  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.
