Open AccessAn SIR epidemic model with vaccination in a patchy environment
Author(s) -
Qianqian Cui,
Zhipeng Qiu,
Ling Ding
Publication year - 2017
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2017059
Subject(s) - outbreak , epidemic model , basic reproduction number , vaccination , stability (learning theory) , infectious disease (medical specialty) , boundary (topology) , mathematics , biology , computer science , demography , virology , disease , medicine , mathematical analysis , sociology , population , pathology , machine learning
In this paper, an SIR patch model with vaccination is formulated to investigate the effect of vaccination coverage and the impact of human mobility on the spread of diseases among patches. The control reproduction number Rv is derived. It shows that the disease-free equilibrium is unique and is globally asymptotically stable if Rv< 1, and unstable if Rv>1. The sufficient condition for the local stability of boundary equilibria and the existence of equilibria are obtained for the case n=2. Numerical simulations indicate that vaccines can control and prevent the outbreak of infectious in all patches while migration may magnify the outbreak size in one patch and shrink the outbreak size in other patch.