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

• Both water and human movement are included in a multi-patch cholera model.
• The basic reproduction number is determined and shown to give a sharp threshold.
• Lyapunov functions are constructed to establish the global dynamics.
• Spanning rooted trees are used to show how water movement affects cholera dynamics.
• Cholera control strategies are quantified using type and target reproduction numbers.

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 R0R0 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 R0R0 on the connectivity and movement of water, and to prove the global stability of the endemic equilibrium when R0>1R0>1. The type/target reproduction numbers are derived to measure the control strategies that are required to eradicate cholera from all patches.