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

Marisa C Eisenberg; Zhisheng Shuai; Joseph H Tien; P van den Driessche

doi:10.1016/j.mbs.2013.08.003

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

Math Biosci. 2013 Nov;246(1):105-12. doi: 10.1016/j.mbs.2013.08.003. Epub 2013 Aug 16.

Authors

Marisa C Eisenberg¹, Zhisheng Shuai, Joseph H Tien, P van den Driessche

Affiliation

¹ Department of Epidemiology, University of Michigan, Ann Arbor, MI 48109, United States; Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, United States. Electronic address: marisae@umich.edu.

PMID: 23958383
DOI: 10.1016/j.mbs.2013.08.003

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 R0 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 R0 on the connectivity and movement of water, and to prove the global stability of the endemic equilibrium when R0>1. The type/target reproduction numbers are derived to measure the control strategies that are required to eradicate cholera from all patches.

Keywords: Cholera; Control strategy; Global stability; Human movement; Patch model; Water movement.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Cholera / epidemiology*
Environment*
Humans
Models, Biological*
Movement*
Water*

Substances

Water