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2009, Volume 2009: 630-639. Doi: 10.3934/proc.2009.2009.630 open access
This issue Previous Article Travelling fronts of reaction diffusion systems modeling auto-catalysis Next Article On positivity and boundedness of solutions of nonlinear stochastic difference equations

Stability analysis using an energy estimate approach of a reaction-diffusion model of atherogenesis

  • 1.

    Southern Polytechnic State University, Marietta, GA 30060-2896

  • 2.

    Department of Mathematics and Statistics, Texas Tech University, Lubbock TX, 79409-1042

  • 3.

    Texas A & M Unviersity, College Station, TX 77843

  • 4.

    Scott & White Hospital, Temple, TX 76508

Received:  May 31, 2008
Revised:  June 30, 2009
Published:  August 2009
Abstract Related Papers Cited by
    Abstract
  • This paper considers modeling the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Russell Ross, atherogenesis is viewed as an inflammatory spiral with positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammation is modeled through a system of nonlinear reaction/diffusion/convection partial differential equations. The inflammatory spiral is initiated as an instability from a healthy state which is defined to be an equilib- rium state devoid of certain key inflammatory markers. Disease initiation is studied through a linear, asymptotic stability analysis of a healthy equilibrium state. Conditions on system parameters guaranteeing stability of the health state and conditions on system parameters leading to instability are given. Among the questions addressed in the analysis is the possible mitigating effect of anti-oxidants upon transition to the inflammatory spiral.
    Mathematics Subject Classification: 35K55, 92C17, 92C50.

    Citation:
    shu

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