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A nonlinear reaction-diffusion system with cross-diffusion describing theCOVID-19 outbreak is studied using the Lie symmetry method. A complete Liesymmetry classification is derived and it is shown that the system withcorrectly-specified parameters admits highly nontrivial Lie symmetry operators,which do not occur for all known reaction-diffusion systems. The symmetriesobtained are also applied for finding exact solutions of the system in the mostinteresting case from applicability point of view. It is shown that the exactsolutions derived possess all necessary properties for describing the pandemicspread under 1D approximation in space and lead to the distributions, whichqualitatively correspond to the measured data of the COVID-19 spread inUkraine.

A reaction-diffusion system with cross-diffusion: Lie symmetry, exact solutions and their applications in the pandemic modeling