Numerical Solutions of the SIRD Cholera Model Using the HPM and RKM Methods

Munira Salisu¹ , Mohammed Salahuddeen Atureta² , Muhammad Manga³

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.3 , pp.75-79, Jun-2024

Online published on Jun 30, 2024

Copyright © Munira Salisu, Mohammed Salahuddeen Atureta, Muhammad Manga . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this study we have modified SIRD model for the treatment of Cholera disease by the four control strategies such as the Vaccination, surveillance, washing of food items and therapeutic treatment. Using Homotopy perturbation method and the Runge kutta method. The susceptible class,Infected class and the recovered and the death category is being related with the homotopy perturbation method and the runge kutta method to observe the most efficient method to use to control the disease better.

Key-Words / Index Term :
SIRD model, Susceptible, Infected, Recovered, Death, Runge kutta(order 4and order 5) method, Homotopy perturbation method

References :
[1] A.A Ayoade and O.J Peter ‘’ on global stability of cholera model with prevention and control, Malaysian journal of computing ‘’ Vol.3(1) pp 28-36. 2018.
[2] A.S. Mohammed and M.G salisu ‘’Global stability of SEIR model with holling type 11 incidence function : computational and mathematical methods in medicine.’’ Vol.2012 article ID 826052 pp1-8 2012.
[3] B.O Akogwu, and J.O. Fatoba ‘’Numerical solutions of Covid 19 SIRD model in Nigeria’’. Vol. 6 no 4 pp 66-67 (2022).
[4] D.N. Kwasi and C. Afriyel ‘’ control measures and the environment in the transmission dynamics of cholera’’ Vol. 2020 article ID 2485979 pp 1-16. 2020.
[5] J.H. He’’ Comparison of homotopy perturbation method and homotopy analysis method’’. Applied mathematics and computation.. Vol 156 pp 527-539 .2004.
[6] K.H. hantsa and B.N Kahsay.’’ Analysis of Cholera epidemic controlling using mathematical modelling’’ Vol. 2020 article ID 7369204 pp 1-14. 2020
[7] M.A Islam ‘’Comparative study on numerical solutions of initial value problems ivp for ordinary differential equations (ODE) with Euler and Runge kutta method’’ Vol 5 pp 393-404. 2015.
[8] N.K soopy,S Aman,K. Shah,H. Alarabiah and M.Arfan ‘’Mathematical analysis of SIRD model of COVID 19 with capputo fractional derivative based real data’’ Vol 103772 pp2211-3797.2020.
[9] O.L Paride and H.mlyashimbi ‘’ fractional order model for cholera disease transmission with control strategies’’ Vol. 2022-R issue10 pp28919. 2020.
[10] P.Panjah’’ optimal control analsys of a cholera model’’ Biophysical reviews and letters. Vol. 14(1) pp 27-48. 2021.