Chaos, Solitons and Fractals 99 (2017) 297–311 Contents lists available at ScienceDirect Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos A chemotherapy combined with an anti-angiogenic drug applied to a cancer model including angiogenesis Christophe Letellier a,* , Sourav Kumar Sasmal b , Clément Draghi a , Fabrice Denis c , Dibakar Ghosh d a CORIA - Normandie University, Avenue de l’Université, F-76800 Saint-Etienne du Rouvray, France b Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata, 700108, India c Institut inter-régional Jean-Bernard, 9 rue Beauverger, F-72000 Le Mans, France d Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata, 700108, India a r t i c l e i n f o Article history: Received 3 April 2017 Accepted 6 April 2017 Keywords: Chemotherapy Anti-angiogenic drug Tumor cells Endothelial cells Tumor micro-environment a b s t r a c t Combined therapy made of a chemotherapy and antiangiogenic agents is a clinical treatment recom- mended for its efficiency. Since the optimization of a treatment against cancer relasp is still mostly based on oncologist’s know-how, it is desirable to develop different approaches for such a task. Mathematical modelling is one of the promising ways. We here investigated the action of a combined therapy inserted to a mathematical cancer model in order to determine how the dynamics underlying tumor growth is governed by some key parameters. We here retained a chemotherapy (for instance, paclitaxel and carbo- platin) combined with an antiangiogenic drug (as bevacizumab) applied to a cancer model describing the interactions between host, immune, tumor and endothelial cells. The effects of such a therapy are inves- tigated and the relevant role played by the “normal” tissue of the tumor micro-environment is evidenced. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction According to a report by the National Cancer Institute, roughly 40% of humans develop a cancer during their lifetime [1]. For in- stance, in Australia, 254,000 potential years of life were estimated to be lost each year due to cancer-induced death before the age of 75 years [2]. Currently, cancer causes 29% male and 25% female deaths. To reduce this deleterious outcome induced by cancer, on- cologists use several kinds of treatments like surgery, radiotherapy, immunotherapy, chemotherapy, anti-angiogenic drugs, etc. In spite of this, the rate of cancer-induced deaths for males only decreased annually by 1.8% between 2007 and 2011, and remained nearly constant for females between 1998 and 2011 [3]. Among different therapies, immunotherapy harnesses the immune response to recognize and to control malignant tumors [4,5], mostly because it is known that anti-tumor activity can be enhanced by stimulating immune cells [6,7]. Nevertheless, it is also known that tumor cells, when a cancer is diagnosed, may be already resistant to immune elimination and an immunotherapy is not efficient against tumor progression [8,9]. Immunotherapy is thus only able to cure a rather limited number of patients with * Corresponding author. E-mail address: christophe.letellier@coria.fr (C. Letellier). advanced cancers whose micro-environment was not immuno- suppressive. To overcome this limited success, chemotherapy is often applied but this is not always a successful strategy since, as any other therapy, it also kills a large amount of normal cells and has many side effects. Chemotherapy remains therefore a challenging topic of research to improve not only the selectivity of such treatment but also its efficacy with a reduced number of side effects [11]. Although medical studies can distinguish different mechanisms responsible for tumor growth [12], the mathematical analysis of realistic cancer models is also one of the possible ways to understand the dynamics underlying tumor growth [13–15]. Moreover, there is not yet a sufficient understanding in the inter- actions between a tumor and its micro-environment [10] and only very few cancer models were devoted to these interactions. When a cancer is in an advanced stage, metastasis can occur. Metastasis result from complex processes according which malig- nant cells from a primary tumor can be spread at distant sites. Such a feature requires new blood vessels, created from the pre- existing ones to improve the transport of nutrients and oxygen to tumor cells [16]. This process, named angiogenesis, allows tumor cells to circulate in the whole vascular system. When it is limited, angiogenesis may be responsible for in tumor dormancy [17–21]. Contrary to this, when it is well developed, the neoangiogenesis and its related metastatic spread is clearly a deleterious process to avoid since almost 90% of patients with a cancer die when http://dx.doi.org/10.1016/j.chaos.2017.04.013 0960-0779/© 2017 Elsevier Ltd. All rights reserved.