Mathematical analysis and pattern formation for a partial immune system modeling the spread of an epidemic disease

DOI10.1007/s10440-010-9569-3zbMath1252.35053OpenAlexW2039212749MaRDI QIDQ634659

Mostafa Bendahmane, Mazen Saad

Publication date: 16 August 2011

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-010-9569-3

zbMATH Keywords

Neumann boundary conditionsnumerical schemes

Mathematics Subject Classification ID

Epidemiology (92D30) Nonlinear parabolic equations (35K55) Reaction-diffusion equations (35K57) Developmental biology, pattern formation (92C15) Initial-boundary value problems for second-order parabolic systems (35K51) Pattern formations in context of PDEs (35B36)

Related Items

Stability analysis in a diffusional immunosuppressive infection model with delayed antiviral immune response ⋮ On the efficacy of a control volume finite element method for the capture of patterns for a volume-filling chemotaxis model ⋮ Analysis of a diffusive Leslie-Gower predator-prey model with nonmonotonic functional response ⋮ Complex dynamics of a reaction-diffusion epidemic model ⋮ An \(L^1\)-theory for a nonlinear temporal periodic problem involving \(p(x)\)-growth structure with a strong dependence on gradients ⋮ Integral solution for a parabolic equation driven by the \(p(x)\)-Laplacian operator with nonlinear boundary conditions and \(L^1\) data ⋮ Mathematical and numerical analysis of an acid-mediated cancer invasion model with nonlinear diffusion ⋮ Global existence for semilinear reaction-diffusion systems on evolving domains ⋮ Existence and uniqueness of renormalized periodic solution to a nonlinear parabolic problem with variable exponent and \(L^1\) data ⋮ Solvability of reaction–diffusion model with variable exponents ⋮ Time periodic solutions for strongly nonlinear parabolic systems with \(p(x)\)-growth conditions ⋮ Stationary patterns of a cross-diffusion epidemic model ⋮ Nonlinear parabolic equation having nonstandard growth condition with respect to the gradient and variable exponent

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A two-dimensional numerical study of spatial pattern formation in interacting Turing systems
• A mathematical model for indirectly transmitted diseases
• Compact sets in the space \(L^ p(0,T;B)\)
• Doubly nonlinear parabolic-type equations as dynamical systems
• The dynamics of two viral infections in a single host population with applications to hantavirus.
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• Global Existence for Semilinear Parabolic Systems
• Boundedness and Decay Results for Reaction-Diffusion Systems
• Global Existence and Boundedness in Reaction-Diffusion Systems
• The chemical basis of morphogenesis
• The Existence of Periodic Solutions to Reaction-Diffusion Systems with Periodic Data