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Homework Help: Diffusion - Epidemiology PDE Model

  1. Nov 30, 2006 #1
    1. The problem statement, all variables and given/known data

    I'm wondering if there is an explicit traveling wave solution to a simple epidemiology diffusion model. This model is a basic representation of rabies spread among organisms. Rabies causes its victims to become delirious; hence the diffusion there.

    Here x is the spatial variable and t is the temporal variable. r, a, and D are all positive parameters. S represents susceptible fox not yet infected with rabies and I represents infected fox. S_0 in particular is the initial number of susceptible fox.

    2. Relevant equations

    The system is

    partialS/partialt = -rIS
    partialI/partialt = rIS - aI + D*(partial^2 I/partial x^2)

    with boundary conditions S(inf)=1, I(inf)=0, S'(-inf)=0, I(-inf)=0 and initial condition (S,I) = (S_0, 0).

    3. The attempt at a solution

    I have a DVI solution file I wrote showing that a solution exists (I find a heterocline between the two relevant equlibria in the SI-plane). It uses linear stability/nullcline analysis, not terribly complicated. Email me (retrofit81@aol.com) or respond here and I can send it to you.

    I'd really just like to know if a closed-form expression exists, and if so, maybe a hint on how I can start finding it...?


    Regards and thank you in advance,

    Michael
     
  2. jcsd
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