Global dynamics of a network epidemic model for waterborne diseases spread

Abstract

A network epidemic model for waterborne diseases spread is formulated, which incorporates both indirect environment-to-human and direct human-to-human transmission routes. We consider direct human contacts as a heterogeneous network and assume homogeneous mixing between the environment and human population. The basic reproduction number R0 is derived through the local stability of disease-free equilibrium and established as a sharp threshold that governs the disease dynamics. In particular, we have shown that the disease-free equilibrium is globally asymptotically stable if R0<1; while if R0>1, in case of permanent immunity the endemic equilibrium is globally asymptotically stable based on Kirchhoff’s matrix tree theorem, and in case of temporal immunity sufficient conditions are given to guarantee global stability of the endemic equilibrium. Moreover, various immunization strategies are investigated and compared. The results obtained are informative for us to further understand the disease propagation in multiple transmission routes and devise some effective intervening measures to fight against the diseases spread.