Tang, Biao, Xiao, Yanni, Tang, Sanyi and Cheke, Robert ORCID: 0000-0002-7437-1934 (2016) A feedback control model of immunogenic tumours with comprehensive therapy. International Journal of Bifurcation and Chaos, 26 (3):1650039. pp. 1-22. ISSN 0218-1274 (doi:https://doi.org/10.1142/S0218127416500395)

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Abstract

Surgery is the traditional method for treating cancers, but it often fails to cure patients for complex reasons so new therapeutic approaches that include both surgery and immunotherapy have recently been proposed. These have been shown to be effective, clinically, in inhibiting cancer cells while allowing retention of immunologic memory. This comprehensive strategy is guided by whether a population of tumour cells has or has not exceeded a threshold density. Conditions for successful control of tumours in an immune tumour system were modeled and the related dynamics were addressed. A mathematical model with state-dependent impulsive interventions is formulated to describe combinations of surgery with immunotherapy. By analysing the properties of the Poincar´e map, we examine the global dynamics of the immune tumour system with state-dependent feedback control, including the existence and stability of the semi-trivial order-1 periodic solution and the positive order-k periodic solution. The main results showed that surgery alone can only control the tumour size below a certain level while there is no immunologic memory. If comprehensive therapy involving combining surgery with immunotherapy is considered, then not only can the cancers be controlled below a certain level, but the immune system can also retain its activity. The existence of positive order-k periodic solutions implies that periodical therapy is needed to control the cancers. However, choosing the treatment frequency and the strength of the therapy remains challenging, and hence a strategy of individual-based therapy is suggested.

Item Type:	Article
Additional Information:	Published title: A Feedback Control Model of Comprehensive Therapy for Treating Immunogenic Tumours. Electronic version of an article published as Biao Tang et al, Int. J. Bifurcation Chaos 26, 1650039 (2016) [22 pages] DOI: 10.1142/S0218127416500395 © World Scientific Publishing http://www.worldscientific.com/
Uncontrolled Keywords:	Tumour cell, immunotherapy, Poincare map, state-dependent feedback control, order-k periodic solution
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science Faculty of Engineering & Science > Natural Resources Institute Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Last Modified:	25 Sep 2017 14:37
URI:	http://gala.gre.ac.uk/id/eprint/14907

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