COVID-19: data-driven dynamics, statistical and distributed delay models, and observations

COVID-19 was declared as a pandemic by the World Health Organization on March 11, 2020. Here, the dynamics of this epidemic is studied by using a generalized logistic function model and extended compartmental models with and without delays. For a chosen population, it is shown as to how forecasting may be done on the spreading of the infection by using a generalized logistic function model, which can be interpreted as a basic compartmental model. In an extended compartmental model, which is a modified form of the SEIQR model, the population is divided into susceptible, exposed, infectious, quarantined, and removed (recovered or dead) compartments, and a set of delay integral equations is used to describe the system dynamics. Time-varying infection rates are allowed in the model to capture the responses to control measures taken, and distributed delay distributions are used to capture variability in individual responses to an infection. The constructed extended compartmental model is a nonlinear dynamical system with distributed delays and time-varying parameters. The critical role of data is elucidated, and it is discussed as to how the compartmental model can be used to capture responses to various measures including quarantining. Data for different parts of the world are considered, and comparisons are also made in terms of the reproductive number. The obtained results can be useful for furthering the understanding of disease dynamics as well as for planning purposes.