Modelling the impact of precaution on disease dynamics and its evolution.

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Tianyu Cheng, Xingfu Zou
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Abstract

In this paper, we introduce the notion of practically susceptible population, which is a fraction of the biologically susceptible population. Assuming that the fraction depends on the severity of the epidemic and the public's level of precaution (as a response of the public to the epidemic), we propose a general framework model with the response level evolving with the epidemic. We firstly verify the well-posedness and confirm the disease's eventual vanishing for the framework model under the assumption that the basic reproduction number R 0 < 1 . For R 0 > 1 , we study how the behavioural response evolves with epidemics and how such an evolution impacts the disease dynamics. More specifically, when the precaution level is taken to be the instantaneous best response function in literature, we show that the endemic dynamic is convergence to the endemic equilibrium; while when the precaution level is the delayed best response, the endemic dynamic can be either convergence to the endemic equilibrium, or convergence to a positive periodic solution. Our derivation offers a justification/explanation for the best response used in some literature. By replacing "adopting the best response" with "adapting toward the best response", we also explore the adaptive long-term dynamics.

Abstract Image

模拟预防措施对疾病动态及其演变的影响。
在本文中,我们引入了实际易感人群的概念,即生物易感人群的一部分。假定这一部分取决于疫情的严重程度和公众的预防水平(作为公众对疫情的反应),我们提出了一个反应水平随疫情变化的一般框架模型。首先,我们验证了框架模型的拟合优度,并确认在基本繁殖数 R 0 1 的假设条件下,疾病最终消失。当 R 0 > 1 时,我们将研究行为反应如何随流行病演变,以及这种演变如何影响疾病动力学。更具体地说,当预防水平被视为文献中的瞬时最佳反应函数时,我们证明地方病动态收敛于地方病均衡;而当预防水平为延迟最佳反应时,地方病动态既可以收敛于地方病均衡,也可以收敛于正周期解。我们的推导为一些文献中使用的最佳反应提供了理由/解释。将 "采用最佳响应 "替换为 "适应最佳响应",我们还探讨了适应性长期动态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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