Disease invasion on community networks with environmental pathogen movement

    Authors

    J. H. Tien; Z. S. Shuai; M. C. Eisenberg;P. van den Driessche

    Comments

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    Abbreviated Journal Title

    J. Math. Biol.

    Keywords

    Cholera; Waterborne disease; Basic reproduction number; Spanning trees; Group inverse; CHOLERA; EPIDEMIC; DYNAMICS; HAITI; MODELS; ORIGIN; WORLD; Biology; Mathematical & Computational Biology

    Abstract

    The ability of disease to invade a community network that is connected by environmental pathogen movement is examined. Each community is modeled by a susceptible-infectious-recovered (SIR) framework that includes an environmental pathogen reservoir, and the communities are connected by pathogen movement on a strongly connected, weighted, directed graph. Disease invasibility is determined by the basic reproduction number for the domain. The domain is computed through a Laurent series expansion, with perturbation parameter corresponding to the ratio of the pathogen decay rate to the rate of water movement. When movement is fast relative to decay, is determined by the product of two weighted averages of the community characteristics. The weights in these averages correspond to the network structure through the rooted spanning trees of the weighted, directed graph. Clustering of disease "hot spots" influences disease invasibility. In particular, clustering hot spots together according to a generalization of the group inverse of the Laplacian matrix facilitates disease invasion.

    Journal Title

    Journal of Mathematical Biology

    Volume

    70

    Issue/Number

    5

    Publication Date

    1-1-2015

    Document Type

    Article

    Language

    English

    First Page

    1065

    Last Page

    1092

    WOS Identifier

    WOS:000351175300004

    ISSN

    0303-6812

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