Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis

Joseph Malinzi; Rachid Ouifki; Amina Eladdadi; Delfim F. M. Torres; K. A. Jane White; Joseph Malinzi; Rachid Ouifki; Amina Eladdadi; Delfim F. M. Torres; K. A. Jane White

doi:10.3934/mbe.2018066

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 6: 1435-1463. doi: 10.3934/mbe.2018066

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Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis

1.
Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X 20, Hatfield, Pretoria 0028, South Africa
2.
Department of Mathematics, The College of Saint Rose, Albany, New York, USA
3.
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
4.
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK

Received: 27 March 2018 Accepted: 10 July 2018 Published: 01 December 2018
MSC : Primary: 49K15; Secondary: 92B05

Oncolytic virotherapy has been emerging as a promising novel cancer treatment which may be further combined with the existing therapeutic modalities to enhance their effects. To investigate how virotherapy could enhance chemotherapy, we propose an ODE based mathematical model describing the interactions between tumour cells, the immune response, and a treatment combination with chemotherapy and oncolytic viruses. Stability analysis of the model with constant chemotherapy treatment rates shows that without any form of treatment, a tumour would grow to its maximum size. It also demonstrates that chemotherapy alone is capable of clearing tumour cells provided that the drug efficacy is greater than the intrinsic tumour growth rate. Furthermore, virotherapy alone may not be able to clear tumour cells from body tissue but would rather enhance chemotherapy if viruses with high viral potency are used. To assess the combined effect of virotherapy and chemotherapy we use the forward sensitivity index to perform a sensitivity analysis, with respect to chemotherapy key parameters, of the virus basic reproductive number and the tumour endemic equilibrium. The results from this sensitivity analysis indicate the existence of a critical dose of chemotherapy above which no further significant reduction in the tumour population can be observed. Numerical simulations show that a successful combinational therapy of the chemotherapeutic drugs and viruses depends mostly on the virus burst size, infection rate, and the amount of drugs supplied. Optimal control analysis was performed, by means of the Pontryagin's maximum principle, to further refine predictions of the model with constant treatment rates by accounting for the treatment costs and sides effects. Results from this analysis suggest that the optimal drug and virus combination correspond to half their maximum tolerated doses. This is in agreement with the results from stability and sensitivity analyses.
- Chemovirotherapy,
- oncolytic virotherapy,
- optimal drug and virus combination
Citation: Joseph Malinzi, Rachid Ouifki, Amina Eladdadi, Delfim F. M. Torres, K. A. Jane White. Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis[J]. Mathematical Biosciences and Engineering, 2018, 15(6): 1435-1463. doi: 10.3934/mbe.2018066

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Abstract

Oncolytic virotherapy has been emerging as a promising novel cancer treatment which may be further combined with the existing therapeutic modalities to enhance their effects. To investigate how virotherapy could enhance chemotherapy, we propose an ODE based mathematical model describing the interactions between tumour cells, the immune response, and a treatment combination with chemotherapy and oncolytic viruses. Stability analysis of the model with constant chemotherapy treatment rates shows that without any form of treatment, a tumour would grow to its maximum size. It also demonstrates that chemotherapy alone is capable of clearing tumour cells provided that the drug efficacy is greater than the intrinsic tumour growth rate. Furthermore, virotherapy alone may not be able to clear tumour cells from body tissue but would rather enhance chemotherapy if viruses with high viral potency are used. To assess the combined effect of virotherapy and chemotherapy we use the forward sensitivity index to perform a sensitivity analysis, with respect to chemotherapy key parameters, of the virus basic reproductive number and the tumour endemic equilibrium. The results from this sensitivity analysis indicate the existence of a critical dose of chemotherapy above which no further significant reduction in the tumour population can be observed. Numerical simulations show that a successful combinational therapy of the chemotherapeutic drugs and viruses depends mostly on the virus burst size, infection rate, and the amount of drugs supplied. Optimal control analysis was performed, by means of the Pontryagin's maximum principle, to further refine predictions of the model with constant treatment rates by accounting for the treatment costs and sides effects. Results from this analysis suggest that the optimal drug and virus combination correspond to half their maximum tolerated doses. This is in agreement with the results from stability and sensitivity analyses.

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