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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

The Spatial Pattern Dynamics of Reaction-Diffusion Instability in Tumor Cell--Immune Cell System

Journal of Applied Nonlinear Dynamics 10(2) (2021) 245--261 | DOI:10.5890/JAND.2021.06.005

Md. Nazmul Hasan$^1$ , Khan Rubayat Rahaman$^2$, Sabbir Janee$^3$

$^1$ Department of Mathematics, Jahangirnagar University, Savar, Dhaka, Bangladesh

$^2$ St. Marys University, 923 Robie Street, Halifax, NS, Canada B3H 3C3

$^3$ Department of Biotechnology and Genetic Engineering, Jahangirnagar University, Savar, Dhaka, Bangladesh

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Abstract

In this paper, spatial patterns of a diffusive Tumor cell and immune cell model with sigmoid ratio-dependent functional response are investigated. The asymptotic stability behavior of the corresponding nonspatial model around the unique positive interior equilibrium point in homogeneous steady state is obtained. We have obtained the optimal condition under which the system loses stability and a Turing pattern occurs. Numerical simulations have been carried out in order to show the significant role of reaction-diffusion coefficients and other important parameters of the system. Various contour figures of spatial patterns through Turing instability are portrayed and analyzed in order to substantiate the applicability of the present model. The paper ends with an extended discussion of biological implications of the immune system.

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