Immunity Shield Protection Mathematical Model of SARS-CoV-2 Virus Outbreak with Emphasis on Impreciseness in Terms of Intuitionistic Fuzziness

IF 0.6 Q3 ENGINEERING, MULTIDISCIPLINARY

Journal of Applied Nonlinear Dynamics Pub Date : 2023-03-01 DOI:10.5890/jand.2023.03.001

Subhashis Das, S. Mahato, Prasenjit Mahato

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Abstract

In this paper, we develop a COVID-19 mathematical model and divide the entire populations into six classes, namely susceptible, susceptible quarantined, exposed, infected, infected quarantined and recovered. We utilize the concept of "shield immunity” which is a different concept to herd immunity and could play a key role in getting back to normal. We consider that the recovered people are absolutely virus negative, produce antibodies to defend themselves against the virus and are able to interact with susceptible and infected people. We also assume that the recovered people may be infected when they come in contact with the infected people. Moreover, the control parameters are taken as triangular intuitionistic fuzzy numbers to incorporate the uncertainty. The model is converted to intuitionistic fuzzy model and analysed the boundedness, local and global stability, calculated the equilibrium points and basic reproduction number. We also studied optimal control of the model. The MATLAB codes are implemented to solve the system of ordinary nonlinear differential equations and to predict different scenarios for different values of the control parameters involved in the dynamical system. The sensitivities of the control parameters have also been performed to forecast the behaviour of the virus © 2023 L&H Scientific Publishing, LLC. All rights reserved

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严重急性呼吸系统综合征冠状病毒2型疫情免疫防护数学模型的直觉模糊性

本文建立了新型冠状病毒肺炎数学模型，将整个人群分为易感人群、隔离易感人群、暴露人群、感染人群、隔离感染人群和康复人群6类。我们利用“盾牌免疫”的概念，这是一个不同于群体免疫的概念，可以在恢复正常方面发挥关键作用。我们认为康复的人绝对是病毒阴性的，他们会产生抗体来保护自己免受病毒的侵害，并且能够与易感人群和感染者互动。我们还假设康复的人可能在与感染者接触时被感染。此外，控制参数采用三角直觉模糊数来考虑不确定性。将该模型转化为直观模糊模型，分析了系统的有界性、局部稳定性和全局稳定性，计算了系统的平衡点和基本再生数。并对模型的最优控制进行了研究。实现了求解常非线性微分方程系统的MATLAB代码，并对动力系统中涉及的不同控制参数值的不同情况进行了预测。控制参数的灵敏度也被用来预测病毒的行为©2023 L&H科学出版有限责任公司版权所有

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来源期刊

Journal of Applied Nonlinear Dynamics Engineering-Mechanical Engineering

CiteScore

1.20

自引率

20.00%

发文量

期刊介绍： The aim of the journal is to stimulate more research interest and attention for nonlinear dynamical behaviors and engineering nonlinearity for design. The manuscripts in complex dynamical systems with nonlinearity and chaos are solicited, which includes physical mechanisms of complex systems and engineering applications of nonlinear dynamics. The journal provides a place to researchers for the rapid exchange of ideas and techniques in nonlinear dynamics and engineering nonlinearity for design. Topics of Interest Complex dynamics in engineering Nonlinear vibration and dynamics for design Nonlinear dynamical systems and control Fractional dynamics and applications Chemical dynamics and bio-systems Economical dynamics and predictions Dynamical systems synchronization Bio-mechanical systems and devices Nonlinear structural dynamics Nonlinear multi-body dynamics Multiscale wave propagation in materials Nonlinear rotor dynamics Nonlinear waves and acoustics.