Stability (learning theory)

Physics

Pathology

Sociology

Nonlinear system

Consistency (knowledge bases)

Disease

Population

Coronavirus disease 2019 (COVID-19)

Mathematics

Infectious disease (medical specialty)

Diffusion

Reaction–diffusion system

Statistical physics

Statistics

Machine learning

Demography

Mathematical analysis

Epidemic model

Geometry

Computer science

Quantum mechanics

State space

Applied mathematics

Equilibrium point

Computer simulation

Medicine

Thermodynamics

Nonlinear Dynamics

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.

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