Advances in Research 19(1): 1-10, 2019; Article no.AIR.49220 ISSN: 2348-0394, NLM ID: 101666096 A Short Review and the Prediction of Tumor Growth based on Numerical Analysis Zakir Hossine 1 , Afrina Asad Meghla 1 and Md. Kamrujjaman 2 * 1 Department of Applied Mathematics, University of Dhaka, Dhaka 1000, Bangladesh. 2 Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh. Authors’ contributions This work was carried out in collaboration among all authors. All authors read and approved the final manuscript. Article Information DOI: 10.9734/AIR/2019/v19i130115 Editor(s): (1) Dr. Farooq Ahmed Shah, Department of Mathematics, COMSATS Institute of Information Technology, Pakistan. Reviewers: (1) Shaibu Osman, Catholic University of Eastern Africa, Kenya. (2) E. Ahmed, Mansoura University. Egypt. (3) Abdullah Sonmezoglu, Yozgat Bozok university, Turkey. Complete Peer review History: http://www.sdiarticle3.com/review-history/49220 Received: 10 March 2019 Accepted: 19 May 2019 Review Article Published: 23 May 2019 Abstract In this study, we consider Murray’s and Glioma’s tumor growth models based on reaction- diffusion equation. Mathematical modeling of tumor development are involved with the associated experimental work, reasoning the final relationship between experimental and theoretical approaches and these lead a path to model the prediction of tumor growth. Initially, we study the primary model of tumor growth which is connected with the ordinary differential equations and finally extended the problem to reaction-diffusion models. We predict the tumor growth model using numerical study and the observation in different zone of time. The goal of tumor growth prediction is to model the tumor growth process, which can be achieved by theoretical mathematical modeling collaboration with the model personalization from clinical assessment. After certain time period, it is shown that the mathematical model shows the tumor cell population reaching a maximum cell number that the tissue can carry. Keywords: Tumors growth; reaction-diffusion; spatial heterogeneity; numerical analysis. 2010 Mathematics Subject Classification: 92D25, 35K57 (primary), 35K61, 37N25 *Corresponding author: E-mail: kamrujjaman@du.ac.bd