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

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• 作者：Marisa C. Eisenberg ; Zhisheng Shuai ; Joseph H. Tien ; P. van den Driessche
• 关键词：Cholera ; Patch model ; Water movement ; Human movement ; Global stability ; Control strategy
• 刊名：Mathematical Biosciences
• 出版年：November, 2013
• 年：2013
• 卷：246
• 期：1
• 页码：105-112
• 全文大小：475 K

文摘

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 is defined and shown to give a sharp threshold that determines whether or not the disease dies out. Kirchhoff鈥檚 Matrix Tree Theorem from graph theory is used to investigate the dependence of on the connectivity and movement of water, and to prove the global stability of the endemic equilibrium when . The type/target reproduction numbers are derived to measure the control strategies that are required to eradicate cholera from all patches.