title: Mathematical modeling and its analysis for instability of the immune system induced by chemotaxis.
abstract: In this paper, we study how chemotaxis affects the immune system by proposing a minimal mathematical model, a reaction-diffusion-advection system, describing a cross-talk between antigens and immune cells via chemokines. We analyze the stability and instability arising in our chemotaxis model and find their conditions for different chemotactic strengths by using energy estimates, spectral analysis, and bootstrap argument. Numerical simulations are also performed to the model, by using the finite volume method in order to deal with the chemotaxis term, and the fractional step methods are used to solve the whole system. From the analytical and numerical results for our model, we explain not only the effective attraction of immune cells toward the site of infection but also hypersensitivity when chemotactic strength is greater than some threshold.
authors.affiliation: National Institute for Mathematical Sciences, Daejeon, Republic of Korea.
authors.forename: Seongwon
authors.initials: S
authors.lastname: Lee
authors.affiliation: Pohang University of Science and Technology, Pohang, Republic of Korea.
authors.forename: Se-Woong
authors.initials: SW
authors.lastname: Kim
authors.affiliation: Pohang University of Science and Technology, Pohang, Republic of Korea.
authors.forename: Youngmin
authors.initials: Y
authors.lastname: Oh
authors.affiliation: Pohang University of Science and Technology, Pohang, Republic of Korea. hjhwang@postech.ac.kr.
authors.forename: Hyung Ju
authors.initials: HJ
authors.lastname: Hwang
mesh_terms: D000818:Animals; D000941:Antigens / Q000276:immunology; D018925:Chemokines / Q000276:immunology; D002633:Chemotaxis / Q000276:immunology*; D003198:Computer Simulation; D006801:Humans; D016014:Linear Models; D055641:Mathematical Concepts; D018448:Models, Immunological; D017711:Nonlinear Dynamics
chemical_list: D000941:Antigens; D018925:Chemokines
keywords: Chemotaxis; Instability; Mathematical model