Mathematical modeling is a powerful tool to study the process of the spread of infectious diseases. Among various mathematical methods for describing the spread of infectious diseases, the cellular automaton makes it possible to explicitly simulate both the spatial and temporal evolution of epidemics with intuitive local rules. In this paper, a model is proposed and realized on a cellular automata platform, which is applied to simulate the spread of coronavirus disease 2019 (COVID-19) for different administrative districts. A simplified social community is considered with varying parameters, e.g., sex ratio, age structure, population movement, incubation and treatment period, immunity, etc. COVID-19 confirmation data from New York City and Iowa are adopted for model validation purpose. It can be observed that the disease exhibits different spread patterns in different cities, which could be well accommodated by this model. Then, scenarios under different control strategies in the next 100 days in Iowa are simulated, which could provide a valuable reference for decision makers in identifying the critical factors for future infection control in Iowa.

Dendrite is among the most frequently observed structures during the solidification process. Different dendrite morphologies caused by environmental conditions can affect the physical properties of materials. The formation of snowflakes can generate various morphologies under different conditions, and is used in this work as an example. Simulation technologies provide insight into the correlation between a resulting morphology and its impact parameter, including the phase-field method (PF) and cellular automaton (CA). The PF method is derived from thermodynamic functions and kinetic equations, while the CA model is established by interaction rules between subsystems. It is difficult to solve the PF method due to the coupled differential equations, wherein the actual physical parameters are included. The CA model is conceptually simple and computationally efficient; however, the physical meaning of the parameters is absent. In this work, an example of snowflake formation is considered by PF with all the impact factors defined first, and then parameters in CA are searched by iterations to approximate the result, i.e., latent heat and the anisotropic coefficient in the PF method correspond to the initial distribution and the environmental effect in the CA model. In addition, the discrete time of each iteration in the CA model is identified according to the dendritic growth speed of these two models. A systematic identification process for the CA parameters’ physical meaning is demonstrated by the comparison with the PF method, and an approximate simulation of the PF method can be obtained simply by the CA model. The combination of the PF method and the CA model can be used to investigate the influence of environmental factors on dendritic morphology.

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