Original Article

Bulletin of Mathematical Biology

, Volume 74, Issue 10, pp 2474-2487

First online:

A Vaccination Model for a Multi-City System

  • Menachem LachianyAffiliated withDepartment of Physics, Bar Ilan UniversityBioMathematics Unit, Department of Zoology, Faculty of Life Sciences, Tel Aviv University Email author 
  • , Lewi StoneAffiliated withBioMathematics Unit, Department of Zoology, Faculty of Life Sciences, Tel Aviv University

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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