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Fractional model for the spread of COVID-19 subject to government intervention and public perception

机译：Covid-19传播的分数模型受政府干预和公众感知的影响

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摘要

COVID-19 pandemic has impacted people all across the world. As a result, there has been a collective effort to monitor, predict, and control the spread of this disease. Among this effort is the development of mathematical models that could capture accurately the available data and simulate closely the futuristic scenarios. In this paper, a fractional-order memory-dependent model for simulating the spread of COVID-19 is proposed. In this model, the impact of governmental interventions and public perception are incorporated as part of the nonlinear time-varying transmission rate. In addition, an algorithm for approximating the optimal values of the fractional order and strength of governmental interventions is provided. This approach makes our model suitable for capturing the given data set and consequently reliable for future predictions. The model simulation is performed using the two-step generalized exponential time-differencing method and tested for data from Mainland China, Italy, Saudi Arabia and Brazil. The simulation results demonstrate that the fractional order model calibrates to the data better than its integer order counterpart. This observation is further endorsed by the calculated error metrics.
机译：Covid-19大流行影响了世界各地的人们。因此，有一个集体努力监测，预测和控制这种疾病的传播。在这种努力中，可以在数学模型的发展中，可以准确地捕获可用数据并密切模拟未来主义情景。在本文中，提出了一种用于模拟Covid-19的扩展的分数阶存储依赖模型。在该模型中，政府干预和公众感知的影响被纳入非线性时变传输率的一部分。此外，还提供了一种近似近似值和政府干预强度的最佳价值的算法。这种方法使我们的模型适合于捕获给定的数据集并因此可靠地用于未来的预测。使用两步通用指数时间差异方法进行模型仿真，并测试了来自中国大陆，意大利，沙特阿拉伯和巴西的数据。仿真结果表明，小数阶模型比其整数顺序对应物更好地校准数据。该观察结果进一步通过计算出的误差度量来认可。

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