CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

Stochastic SEIR Model for Measles with Differential Transformation Method (DTM)

by Hammad Khalid, Hamna Khalid, Maira Shafiq
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 184 - Number 2
Year of Publication: 2022
Authors: Hammad Khalid, Hamna Khalid, Maira Shafiq
10.5120/ijca2022922013

Hammad Khalid, Hamna Khalid, Maira Shafiq . Stochastic SEIR Model for Measles with Differential Transformation Method (DTM). International Journal of Computer Applications. 184, 2 ( Mar 2022), 9-13. DOI=10.5120/ijca2022922013

@article{ 10.5120/ijca2022922013,
author = { Hammad Khalid, Hamna Khalid, Maira Shafiq },
title = { Stochastic SEIR Model for Measles with Differential Transformation Method (DTM) },
journal = { International Journal of Computer Applications },
issue_date = { Mar 2022 },
volume = { 184 },
number = { 2 },
month = { Mar },
year = { 2022 },
issn = { 0975-8887 },
pages = { 9-13 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume184/number2/32303-2022922013/ },
doi = { 10.5120/ijca2022922013 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T01:20:23.031574+05:30
%A Hammad Khalid
%A Hamna Khalid
%A Maira Shafiq
%T Stochastic SEIR Model for Measles with Differential Transformation Method (DTM)
%J International Journal of Computer Applications
%@ 0975-8887
%V 184
%N 2
%P 9-13
%D 2022
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The epidemic models are important to study and control epidemiological diseases. The SEIR model of measles disease in children has been solved and evaluated using the differential transformation method (DTM). This is a numerical and semi-analytic technique that is used to solve differential and integral equations.We solved a measles model with the help of differential transformation method and discussed two cases one is endemic and other is a disease-free state. In both cases, if threshold number R0 < 1 then we get a locally stable situation while at R0 > 1 we get a locally unstable situation. Also, compared it with [6] to prove better convergence of differential transformation method. This approach offers solutions for converging a series of conveniently computable components. DTM is an efficient tool to solve linear and non-linear differential equations. We compare results with Runge-Kutta fourth order. DTM is much convenient and gives better results.

References
  1. FNM Al-Showaikh and Edward H Twizell. One-dimensional measles dynamics. Applied mathematics and computation, 152(1):169–194, 2004.
  2. Suwardi Annas, Muh Isbar Pratama, Muh Rifandi, Wahidah Sanusi, and Syafruddin Side. Stability analysis and numerical simulation of seir model for pandemic covid-19 spread in indonesia. Chaos, Solitons &amp; Fractals, 139:110072, 2020.
  3. Alexander D Becker, Amy Wesolowski, Ottar N Bjørnstad, and Bryan T Grenfell. Long-term dynamics of measles in london: Titrating the impact of wars, the 1918 pandemic, and vaccination. PLoS computational biology, 15(9):e1007305, 2019.
  4. Muhammad Farman, Muhammad Umer Saleem, Aqeel Ahmad, and MO Ahmad. Analysis and numerical solution of seir epidemic model of measles with non-integer time fractional derivatives by using laplace adomian decomposition method. Ain Shams Engineering Journal, 9(4):3391–3397, 2018.
  5. Veronika Grimm, Friederike Mengel, and Martin Schmidt. Extensions of the seir model for the analysis of tailored social distancing and tracing approaches to cope with covid-19. Scientific Reports, 11(1):1–16, 2021.
  6. AAM Hassan, SA Hoda Ibrahim, and Mohamed GM Ibrahim. Numerical solution of a system seir nonlinear odes by rungekutta fourth order method. International Journal of Computer Applications, 124(3), 2015.
  7. Shaobo He, Yuexi Peng, and Kehui Sun. Seir modeling of the covid-19 and its dynamics. Nonlinear Dynamics, 101(3):1667–1680, 2020.
  8. Hai-Feng Huo, Qian Yang, and Hong Xiang. Dynamics of an edge-based seir model for sexually transmitted diseases. Math. Biosci. Eng, 17(1):669–699, 2020.
  9. Matt J Keeling and Bryan T Grenfell. Understanding the persistence of measles: reconciling theory, simulation and observation. Proceedings of the Royal Society of London. Series B: Biological Sciences, 269(1489):335–343, 2002.
  10. MdR de Pinho M. H. A. Biswas, L. T. Paiva. A seir model for control of infectious diseases with constraints. Mathematical Biosciences and Engineering, 11(1551-0018-2014-4- 761):761, 2014.
  11. Farshid Mirzaee. Differential transform method for solving linear and nonlinear systems of ordinary differential equations. 5(70):3465 – 3472, 2011.
  12. Sucheta Moharir and Narhari Patil. Application of differential transform method for solving differential and integral equations. 2012.
  13. A.A. Momoh, I.J. Uwanta M.O. Ibrahim, and S.B. Manga4. Mathematical model for control of measles epidemiology. International Journal of Pure and Applied Mathematics, 15(5):707–718, 2013.
  14. Samuel O Sowole, Daouda Sangare, Abdullahi A Ibrahim, and Isaac A Paul. On the existence, uniqueness, stability of solution and numerical simulations of a mathematical model for measles disease. International journal of advances in mathematics, 4:84–111, 2019.
  15. Jing Zhou. Differential transformation and application for electrical circuits. Huazhong University Press, Wuhan, China;, 1986.
Index Terms

Computer Science
Information Sciences

Keywords

Deterministic and stochastic modeling numerical method differential transformation method solution of the measles SEIR model

Powered by PhDFocusTM