Analyzing the COVID-19 transmission dynamics with the stretched logistic model: Origin of anomalous time-dependent infection rates

The COVID-19 pandemic has presented unprecedented challenges globally, necessitating a deep understanding of its complex dynamics for effective mitigation strategies. We find that the intricate pattern of the pandemic is replicated well by the stretched logistic equation (SLE), which is a modification of the traditional logistic equation (TLE). The intrinsic infection rate involved in the logistic equation decreases with time (time-dependent) in the SLE, while it is a constant in the TLE. It is suggested that an anomalous sub-diffusion of the virus related to complex human activities is the main reason for the time-dependent spreading reaction rate. The SLE is compared with the compressed logistic equation, which can be applied to the closed system, such as bacterial growth, and the other approaches applied to COVID-19.