Spatiotemporal Modeling of Cancer Immunotherapy

Partial Differential Equation Analysis in R

  • William E. Schiesser

Table of contents

  1. Front Matter
    Pages i-viii
  2. William E. Schiesser
    Pages 1-15
  3. William E. Schiesser
    Pages 17-41
  4. William E. Schiesser
    Pages 43-67
  5. William E. Schiesser
    Pages 69-89
  6. William E. Schiesser
    Pages 91-108
  7. Back Matter
    Pages 109-112

About this book


The focus of this book is a detailed discussion of 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.


A computer implementation of the model is discussed in detail for the quantitative evaluation of CV-ICI therapy. The coding (programming) consists of a series of routines in R, a quality, open-source scientific computing system that is readily available from the internet. The routines are based on the method of lines (MOL), a general PDE algorithm that can be executed on modest computers within the basic R system. The reader can download and use the routines to confirm the model solutions reported in the book, then experiment with the model by varying the parameters and modifying/extending the equations, and even studying alternative models with the PDE methodology demonstrated by the CV-ICI model.


Spatiotemporal Modeling of Cancer Immunotherapy: Partial Differential Equation Analysis in R facilitates the use of the model, and more generally, computer- based analysis of cancer immunotherapy mathematical models, as a step toward the development and quantitative evaluation of the immunotherapy approach to the treatment of cancer.


Fixed Boundary PDE Model Boundary PDE Model Output Moving Boundary PDE Model cancer vaccine cancer vaccine immune checkpoint immune checkpoint inhibitor cancer pde model output ODE/MOL routine Model PDEs Model PDEs cancer

Authors and affiliations

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

Bibliographic information

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