A cholera model in a patchy environment with water and human movement

    Authors

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

    Comments

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    Abbreviated Journal Title

    Math. Biosci.

    Keywords

    Cholera; Patch model; Water movement; Human movement; Global stability; Control strategy; MULTIPLE TRANSMISSION PATHWAYS; DISEASE TRANSMISSION; POPULATION; DISPERSAL; INFECTIOUS-DISEASE; GLOBAL DYNAMICS; SPATIAL SPREAD; EPIDEMIC; HAITI; Biology; Mathematical & Computational Biology

    Abstract

    A mathematical model for cholera is formulated that incorporates direct and indirect transmission, patch structure, and both water and human movement. The basic reproduction number 72.0 is defined and shown to give a sharp threshold that determines whether or not the disease dies out. Kirchhoff's Matrix Tree Theorem from graph theory is used to investigate the dependence of R-0 on the connectivity and movement of water, and to prove the global stability of the endemic equilibrium when R-0 > 1. The type/target reproduction numbers are derived to measure the control strategies that are required to eradicate cholera from all patches. (C) 2013 Elsevier Inc. All rights reserved.

    Journal Title

    Mathematical Biosciences

    Volume

    246

    Issue/Number

    1

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    105

    Last Page

    112

    WOS Identifier

    WOS:000327567100011

    ISSN

    0025-5564

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