Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA.
Department of Mathematics, Washington State University, Pullman, WA, 99164, USA.
Bull Math Biol. 2017 Sep;79(9):2109-2131. doi: 10.1007/s11538-017-0322-1. Epub 2017 Jul 26.
We propose two differential equation-based models to investigate the impact of awareness programs on cholera dynamics. The first model represents the disease transmission rates as decreasing functions of the number of awareness programs, whereas the second model divides the susceptible individuals into two distinct classes depending on their awareness/unawareness of the risk of infection. We study the essential dynamical properties of each model, using both analytical and numerical approaches. We find that the two models, though closely related, exhibit significantly different dynamical behaviors. Namely, the first model follows regular threshold dynamics while rich dynamical behaviors such as backward bifurcation may arise from the second one. Our results highlight the importance of validating key modeling assumptions in the development and selection of mathematical models toward practical application.
我们提出了两个基于微分方程的模型，以研究意识提升计划对霍乱动力学的影响。第一个模型将疾病传播率表示为意识提升计划数量的递减函数，而第二个模型则根据易感人群对感染风险的意识程度，将其分为两个不同的类别。我们使用分析和数值方法研究了每个模型的基本动力学特性。我们发现，这两个模型虽然密切相关，但表现出显著不同的动力学行为。具体来说，第一个模型遵循常规的阈值动力学，而第二个模型可能会出现丰富的动力学行为，如反向分歧。我们的研究结果强调了在开发和选择数学模型以实现实际应用时，验证关键建模假设的重要性。
