• Differential equations related to the Williams-Bjerknes tumour model

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      https://www.ias.ac.in/article/fulltext/pmsc/110/03/0323-0334

    • Keywords

       

      Williams-Bjerknes tumour model; expected number of cancerous cells

    • Abstract

       

      We investigate an initial value problem which is closely related to the Williams-Bjerknes tumour model for a cancer which spreads through an epithelial basal layer modeled onI ⊂ Z2. The solution of this problem is a familyp = (pi(t)), where eachpi(t)could be considered as an approximation to the probability that the cell situated ati is cancerous at timet. We prove that this problem has a unique solution, it is defined on [0, +∞[, and, for some relevant situations, limt→∞Pi(t) = 1 for alli ∈ I. Moreover, we study the expected number of cancerous cells at timet.

    • Author Affiliations

       

      F Martinez1 A R Villena1 2

      1. Departamento de Estaditica e I.O., Facultad de Ciencias, Universidad de Granada, Granada - 18071, Spain
      2. Departamento de Analisis Matematico, Facultad de Ciencias, Universidad de Granada, Granada - 18071, Spain
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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