Overview

Despite major advances in healthcare over the past century, the successful treatment of cancer has remained a significant challenge, and cancers are the second leading cause of death worldwide behind cardiovascular disease. Early detection and survival are important issues to control cancer. The development of quantitative methods and computer technology has facilitated the formation of new models in medical and biological sciences. The application of mathematical modelling in solving many real-world problems in medicine and biology has yielded fruitful results. In spite of advancements in instrumentations technology and biomedical equipment, it is not always possible to perform experiments in medicine and biology for various reasons. Thus, mathematical modelling and simulation are viewed as viable alternatives in such situations, and are discussed in this book. The conventional diagnostic techniques of cancer are not always effective as they rely on the physical and morphological appearance of the tumour. Early stage prediction and diagnosis is very difficult with conventional techniques. It is well known that cancers are involved in genome level changes. As of now, the prognosis of various types of cancer depends upon findings related to the data generated through different experiments. Several machine learning techniques exist in analysing the data of expressed genes; however, the recent results related with deep learning algorithms are more accurate and accommodative, as they are effective in selecting and classifying informative genes. This book explores the probabilistic computational deep learning model for cancer classification and prediction.

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Dr Akshara Makrariya has a PhD in Mathematics from the National Institute of Technology (SVNIT) Surat, India, specializing in computational and bio mathematics. She completed her Post-Doctoral Research under the Young Scientist Fellowship (NPDF) programme, from the Science & Engineering Research Board (SERB), DST, and Government of India. Her research interest includes computational models to study temperature distribution in extended spherical and ellipsoidal shaped human organs, computational models to study thermal disturbances due to tumours, and their modelling with different numerical methods like fractional calculus, and the finite volume method, and by using optimization techniques. Dr Jha obtained his PhD in Mathematics in the year 2013 from the National Institute of Technology (SVNIT) Surat, India. His research area includes mathematical modelling and simulation of calcium dynamics in astrocytes, finite element modelling of biological problems, and fractional differential equations and their applications in physiological problems. Dr Rabia Musheer has a Doctorate in Applied Mathematics from Maulana Azad National Institute of Technology, Bhopal, India. Her research interests include mathematical machine learning and data science application of mathematical modelling and optimization, soft computing, big data and bioinformatics. Dr Anant Kant Shukla has a Doctorate from the VIT Vellore and CSIR-Fourth Paradigm Institute, Bengaluru. His research is in the area of analytical solutions and nonlinear systems. Dr Jha obtained his PhD in Mathematics in the year 2013 from National Institute of Technology (SVNIT) Surat, India. Her research area includes mathematical modeling and simulation of calcium dynamics in neuron cell, and finite element modelling of biological problems. Dr Parvaiz Ahmad Naik is working as Assistant Professor in Mathematics at the School of Mathematics and Statistics, Xi’an Jiaotong University P. R. China. He received his PhD in Applied Mathematics (Mathematical Biology) in 2015. His interest areas include differential equations, mathematical biology, fractional calculus, calcium dynamics, transmission dynamics of infectious diseases, etc.

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