@article{MAKHILLJMMS201913428208,
    title = {Mathematical Model and Numerical Analysis of Tumor Treatment with the Application of
Anti-Angiogenesis},
    journal = {Journal of Modern Mathematics and Statistics},
    volume = {13},
    number = {4},
    pages = {46-52},
    year = {2019},
    issn = {1994-5388},
    doi = {jmmstat.2019.46.52},
    url = {https://makhillpublications.co/view-article.php?issn=1994-5388&doi=jmmstat.2019.46.52},
    author = {M.M. and},
    keywords = {Tumor angiogenesis,anti-angiogenesis,finite difference method,avascular,endothelial cell},
    abstract = {Explanation of cell movement and cell
population in biology is one of the most interesting
themes of the mathematical oncology. This study targets
to produce numerical solutions of system of equation
produced by the process of angiogenesis in development
of tumor from vascular to avascular and then metastesis.
We consider a situation in which anti-angiogenesis
treatment is administered before a tumor is vascularized.
This involve the treatment by preventing the angiogenesis
by anti angiogenic agent namely said an Anti-Angiogenic
Factors (AAF). We developed the governing equations for
the conservation of endothelial cells, tumor angiogenic
factors and fibronectin concentrations. To solve these
equation a finite difference method is applied. Which is
consider to be very reliable and stable for parabolic partial
differential equations. After the discretization process of
equations, we get the matrices which solve by MATLAB
Simulations. We have used the previously published
parametric values which are chosen to suit this study.
Results obtained designate that when we applied the
antiangiogenic term to the equation for endothelial cell
concentration, endothelial cells concentration declines
identically. This can make huge inferences for cancer
treatment.}
    }