TITLE:
Traveling Wave Solutions of a SIR Epidemic Model with Spatio-Temporal Delay
AUTHORS:
Zhihe Hou
KEYWORDS:
Susceptible-Infected-Recovered Epidemic Model, Traveling Wave Solutions, Spatio-Temporal Delay, Schauder Fixed Point Theorem
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.10,
October
22,
2024
ABSTRACT: In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number
R
0
and the minimum wave speed
c
*
of the corresponding ordinary differential equations. The methods used in this paper are primarily the Schauder fixed point theorem and comparison principle. We have proved that when
R
0
>1
and
c>
c
*
, the model has a non-negative and non-trivial traveling wave solution. However, for
R
0
<1
and
c≥0
or
R
0
>1
and
0