Ghosh Indrajit, Martcheva Maia
Department of Computational and Data Sciences, Indian Institute of Science, Bengaluru, 560012 Karnataka India.
Department of Mathematics, University of Florida, Gainesville, FL 32611 USA.
Nonlinear Dyn. 2021;104(4):4681-4700. doi: 10.1007/s11071-021-06489-x. Epub 2021 May 1.
The ongoing COVID-19 pandemic has affected most of the countries on Earth. It has become a pandemic outbreak with more than 50 million confirmed infections and above 1 million deaths worldwide. In this study, we consider a mathematical model on COVID-19 transmission with the prosocial awareness effect. The proposed model can have four equilibrium states based on different parametric conditions. The local and global stability conditions for awareness-free, disease-free equilibrium are studied. Using Lyapunov function theory and LaSalle invariance principle, the disease-free equilibrium is shown globally asymptotically stable under some parametric constraints. The existence of unique awareness-free, endemic equilibrium and unique endemic equilibrium is presented. We calibrate our proposed model parameters to fit daily cases and deaths from Colombia and India. Sensitivity analysis indicates that the transmission rate and the learning factor related to awareness of susceptibles are very crucial for reduction in disease-related deaths. Finally, we assess the impact of prosocial awareness during the outbreak and compare this strategy with popular control measures. Results indicate that prosocial awareness has competitive potential to flatten the COVID-19 prevalence curve.
持续的新冠疫情已经影响到地球上的大多数国家。它已成为一场大流行疫情，全球确诊感染病例超过5000万例，死亡人数超过100万例。在本研究中，我们考虑一个具有亲社会意识效应的新冠病毒传播数学模型。所提出的模型基于不同的参数条件可以有四种平衡状态。研究了无意识、无疾病平衡的局部和全局稳定性条件。利用李雅普诺夫函数理论和拉萨尔不变性原理，在一些参数约束下，无疾病平衡被证明是全局渐近稳定的。给出了唯一的无意识、地方病平衡和唯一的地方病平衡的存在性。我们校准所提出的模型参数以拟合哥伦比亚和印度的每日病例和死亡情况。敏感性分析表明，传播率和与易感者意识相关的学习因子对于减少疾病相关死亡非常关键。最后，我们评估了疫情爆发期间亲社会意识的影响，并将这种策略与流行的控制措施进行比较。结果表明，亲社会意识具有使新冠疫情流行曲线变平缓的竞争潜力。
