Dynamics of Breast Cancer under Different Rates of Chemoradiotherapy

A type of cancer which originates from the breast tissue is referred to as breast cancer. Globally, it is the most common cause of death in women. Treatments such as radiotherapy, chemotherapy, hormone therapy, immunotherapy, and gene therapy are the main strategies in the fight against breast cancer. The present study aims at investigating the effects of the combined radiotherapy and chemotherapy as a way to treat breast cancer, and different treatment approaches are incorporated into the model. Also, the model is fitted to data on patients with breast cancer in Tanzania. We determine new treatment strategies, and finally, we show that when sufficient amount of chemotherapy and radiotherapy with a low decay rate is used, the drug will be significantly more effective in combating the disease while health cells remain above the threshold.

[1]  Sanjeev Kumar,et al.  A Mathematical Model of Chemotherapy for Tumor Treatment Deep , 2011 .

[2]  Franziska Michor,et al.  Pharmacokinetics and Drug Interactions Determine Optimum Combination Strategies in Computational Models of Cancer Evolution. , 2017, Cancer research.

[3]  Edward T. Chiyaka,et al.  Assessing the Effects of Estrogen on the Dynamics of Breast Cancer , 2012, Comput. Math. Methods Medicine.

[4]  T. Witten,et al.  Modeling drug resistance in a conjoint normal-tumor setting , 2015, Theoretical Biology and Medical Modelling.

[5]  J. Tsoka-Gwegweni,et al.  Breast cancer among women in sub-Saharan Africa: prevalence and a situational analysis , 2017 .

[6]  Subhas Khajanchi,et al.  A Mathematical Model to Elucidate Brain Tumor Abrogation by Immunotherapy with T11 Target Structure , 2014, PloS one.

[7]  Konstantin E. Starkov,et al.  On Some Dynamical Properties of a Seven-Dimensional Cancer Model with Immunotherapy , 2014, Int. J. Bifurc. Chaos.

[8]  Doron Levy,et al.  A Mathematical Model of the Enhancement of Tumor Vaccine Efficacy by Immunotherapy , 2012, Bulletin of mathematical biology.

[9]  H. Namazi,et al.  Mathematical Modelling and Prediction of the Effect of Chemotherapy on Cancer Cells , 2015, Scientific Reports.

[10]  A. Buzaid,et al.  Identifying important breast cancer control strategies in Asia, Latin America and the Middle East/North Africa , 2011, BMC health services research.

[11]  Xuefang Li,et al.  A mathematical model of tumor-immune interactions incorporated with danger model , 2015, 2015 10th Asian Control Conference (ASCC).

[12]  D. Kirschner,et al.  Modeling immunotherapy of the tumor – immune interaction , 1998, Journal of mathematical biology.

[13]  A. Radunskaya,et al.  Mixed Immunotherapy and Chemotherapy of Tumors: Modeling, Applications and Biological Interpretations , 2022 .

[14]  K. Starkov,et al.  Modeling cancer evolution: evolutionary escape under immune system control , 2017 .

[15]  P. Sibanda,et al.  Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment , 2017, Journal of biological dynamics.

[16]  Mustafa Mamat,et al.  Mathematical Model of Cancer Treatments Using Immunotherapy, Chemotherapy and Biochemotherapy , 2013 .

[17]  H M Byrne,et al.  A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy. , 2000, Mathematical biosciences.

[18]  Alain Goriely,et al.  A mathematical model of tumor-immune interactions. , 2012, Journal of theoretical biology.

[19]  S. Balamuralitharan,et al.  HPM OF ESTROGEN MODEL ON THE DYNAMICS OF BREAST CANCER , 2018 .

[20]  Ami Radunskaya,et al.  A delay differential equation model for tumor growth , 2003, Journal of mathematical biology.

[21]  T. Tembo,et al.  From Community Laywomen to Breast Health Workers: A Pilot Training Model to Implement Clinical Breast Exam Screening in Malawi , 2016, PloS one.

[22]  D. Earn,et al.  Interactions Between the Immune System and Cancer: A Brief Review of Non-spatial Mathematical Models , 2011, Bulletin of mathematical biology.

[23]  Robert J. Gillies,et al.  Current Advances in Mathematical Modeling of Anti-Cancer Drug Penetration into Tumor Tissues , 2013, Front. Oncol..

[24]  S. Merajver,et al.  Clinical and epidemiologic profile of breast cancer in Tanzania. , 2010, Breast disease.

[25]  F. Bozkurt Stability Analysis of a Fractional-Order Differential Equation System of a GBM-IS Interaction Depending on the Density , 2014 .

[26]  G. Abdulrahman,et al.  Epidemiology of Breast Cancer in Europe and Africa , 2012, Journal of cancer epidemiology.

[27]  A. Morley,et al.  Mutation rate of normal and malignant human lymphocytes. , 1987, Cancer research.

[28]  Mark A. J. Chaplain,et al.  Towards Predicting the Response of a Solid Tumour to Chemotherapy and Radiotherapy Treatments: Clinical Insights from a Computational Model , 2013, PLoS Comput. Biol..

[29]  T. Witten,et al.  Modeling the Effects of a Simple Immune System and Immunodeficiency on the Dynamics of Conjointly Growing Tumor and Normal Cells , 2011, International journal of biological sciences.

[30]  Raul Isea,et al.  A Mathematical Model of Cancer Under Radiotherapy , 2015 .

[31]  T. Sreelekha,et al.  Nanostrategies in the war against multidrug resistance in leukemia , 2013 .

[32]  F. Berezovskaya,et al.  Cancer immunoediting: A process driven by metabolic competition as a predator-prey-shared resource type model. , 2015, Journal of theoretical biology.

[33]  D. Kirschner,et al.  A methodology for performing global uncertainty and sensitivity analysis in systems biology. , 2008, Journal of theoretical biology.

[34]  H. Braak,et al.  Staging of Alzheimer disease-associated neurofibrillary pathology using paraffin sections and immunocytochemistry , 2006, Acta Neuropathologica.

[35]  Rafic Younes,et al.  Review of Optimization Methods for Cancer Chemotherapy Treatment Planning , 2015 .

[36]  S. Gardner Scheduling Chemotherapy: Catch 22 between Cell Kill and Resistance Evolution , 2000 .

[37]  Dongxi Li,et al.  Stochastic responses of tumor–immune system with periodic treatment , 2017 .

[38]  A. Jemal,et al.  Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries , 2018, CA: a cancer journal for clinicians.

[39]  Hsiu-Chuan Wei A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease , 2018, Journal of biological dynamics.

[40]  Ami Radunskaya,et al.  A mathematical tumor model with immune resistance and drug therapy: an optimal control approach , 2001 .