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严重急性呼吸综合征冠状病毒2型（SARS-CoV-2）与结核病合并感染的数学建模与最优控制：以印度尼西亚为例

Mathematical modeling and optimal control of SARS-CoV-2 and tuberculosis co-infection: a case study of Indonesia.

作者信息

Rwezaura H, Diagne M L, Omame A, de Espindola A L, Tchuenche J M

机构信息

Mathematics Department, University of Dar es Salaam, P.O. Box 35062, Dar es Salaam, Tanzania.

Département de Mathématiques, UFR des Sciences et Technologies, Université de Thiés, BP 967, Thiés, Senegal.

出版信息

Model Earth Syst Environ. 2022;8(4):5493-5520. doi: 10.1007/s40808-022-01430-6. Epub 2022 Jul 4.

DOI:10.1007/s40808-022-01430-6
PMID:35814616
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9251044/
Abstract

A new mathematical model incorporating epidemiological features of the co-dynamics of tuberculosis (TB) and SARS-CoV-2 is analyzed. Local asymptotic stability of the disease-free and endemic equilibria are shown for the sub-models when the respective reproduction numbers are below unity. Bifurcation analysis is carried out for the TB only sub-model, where it was shown that the sub-model undergoes forward bifurcation. The model is fitted to the cumulative confirmed daily SARS-CoV-2 cases for Indonesia from February 11, 2021 to August 26, 2021. The fitting was carried out using the fmincon optimization toolbox in MATLAB. Relevant parameters in the model are estimated from the fitting. The necessary conditions for the existence of optimal control and the optimality system for the co-infection model is established through the application of Pontryagin's Principle. Different control strategies: face-mask usage and SARS-CoV-2 vaccination, TB prevention as well as treatment controls for both diseases are considered. Simulations results show that: (1) the strategy against incident SARS-CoV-2 infection averts about 27,878,840 new TB cases; (2) also, TB prevention and treatment controls could avert 5,397,795 new SARS-CoV-2 cases. (3) In addition, either SARS-CoV-2 or TB only control strategy greatly mitigates a significant number of new co-infection cases.

摘要

分析了一个纳入结核病（TB）和SARS-CoV-2共同动态流行病学特征的新数学模型。当各自的繁殖数低于1时，显示了子模型中无病平衡点和地方病平衡点的局部渐近稳定性。对仅TB子模型进行了分岔分析，结果表明该子模型经历了正向分岔。该模型拟合了印度尼西亚2021年2月11日至2021年8月26日的每日SARS-CoV-2累计确诊病例。拟合使用MATLAB中的fmincon优化工具箱进行。模型中的相关参数通过拟合进行估计。通过应用庞特里亚金原理，建立了共感染模型最优控制存在的必要条件和最优系统。考虑了不同的控制策略：使用口罩和接种SARS-CoV-2疫苗、结核病预防以及两种疾病的治疗控制。模拟结果表明：（1）针对新发SARS-CoV-2感染的策略可避免约27878840例新的结核病病例；（2）此外，结核病预防和治疗控制可避免5397795例新的SARS-CoV-2病例。（3）此外，仅针对SARS-CoV-2或结核病的控制策略可大大减轻大量新的共感染病例。

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