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