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With the prevalence of COVID-19, the modeling of epidemic propagation and its analyses have played a significant role in controlling epidemics. However, individual behaviors, in particular the self-protection and migration, which have a strong influence on epidemic propagation, were always neglected in previous studies. In this paper, we mainly propose two models from the individual and population perspectives. In the first individual model, we introduce the individual protection degree that effectively suppresses the epidemic level as a stochastic variable to the SIRS model. In the alternative population model, an open Markov queueing network is constructed to investigate the individual number of each epidemic state, and we present an evolving population network via the migration of people. Besides, stochastic methods are applied to analyze both models. In various simulations, the infected probability, the number of individuals in each state and its limited distribution are demonstrated. [ABSTRACT FROM AUTHOR]

Under the background of the wanton spread of the coronavirus disease (COVID-19), the pandemic is changing and hitting lives all over the world. Fortunately, Spatio-temporal processes bear essential importance in many applied scientific fields. And the disease pandemic can be viewed as Spatio-temporal dynamics processes. Generally, partial differential equations (PDEs) have been widely used to investigate interfacial dynamic processes. In this work, we use a physical-constraint neural network learning the Spatio-temporal mean-field dynamics to control the propagation of epidemics. Also, we use the AI-based algorithm physical-constraint learning (PCL) to solve the minimization problems of the mean-field game (MFG) and control (MFC) problems instead of the traditional computational method. In PCL, the PDEs are encoded into the loss function, where partial derivatives can be obtained through automatic differentiation (AD). We demonstrate how they can be applied in practice by considering the problem of controlling the propagation of epidemics. Numerical experiments on different input data are implemented to demonstrate the effectiveness and superiority of the proposed models compared to the state-of-the-art approach and illustrate how to separate the infected patients in a spatial domain effectively. [ABSTRACT FROM AUTHOR]