Numerical solution of an optimal control model of dendritic cell treatment of a growing tumour

Trisilowati, , McCue, Scott W., & Mallet, Daniel G. (2013) Numerical solution of an optimal control model of dendritic cell treatment of a growing tumour. ANZIAM Journal, 54, C664-C680.

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Abstract

A new optimal control model of the interactions between a growing tumour and the host immune system along with an immunotherapy treatment strategy is presented. The model is based on an ordinary differential equation model of interactions between the growing tu- mour and the natural killer, cytotoxic T lymphocyte and dendritic cells of the host immune system, extended through the addition of a control function representing the application of a dendritic cell treat- ment to the system. The numerical solution of this model, obtained from a multi species Runge–Kutta forward-backward sweep scheme, is described. We investigate the effects of varying the maximum al- lowed amount of dendritic cell vaccine administered to the system and find that control of the tumour cell population is best effected via a high initial vaccine level, followed by reduced treatment and finally cessation of treatment. We also found that increasing the strength of the dendritic cell vaccine causes an increase in the number of natural killer cells and lymphocytes, which in turn reduces the growth of the tumour.

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ID Code: 60717
Item Type: Journal Article
Refereed: Yes
Keywords: tumour, optimal control, mathematical model, immune system
ISSN: 1446-1811
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Optimisation (010303)
Australian and New Zealand Standard Research Classification > MEDICAL AND HEALTH SCIENCES (110000) > ONCOLOGY AND CARCINOGENESIS (111200) > Cancer Therapy (excl. Chemotherapy and Radiation Therapy) (111204)
Divisions: Current > Schools > School of Mathematical Sciences
Copyright Owner: Copyright 2013 Australian Mathematical Society
Deposited On: 10 Jun 2013 22:55
Last Modified: 11 Feb 2014 18:49

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