具有不服从行为的反应扩散SIR流行病模型分析
Analysis of a Reaction-Diffusion SIR Epidemic Model with Noncompliant Behavior
AI总结：
本研究提出一个包含不服从行为传播的反应扩散SIR流行病模型，证明解的存在性，进行R0分析并模拟，揭示区别于基本SIR模型的新特征。
摘要：
公共卫生专家的近期工作表明，将人类行为纳入考虑对于忠实模拟流行病至关重要。我们提出了一个包含行为因素的、基于反应扩散偏微分方程的SIR型人群流行病模型。在我们的模型中，疾病通过质量作用定律传播，这在房室模型中很常见。然而，借鉴社会传染理论，我们假设随着疾病的传播和预防措施的实施，对预防措施的不服从行为也在人群中传播。我们证明了该模型经典解的全局存在性，然后进行了R0型分析，并确定了模型在不同参数区域下的渐近行为。最后，我们对模型进行了模拟，并讨论了使我们的模型区别于基本SIR型模型的新特征。
英文摘要：
Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic including behavioral concerns. In our model, the disease spreads via mass action, as is customary in compartmental models. However, drawing from social contagion theory, we assume that as the disease spreads and prevention measures are enacted, noncompliance with prevention measures also spreads throughout the population. We prove global existence of classical solutions of our model, and then perform R0-type analysis and determine asymptotic behavior of the model in different parameter regimes. Finally, we simulate the model and discuss the new facets which distinguish our model from basic SIR-type models.
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