[论文解读] Predicting COVID-19 distribution in Mexico through a discrete and time-dependent Markov chain and an SIR-like model

Alfonso Vivanco-Lira|arXiv (Cornell University)|Mar 15, 2020

COVID-19 Clinical Research StudiesMedicine参考文献 19被引用 18

一句话总结

本研究提出一种混合建模方法，结合离散的、时变的马尔可夫链与改进的SIR模型，以预测墨西哥各州COVID-19病例的时空分布。该方法估计了疾病传播动力学，并为墨西哥早期大流行阶段的公共卫生规划提供了可操作的见解。

ABSTRACT

COVID-19 is an emergent viral infection which rose in December 2019 in a city in the Chinese province of Hubei, Wuhan; the viral aetiology of this infection is now known as COVID-19 virus, which belongs to the Betacoronavirus genus. This virus produces the syndrome of acute respiratory stress that h as been witnessed in other coronaviruses, such as that MERS-CoV in Middle East countries or SARS-CoV which was seen in 2002 and 2003 in China. This virus mediates its entry through its spike (S) proteins interacting with ACE2 receptors in lung epithelial cells, and may promote an inflammatory response by means of inflammasome NLRP3 activation and unfolded protein response (these are possibly consequence of the envelope E protein of COVID-19 virus). Efforts have been made worldwide to prevent further spread of the disease, but in March 2020 the WHO declared it a pandemic emergency and Mexico started to report its first cases. In this paper we attempt to summarize the biological features of the virus and the possible pathophysiological mechanisms of its disease, as well as a stochastic model characterizing the probability distribution of cases in Mexico by states and the estimated number of cases in Mexico through a differential equation model (modified SIR model), thus will we be able to characterize the disease and its course in Mexico in order to display more preparedness and promote more logical actions by both the policy makers as well as the general population.

研究动机与目标

• 使用离散的、时变的马尔可夫链对墨西哥各州COVID-19病例的随机传播过程进行建模。
• 通过改进的SIR型微分方程模型估算墨西哥累计病例数。
• 将SARS-CoV-2的生物学机制与流行病学建模相结合，以提升疾病进程预测的准确性。
• 为决策者和公众提供基于数据、面向准备工作的早期大流行阶段预测。

提出的方法

• 使用离散时间、状态相关的马尔可夫链，对每个时间步长下墨西哥32个州的感染病例概率分布进行建模。
• 马尔可夫模型中的转移概率基于区域传播动态和病例数据推导得出。
• 采用具有时变传播率的改进SIR模型，以模拟墨西哥的整体疫情曲线。
• SIR模型整合了感染率、恢复率以及各州人口规模等参数。
• 利用墨西哥国家卫生当局提供的早期报告病例数据对模型进行校准。
• 将SARS-CoV-2的生物学机制（如ACE2受体结合、NLRP3炎症小体激活等）纳入模型假设，以提供依据。

实验结果

研究问题

• RQ1 时变马尔可夫链在多大程度上能准确表示墨西哥各州COVID-19病例的空间分布？
• RQ2 使用具有时变传播率的改进SIR模型，墨西哥的累计病例数预测结果如何？
• RQ3 SARS-CoV-2的生物学特征如何影响流行病模型的结构与参数？
• RQ4 该组合模型在初期大流行波期间对公共卫生决策支持的效力如何？

主要发现

• 马尔可夫链模型成功捕捉了墨西哥各州病例概率分布随时间的演变。
• 改进的SIR模型预测墨西哥的累计病例数将在初始疫情爆发后数月内达到峰值，与早期数据趋势一致。
• 该模型基于转移概率和早期病例聚集情况，识别出高风险州。
• 将病毒病理生理学特征整合进模型，增强了模型的真实性，并支持了参数的合理性论证。
• 该综合方法为资源有限环境下的实时预测与准备规划提供了框架。