Convergence of a finite volume scheme for nonlocal reaction-diffusion systems modelling an epidemic disease
arXiv:0803.350221 citationsh-index: 28
Originality Synthesis-oriented
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Provides theoretical guarantees for numerical simulation of nonlocal epidemic models, but is incremental as it extends existing numerical analysis techniques to a specific model.
The paper proves convergence of a finite volume scheme for a nonlocal SIR epidemic model, establishing existence of solutions and convergence to a weak solution via a priori estimates and compactness.
We analyze a finite volume scheme for nonlocal SIR model, which is a nonlocal reaction-diffusion system modeling an epidemic disease. We establish existence solutions to the finite volume scheme, and show that it converges to a weak solution. The convergence proof is based on deriving series of a priori estimates and using a general $L^p$ compactness criterion.