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

A non-linear 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 non-trivial Lie symmetry operator...

Full description

Saved in:
Bibliographic Details
Published in:European journal of applied mathematics 2022-10, Vol.33 (5), p.785-802
Main Authors: CHERNIHA, ROMAN M., DAVYDOVYCH, VASYL V.
Format: Article
Language:English
Subjects:
Applied mathematics
Coronaviruses
COVID-19
Disease transmission
Exact solutions
Lie groups
Mathematical models
Ordinary differential equations
Pandemics
Partial differential equations
Symmetry
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A non-linear 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 non-trivial 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 typical 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.
ISSN:0956-7925
1469-4425
DOI:10.1017/S095679252100022X