Omede B I, Odionyenma U B, Ibrahim A A, Bolaji Bolarinwa
Mathematical Sciences Department, Kogi State University, Anyigba, Nigeria.
Laboratory of Mathematical Epidemiology and Applied Sciences, Anyigba, Nigeria.
Int J Dyn Control. 2023;11(1):411-427. doi: 10.1007/s40435-022-00982-w. Epub 2022 Jun 23.
The study of COVID-19 pandemic which paralyzed global economy of countries is a crucial research area for effective future planning against other epidemics. Unfortunately, we now have variants of the disease resulting to what is now known as waves of the pandemic. Several mathematical models have been developed to study this disease. While recent models incorporated control measures, others are without optimal control measures or demographic parameters. In this study, we propose a deterministic compartmental epidemiological model to study the transmission dynamic of the spread of the third wave of the pandemic in Nigeria, and we incorporated optimal control measures as strategies to reduce the burden of the deadly disease. Specifically, we investigated the transmission dynamics of COVID-19 model without demographic features. We then conducted theoretical analysis of the model with and without optimal control strategy. In the model without optimal control, we computed the reproduction number, an epidemiological threshold useful for bringing the third wave of the pandemic under check in Nigeria, and we proofed the disease stability and conducted sensitivity analysis in order to identify parameters that can impact the reproduction number tremendously. In a similar reasoning, for the model with control strategy, we check the necessary condition for the model. To validate our theoretical analyses, we illustrated the applications of the proposed model using COVID-19 data for Nigeria for a period when the country was under the yoke of the third wave of the disease. The data were then fitted to the model, and we derived a predictive tool toward making a forecast for the cumulative number of cases of infection, cumulative number of active cases and the peak of the third wave of the pandemic. From the simulations, it was observed that the presence of optimal control parameters leads to significant impact on the reduction of the spread of the disease. However, it was discovered that the success of the control of the disease relies on the proper and effective implementation of the optimal control strategies efficiently and adequately.
对使各国全球经济陷入瘫痪的新冠疫情的研究，是未来针对其他流行病进行有效规划的关键研究领域。不幸的是，现在该疾病出现了变种，导致了如今所说的疫情浪潮。已经开发了几种数学模型来研究这种疾病。虽然最近的模型纳入了控制措施，但其他一些模型没有最优控制措施或人口统计学参数。在本研究中，我们提出了一个确定性的 compartmental 流行病学模型，以研究尼日利亚第三波疫情传播的动态，并纳入最优控制措施作为减轻这种致命疾病负担的策略。具体而言，我们研究了无人口统计学特征的新冠模型的传播动态。然后，我们对有无最优控制策略的模型进行了理论分析。在没有最优控制的模型中，我们计算了繁殖数，这是一个有助于控制尼日利亚第三波疫情的流行病学阈值，我们证明了疾病的稳定性并进行了敏感性分析，以确定可能对繁殖数产生巨大影响的参数。出于类似的推理，对于有控制策略的模型，我们检查了模型的必要条件。为了验证我们的理论分析，我们使用尼日利亚在第三波疫情笼罩下的一段时间的新冠数据说明了所提出模型的应用。然后将数据拟合到模型中，我们得出了一个预测工具，用于预测感染病例的累计数、活跃病例的累计数以及第三波疫情的峰值。从模拟结果可以看出，最优控制参数的存在对减少疾病传播有显著影响。然而，发现疾病控制的成功依赖于最优控制策略的正确、有效且充分的实施。
