[论文解读] A Mathematical Model of Transmission Dynamics of SARS-Cov-2 (Covid-19) with an Underlying Condition of Diabetes

Samuel Okyere, Joseph Ackora-Prah+1 more|arXiv (Cornell University)|Jan 12, 2022

COVID-19 epidemiological studies被引用 6

一句话总结

本研究构建了一个确定性数学模型，以分析糖尿病患者中SARS-CoV-2的传播动力学，结合了封锁和疫苗接种的时间依赖最优控制。结果表明，糖尿病显著增加了新冠肺炎死亡风险，加纳的R₀ = 1.4722，两种干预措施均有效降低了感染人数，凸显了针对糖尿病人群制定有针对性公共卫生策略的必要性。

ABSTRACT

It is well established that people with diabetes are more likely to have serious complications from COVID-19. Nearly 1 in 5 COVID-19 deaths in the African region are linked to diabetes. World Health Organization (WHO) finds that 18.3% of COVID-19 deaths in Africa are among people with diabetes. In this paper, we have formulated and analysed a mathematical comorbidity model of diabetes - COVID-19 of the deterministic type. The basic properties of the model were explored. The basic reproductive number, equilibrium points and stability of the equilibrium points were examined. Sensitivity analysis of the model was carried on to determine the impact of the model parameters on the basic reproduction number of the model. The model had a unique endemic equilibrium point, which was stable for R_0>1. Time-dependent optimal controls were incorporated into the model with the sole aim of determining the best strategy for curtailing the spread of the disease. COVID-19 cases from March to September 2020 in Ghana were used to validate the model. Results of the numerical simulation suggest a greater number of individuals deceased when the infected individual had an underlying condition of diabetes. More so COVID-19 is endemic in Ghana with the basic reproduction number found to be R_0=1.4722. The numerical simulation of the optimal control model reveals the lockdown control minimized the rate of decay of the susceptible individuals whereas the vaccination led to a number of susceptible individuals becoming immune to COVID-19 infections. In all the two preventive control measures were both effective in curbing the spread of the COVID-19 disease as the number of COVID-19 infections was greatly reduced. We conclude that more attention should be paid to COVID-19 patients with an underlying condition of diabetes as the probability of death in this population was significantly higher.

研究动机与目标

• 调查糖尿病作为共病对SARS-CoV-2传播和严重程度的影响。
• 构建一个整合糖尿病与新冠肺炎传播动力学的确定性数学模型。
• 分析平衡点的稳定性并计算基本再生数R₀。
• 应用时间依赖的最优控制策略（封锁和疫苗接种）以最小化疾病传播。
• 利用加纳2020年3月至9月期间的真实新冠肺炎病例数据验证模型。

提出的方法

• 构建了一个确定性分 compartment 模型，包含易感者、感染但无糖尿病者、感染且有糖尿病者、康复者和死亡者等子群。
• 使用下一代矩阵法推导基本再生数R₀，以评估传播潜力。
• 对无病平衡点和地方性平衡点进行稳定性分析，以评估长期行为。
• 进行敏感性分析，识别影响R₀的关键参数，特别是与糖尿病共病相关的参数。
• 引入时间依赖的最优控制变量（封锁和疫苗接种），以最小化感染率。
• 利用初始疫情波期间加纳报告的新冠肺炎病例数据对模型进行校准和验证。

实验结果

研究问题

• RQ1 糖尿病共病如何影响SARS-CoV-2感染的传播动力学和严重程度？
• RQ2 在糖尿病负担较高的群体中，如加纳所观察到的，SARS-CoV-2传播的基本再生数R₀是多少？
• RQ3 在存在糖尿病共病的情况下，哪种控制策略——封锁还是疫苗接种——更有效地减少新发感染数？
• RQ4 无病平衡点和地方性平衡点的稳定性特性如何依赖于模型参数，特别是与糖尿病相关的参数？
• RQ5 最优控制模型的数值模拟在多大程度上反映了加纳早期疫情数据的实际结果？

主要发现

• 基本再生数R₀估计为1.4722，表明在研究期间SARS-CoV-2在加纳持续传播。
• 模型表现出唯一的、当R₀ > 1时稳定的地方性平衡点，证实了疾病在人群中的持续存在。
• 数值模拟显示，糖尿病患者中的死亡人数显著高于无糖尿病者。
• 封锁控制减缓了易感人群的衰减速率，表明其在延迟但无法根除传播方面的作用。
• 疫苗接种控制使易感人群的免疫力显著提高，有效减少了传播。
• 封锁和疫苗接种两种控制措施均有效减少了新发感染数，其中疫苗接种对群体免疫力的长期影响更为可持续。