Din Anwarud, Li Yongjin, Khan Tahir, Zaman Gul
Department of Mathematics Sun Yat-sen University Guangzhou, 510275 P. R. China.
Department of Mathematics, University of Malakand, Chakdara, Pakistan.
Chaos Solitons Fractals. 2020 Dec;141:110286. doi: 10.1016/j.chaos.2020.110286. Epub 2020 Sep 23.
Number of well-known contagious diseases exist around the world that mainly include HIV, Hepatitis B, influenzas etc., among these, a recently contested coronavirus (COVID-19) is a serious class of such transmissible syndromes. Abundant scientific evidence the wild animals are believed to be the primary hosts of the virus. Majority of such cases are considered to be human-to-human transmission, while a few are due to wild animals-to-human transmission and substantial burdens on healthcare system following this spread. To understand the dynamical behavior such diseases, we fitted a susceptible-infectious-quarantined model for human cases with constant proportions. We proposed a model that provide better constraints on understanding the climaxes of such unseen disastrous spread, relevant consequences, and suggesting future imperative strategies need to be adopted. The main features of the work include the positivity, boundedness, existence and uniqueness of solution of the model. The conditions were derived under which the COVID-19 may extinct or persist in the population. Sensitivity and estimation of those important parameters have been carried out that plays key role in the transmission mechanism. To optimize the spread of such disease, we present a control problem for further analysis using two control measures. The necessary conditions have been derived using the Pontryagin's maximum principle. Parameter values have been estimated from the real data and experimental numerical simulations are presented for comparison as well as verification of theoretical results. The obtained numerical results also present the verification, accuracy, validation, and robustness of the proposed scheme.
世界上存在许多著名的传染病，主要包括艾滋病毒、乙型肝炎、流感等，其中，最近备受争议的冠状病毒（COVID-19）是这类可传播综合征中的严重一类。有充分的科学证据表明野生动物被认为是该病毒的主要宿主。大多数此类病例被认为是人际传播，而少数是野生动物传播给人类，并在此传播后给医疗系统带来巨大负担。为了理解此类疾病的动态行为，我们针对人类病例拟合了一个具有恒定比例的易感-感染-隔离模型。我们提出了一个模型，该模型在理解这种无形的灾难性传播的高潮、相关后果以及提出需要采取的未来紧迫策略方面提供了更好的约束。这项工作的主要特点包括模型解的正性、有界性、存在性和唯一性。推导了COVID-19在人群中可能灭绝或持续存在的条件。对在传播机制中起关键作用的那些重要参数进行了敏感性分析和估计。为了优化此类疾病的传播，我们提出了一个控制问题，使用两种控制措施进行进一步分析。利用庞特里亚金极大值原理推导了必要条件。从实际数据估计了参数值，并给出了实验数值模拟以进行比较以及验证理论结果。所获得的数值结果还展示了所提方案的验证、准确性、有效性和鲁棒性。
