scholarly journals Application of Mathematical Model of Cancer Treatment by Radiotherapy

2021 ◽  
Author(s):  
Seyedeh Nasrin Hosseini Motlagh ◽  
Faeze Lari Motefaker
Keyword(s):  
Mathematical Model ◽  
Cancer Treatment ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Volterra Equations ◽  
Adomian Decomposition ◽  
Treatment Stage ◽  
Competitive Model ◽  
The Mathematical Model ◽  
Cancerous Cells

The aim of this study is achieve an analysis of the mathematical model governing radiotherapy as well as to achieve the concentration of healthy and cancerous cells to reduce the length of treatment and less damage to cancer treatment by this type of therapy. In order to obtain this, we used the latest mathematical radiotherapy model based on the Lotka-Volterra competitive equations and the Adomian decomposition method that is the one of the most advanced analytical solutions to solve differential equations to attain our goal. The calculation of the Adomian decomposition method was applied to the mathematical model governing radiotherapy, and then the concentration of healthy and cancerous cells was achieved with a very good approximation. Comparison of the behavior of healthy and cancerous cells concentrations based on experimental cases and the behavior of healthy and cancerous cells concentrations based on computations express the correctness of the work. ADM indicates the concentration of healthy and cancerous cells during the treatment stage and the no treatment stage can be effective in improving the modeling based on the competitive model of the Lotka-Volterra equations, which results in the reduction of the use of diagnostic devices, less radiation, the faster treatment process and decreasing the cost of treatment for patients and governments.

Simulation of cancer treatment using the MATLAB SimBiology application

2021 ◽  
Vol 14 (3) ◽  
pp. 90-96
Author(s):  
Anastasia Goncharova ◽  
Maria Vil'
Keyword(s):  
Mathematical Model ◽  
Cancer Treatment ◽  
Interference Competition ◽  
The Body ◽  
Continuous Treatment ◽  
Constant Concentration ◽  
Application Package ◽  
The Mathematical Model ◽  
Cancerous Cells

The paper presents the implementation of the mathematical model of cancer taking into account interference competition and the model of continuous treatment with a constant concentration of the drug in the patient's blood. The implementation was carried out using the MATLAB SimBiology application package. The principle of implementation of different stages of the course of the disease within the framework of one model is described. On the basis of the constructed models and SimBiology tools, a modification was carried out that implements the discrete administration of doses of the drug in courses and takes into account its dynamics in the body, taking into account the assumption that the drug is consumed only to suppress cancerous cells.

scholarly journals Qualitative Analysis of a Mathematical Model in the Time of COVID-19

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Kamal Shah ◽  
Thabet Abdeljawad ◽  
Ibrahim Mahariq ◽  
Fahd Jarad
Keyword(s):  
Mathematical Model ◽  
Qualitative Analysis ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Point Theory ◽  
Adomian Decomposition ◽  
The Mathematical Model

In this article, a qualitative analysis of the mathematical model of novel corona virus named COVID-19 under nonsingular derivative of fractional order is considered. The concerned model is composed of two compartments, namely, healthy and infected. Under the new nonsingular derivative, we, first of all, establish some sufficient conditions for existence and uniqueness of solution to the model under consideration. Because of the dynamics of the phenomenon when described by a mathematical model, its existence must be guaranteed. Therefore, via using the classical fixed point theory, we establish the required results. Also, we present the results of stability of Ulam’s type by using the tools of nonlinear analysis. For the semianalytical results, we extend the usual Laplace transform coupled with Adomian decomposition method to obtain the approximate solutions for the corresponding compartments of the considered model. Finally, in order to support our study, graphical interpretations are provided to illustrate the results by using some numerical values for the corresponding parameters of the model.

scholarly journals Analytical Solutions for the Mathematical Model Describing the Formation of Liver Zones via Adomian’s Method

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdelhalim Ebaid
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Applied Mathematics ◽  
Mathematical Formulation ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Stationary Solutions ◽  
Proposed Model ◽  
Adomian Decomposition ◽  
The Mathematical Model

The formation of liver zones is modeled by a system of two integropartial differential equations. In this research, we introduce the mathematical formulation of these integro-partial differential equations obtained by Bass et al. in 1987. For better understanding of this mathematical formulation, we present a medical introduction for the liver in order to make the formulation as clear as possible. In applied mathematics, the Adomian decomposition method is an effective procedure to obtain analytic and approximate solutions for different types of operator equations. This Adomian decomposition method is used in this work to solve the proposed model analytically. The stationary solutions (as time tends to infinity) are also obtained through it, which are in full agreement with those obtained by Bass et al. in 1987.

Application of Adomian Decomposition Method on a Mathematical Model of Malaria

2020 ◽  
pp. 417-435
Author(s):  
Adesoye Idowu Abioye ◽  
Olumuyiwa James Peter ◽  
Ayotunde Abayomi Ayoade ◽  
Ohigweren Airenoni Uwaheren ◽  
Mohammed Olanrewaju Ibrahim
Keyword(s):  
Mathematical Model ◽  
Fourth Order ◽  
Decomposition Method ◽  
Deterministic Model ◽  
Adomian Decomposition Method ◽  
Model Solution ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Malaria Model

In this paper, we consider a deterministic model of malaria transmission. Adomian decomposition method (ADM) is used to calculate an approximation to the solution of the non-linear couple of differential equations governing the model. Classical fourth-order Runge-Kutta method implemented in Maple18 confirms the validity of the ADM in solving the problem. Graphical results show that ADM agrees with R-K 4. In order words, these produced the same behaviour, validating ADM's efficiency and accuracy of ADM in finding the malaria model solution.

Analytical Solution for the Subsurface Flow Wetland Model

2012 ◽  
Vol 198-199 ◽  
pp. 894-898
Author(s):  
Feng Lin Cheng
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Decomposition Method ◽  
Sewage Treatment ◽  
Subsurface Flow ◽  
Adomian Decomposition Method ◽  
Diffusion Characteristics ◽  
Adomian Decomposition ◽  
Laplace Transform Technique ◽  
The Laplace Transform

In this paper, the subsurface flow wetland sewage treatment mathematical model is studied. the analytical solution is obtained by using the Laplace transform technique for non-steady subsurface flow wetland model and the diffusion characteristics for some parameters used in the model are analyzed. Then the solution for the model which is added by the source is obtained on two boundary conditions by the adomian decomposition method. The examples are given compare the approximate solution and the exact solutions.

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

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