The Effects of Regional Vaccination Heterogeneity on Measles Outbreaks with France as a Case Study

Elaine T. Alexander; Savanah D. McMahon; Nicholas Roberts; Emilio Sutti; Daniel Burkow; Miles Manning; Kamuela E. Yong; Sergei Suslov

arXiv · 1408.0695

The Effects of Regional Vaccination Heterogeneity on Measles Outbreaks with France as a Case Study

Elaine T. Alexander·Savanah D. McMahon·Nicholas Roberts·Emilio Sutti·Daniel Burkow·Miles Manning·Kamuela E. Yong·Sergei Suslov

View original source ↗Read source document ↗Export metadata ↓

Abstract

The rubeola virus, commonly known as measles, is one of the major causes of vaccine-preventable deaths among children worldwide. This is the case despite the fact that an effective vaccine is widely available. Even in developed countries elimination efforts have fallen short as seen by recent outbreaks in Europe, which had over 30,000 cases reported in 2010. The string of measles outbreaks in France from 2008-2011 is of particular interest due to the documented disparity in regional vaccination coverage. The impact of heterogeneous vaccine coverage on disease transmission is a broad interest and the focus of this study. A Susceptible-Exposed-Infectious-Recovered (SEIR) multi-patch epidemiological model capturing the regional differences in vaccination rates and mixing is introduced. The mathematical analysis of a two-patch system is carried out to help our understanding of the behavior of multi-patch systems. Numerical simulations are generated to aid the study of the system's qualitative dynamics. Data from the recent French outbreaks were used to generate parameter values and to help connect theory with application. Our findings show that heterogeneous vaccination coverage increases controlled reproduction number compared to comparable homogeneous coverage.

Explore related subjects

q-bio.PE

Keep this discovery

BibTeX RIS

Elaine T. Alexander, Savanah D. McMahon, Nicholas Roberts, Emilio Sutti, Daniel Burkow, Miles Manning, Kamuela E. Yong, Sergei Suslov. 2014-08-01. The Effects of Regional Vaccination Heterogeneity on Measles Outbreaks with France as a Case Study. https://arxiv.org/abs/1408.0695

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↗