A REACTION-CONVECTION-DIFFUSION MODEL FOR CHOLERA SPATIAL DYNAMICS

作者：Wang Xueying^*; Posny Drew; Wang Jin

来源：Discrete and Continuous Dynamical Systems-Series B, 2016, 21(8): 2785-2809.

DOI：10.3934/dcdsb.2016073

• Cholera spatial dynamics
• reaction-convection-diffusion model
• traveling wave speeds
• threshold dynamics

In this paper, we propose a general partial differential equation (PDE) model of cholera epidemics that extends previous mathematical cholera studies. Our new formation concerns the impact of the bacterial and human diffusion, bacterial convection, and their interaction with the intrinsic bacterial growth and multiple disease transmission pathways. A sensitivity analysis for a few key model parameters indicates the significance of diffusion and convection in shaping cholera epidemics. We then investigate the traveling wave solutions of our PDE model based on analytical derivation and numerical simulation, with a focus on the interplay of different biological, environmental and physical factors that determines the spatial spreading speeds of cholera. In addition, disease threshold dynamics are studied by computing the basic reproduction number associated with the PDE model, using both asymptotic analysis and numerical calculation.

• 出版日期2016-10