qualitatively different infection dynamics emerging from populations with different commuting distributions. If the commuting distribution is exponentially localized, we recover a reaction-diffusion system and observe Fisher waves traveling at a speed proportional to the characteristic commuting distance. If the commuting distribution has a long tail, then no finite-velocity waves can form, but we show that, in some regimes, there is nontrivial spatial dependence that the well-mixed approximation neglects. We discuss how, in all cases, an initial dispersal-dominated regime can allow the disease to go undetected for a finite amount of time before exponential growth takes over. This "offset time" is a quantity of huge importance for epidemic surveillance and yet largely ignored in the literature.

Explore related subjects

q-bio.PE physics.soc-ph

Keep this discovery

BibTeX RIS

Aaron Winn, Adam Konkol, Eleni Katifori. 2023-03-08. From localized to well-mixed: How commuter interactions shape disease spread. https://arxiv.org/abs/2303.04490

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Competition drives excessive recruitment in collective search

Groups that search collectively often exploit what they find by recruiting: one member directs others to a site it has found. Recruitment raises the number of members foraging at a known site, but the return per forager may fall as that number grows, so there is an intermediate optimal recruitment rate. In addition, a site may be used by more than one group. Here we analyze a model of two groups that forage from a single site whose return declines with the total number of foragers present. The two groups interact only through this shared return. The long-run outcome is either coexistence at the foraging site or monopoly by one group, and we analyze the boundary between these two outcomes. A group's best response to its rival is not monotone: it increases its own recruitment rate with the rival's recruitment rate in an attempt to preserve a monopoly, and then its recruitment rate drops discontinuously when it is no longer optimal to preserve a monopoly. We analyze how model parameters govern this shift: a group relinquishes monopoly when the site saturates at few foragers and when the rival group is small. When the two groups have comparable size there are multiple Nash equilibria, so either group may end up with the larger share. And when two equally matched groups compete, both recruit above the rate that maximizes their common return, so that each individual ends with less than it would in a single undivided group of the same total size.

q-bio.PE↗

arXiv2026

Selection Rules for Species Coexistence in a Hierarchical May-Leonard Model

One of the central challenges in evolutionary dynamics is understanding why some species combinations persist while others disappear. Although cyclic-interaction models have provided fundamental insights into biodiversity maintenance, much less is known about how hierarchical competitive interactions shape long-term community organization. Here, we investigate a hierarchical extension of the May-Leonard model, in which species interact through a directed predation chain while undergoing reproduction and mortality. Combining mean-field analysis with Monte Carlo simulations, we show that the fully coexisting state is generically unstable, causing the dynamics to evolve toward lower-dimensional coexistence states. The simulations further reveal stochastic extinctions dominating small populations with the dynamics progressively approaching the mean-field predictions as the system size increases. Rather than permitting arbitrary species combinations, the hierarchical-interaction structure dynamically constrains coexistence by selecting only specific subsets of species for long-term persistence. We show that these admissible coexistence states have a natural graph-theoretic interpretation as independent sets in the hierarchical interaction network, thereby providing general constraints on coexistence in hierarchical communities. Together, these results establish a theoretical framework linking hierarchical interactions, dynamical selection, graph topology, and biodiversity organization, extending the classical May-Leonard model beyond cyclic competition.

q-bio.PE↗

arXiv2026

Persistence of n-Species Lotka-Volterra Models with Periodic Pulses

Periodic impulsive interventions arise naturally in the management of biological populations, including chemotherapy, pesticide application, and infectious-disease treatment. We develop general conditions for permanence in n-species population models subject to periodic multiplicative pulse disturbances. Our main result provides a sufficient condition for permanence in terms of weighted long-term growth rates on a Morse decomposition of the extinction set, explicitly separating the contributions of continuous population dynamics from those of the periodic pulse. To establish this result, we transform the impulsive system into an associated autonomous continuous-time dynamical system and use this correspondence to extend classical permanence theory to periodically pulsed models. We further show that the same conditions imply robust permanence under sufficiently small perturbations to the continuous dynamics, pulse period, and pulse effects. We illustrate the framework with two Lotka-Volterra models motivated by biological control: competition between chemotherapy-sensitive and chemotherapy-resistant cancer cells, and integrated control of an agricultural pest using pesticides and parasitoids. These examples demonstrate how intervention frequency and intensity interact with underlying ecological interactions to determine whether populations coexist or are excluded. Our results provide a general framework for analyzing persistence in ecological systems subject to repeated discrete disturbances.

q-bio.PE↗