Bulletin of Mathematical Biology

, Volume 74, Issue 10, pp 2474–2487 | Cite as

A Vaccination Model for a Multi-City System

Original Article


A modelling approach is used for studying the effects of population vaccination on the epidemic dynamics of a set of n cities interconnected by a complex transportation network. The model is based on a sophisticated mover-stayer formulation of inter-city population migration, upon which is included the classical SIS dynamics of disease transmission which operates within each city. Our analysis studies the stability properties of the Disease-Free Equilibrium (DFE) of the full n-city system in terms of the reproductive number R 0. Should vaccination reduce R 0 below unity, the disease will be eradicated in all n-cities. We determine the precise conditions for which this occurs, and show that disease eradication by vaccination depend on the transportation structure of the migration network in a very direct manner. Several concrete examples are presented and discussed, and some counter-intuitive results found.


Vaccination Network model Epidemic model Reproduction number 



We are grateful for funding support from the EU FP7 Epiwork grant, the Israel Science Foundation, and the Israel Ministry of Health.


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Copyright information

© Society for Mathematical Biology 2012

Authors and Affiliations

  1. 1.Department of PhysicsBar Ilan UniversityRamat GanIsrael
  2. 2.BioMathematics Unit, Department of Zoology, Faculty of Life SciencesTel Aviv UniversityTel AvivIsrael

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