Fixed Boundary PDE Model Formulation

  • William E. Schiesser


This chapter details a dual cancer vaccine (CV)-immune checkpoint inhibitor (ICI) mathematical model formulated as a system of partial differential equations (PDEs) defining the spatiotemporal distribution of cells and biochemicals during tumor growth. The PDEs, initial conditions (ICs) and boundary conditions (BCs) are specified. The outer BC for the tumor specifies a fixed boundary (FBPDE) which is the starting point for subsequent chapters in which the outer boundary moves (MBPDE) as the tumor grows.


Cancer vaccine (CV) Immune checkpoint inhibitor (ICI) Mathematical model Partial differential equation (PDE) Initial condition (IC) Boundary condition (BC) Fixed boundary Moving boundary 


  1. 1.
    Lai, X., and A. Friedman. 2017. Combination therapy of cancer with cancer vaccine and immune checkpoint inhibitors: A mathematical model. PLoS One 12(5):e0178479.CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • William E. Schiesser
    • 1
  1. 1.Department of Chemical and Biomolecular EngineeringLehigh UniversityBethlehemUSA

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