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Review
. 2022 Mar 17;70(2):12.
doi: 10.1007/s10441-022-09436-4.

Nonlocal Reaction-Diffusion Equations in Biomedical Applications

M Banerjee  1 , M Kuznetsov  2   3 , O Udovenko  2 , V Volpert  4   5   6
Affiliations
Review

Nonlocal Reaction-Diffusion Equations in Biomedical Applications

M Banerjee et al. Acta Biotheor. .

Abstract

Nonlocal reaction-diffusion equations describe various biological and biomedical applications. Their mathematical properties are essentially different in comparison with the local equations, and this difference can lead to important biological implications. This review will present the state of the art in the investigation of nonlocal reaction-diffusion models in biomedical applications. We will consider various models arising in mathematical immunology, neuroscience, cancer modelling, and we will discuss their mathematical properties, nonlinear dynamics, resulting spatiotemporal patterns and biological significance.

Keywords: Nonlocal equations; Pattern formation; Pulses; Reaction–diffusion equations; Travelling waves.

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