Numerical simulation and stability analysis of a novel reaction–diffusion COVID-19 model

In this study, a novel reaction–diffusion model for the spread of the new coronavirus (COVID-19) is investigated. The model is a spatial extension of the recent COVID-19 SEIR model with nonlinear incidence rates by taking into account the effects of random movements of individuals from different com...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics 2021-10, Vol.106 (2), p.1293-1310
Main Authors: Ahmed, Nauman, Elsonbaty, Amr, Raza, Ali, Rafiq, Muhammad, Adel, Waleed
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Coronaviruses
COVID-19
Dynamic stability
Dynamical Systems
Engineering
Finite difference method
Mathematical models
Mechanical Engineering
Original Paper
Parameters
Stability analysis
Vibration
Viral diseases
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:In this study, a novel reaction–diffusion model for the spread of the new coronavirus (COVID-19) is investigated. The model is a spatial extension of the recent COVID-19 SEIR model with nonlinear incidence rates by taking into account the effects of random movements of individuals from different compartments in their environments. The equilibrium points of the new system are found for both diffusive and non-diffusive models, where a detailed stability analysis is conducted for them. Moreover, the stability regions in the space of parameters are attained for each equilibrium point for both cases of the model and the effects of parameters are explored. A numerical verification for the proposed model using a finite difference-based method is illustrated along with their consistency, stability and proving the positivity of the acquired solutions. The obtained results reveal that the random motion of individuals has significant impact on the observed dynamics and steady-state stability of the spread of the virus which helps in presenting some strategies for the better control of it.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-021-06623-9