Abstract
Cholera is a virulent intestinal infection caused by Vibrio cholerae strains. To explore multiple effects of spatial structure, seasonality and human behavior change on cholera transmission, we establish a reaction-advection-diffusion model with a general boundary condition at the downstream end of the river. We derive the basic reproduction number R0 and discuss its asymptotic behaviors. We further show that R0 is a strictly decreasing function of the bacterial loss c, which reveals that the bacterial loss at the downstream end of the river due to water flux reduces the risk of cholera transmission. Then we derive a threshold-type result in terms of R0. More precisely, (i) if R0<1, the disease-free periodic solution is globally attractive; (ii) if R0>1, the disease is uniformly persistent; (iii) if R0=1, the disease-free steady state is globally asymptotically stable in the absence of the advection term, in which the proof is quite challenging due to the introduction of human behavior change, involving some subtle inequalities and estimates. Numerically, an application is demonstrated by investigating the cholera outbreak in Somalia from 1995 to 2016.
Published Version
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