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Global stability of general cholera models with nonlinear incidence and removal rates. (English) Zbl 1395.92172
Summary: In the real world, cholera may be transmitted through both direct human-to-human and indirect water-to-human mechanisms, but most of the previous studies assume linear progression rates for multistage models or linear death rate of infected individuals, which limits well understanding of the transmission dynamics of cholera. In this paper, we formulate a general compartmental multistage cholera model that incorporates nonlinear host recruitment, nonlinear incidence, nonlinear removal and nonlinear progression rates. Under biologically motivated assumptions, the basic reproduction number $$R_0$$ is derived in detail, and presents a sharp threshold property. In particular, if $$R_0<1$$, the disease-free equilibrium is globally asymptotically stable, and cholera dies out from all stages of host and water independent of initial burden; whereas if $$R_0>1$$, by employing Lyapunov functions and graph-theoretic results the endemic equilibrium is globally asymptotically stable, which also guarantees its uniqueness. The results are of biological significance for devising control strategies and possible extensions of the model are also discussed.

##### MSC:
 92D30 Epidemiology 34D23 Global stability of solutions to ordinary differential equations
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