Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: J. O. Takhirov and Z. K. Djumanazarova
Pages: [21] - [47]
Received Date: April 14, 2021
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122201
We investigate an epidemic non-linear reaction-diffusion system with
two free boundaries. A free boundary is introduced to describe the
expanding front of the infectious environment. A priori estimates of
the required functions are established, which are necessary for the
correctness and global solvability of the problem. We get sufficient
conditions for the spread or disappearance of the disease. It has been
proven that with a base reproductive number 
the disease disappears in the long term if the
initial values and the initial area are sufficiently small.
reaction-diffusion systems, epidemic model, free boundary, asymptotic behaviour of the solution.
