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The long-term efficacy of targeted therapeutics for cancer treatment can be significantly limited by the type of therapy and development of drug resistance, inter alia. Experimental studies indicate that the factors enhancing acquisition of drug resistance in cancer cells include cell heterogeneity, drug target alteration, drug inactivation, DNA damage repair, drug efflux, cell death inhibition, as well as microenvironmental adaptations to targeted therapy, among others. Combination cancer therapies (CCTs) are employed to overcome these molecular and pathophysiological bottlenecks and improve the overall survival of cancer patients. CCTs often utilize multiple combinatorial modes of action and thus potentially constitute a promising approach to overcome drug resistance. Considering the colossal cost, human effort, time and ethical issues involved in clinical drug trials and basic medical research, mathematical modeling and analysis can potentially contribute immensely to the discovery of better cancer treatment regimens. In this article, we review mathematical models on CCTs developed thus far for cancer management. Open questions are highlighted and plausible combinations are discussed based on the level of toxicity, drug resistance, survival benefits, preclinical trials and other side effects., Comment: 28 Pages, 1 Figure, 3 Tables

Oncolytic virotherapy (OV) has been emerging as a promising novel cancer treatment that may be further combined with the existing therapeutic modalities to enhance their effects. To investigate how OV could enhance chemotherapy, we propose an ODE based 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, OV 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 OV 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 Pontryagin's principle, to further refine predictions of the model with constant treatment rates by accounting for the treatment costs and sides effects., Comment: This is a preprint of a paper whose final and definite form is with 'Mathematical Biosciences and Engineering', ISSN 1551-0018 (print), ISSN 1547-1063 (online), available at [http://www.aimsciences.org/journal/1551-0018]. Submitted 27-March-2018; revised 04-July-2018; accepted for publication 10-July-2018