Semi - Analytical Solution of Modelled Typhoid  Fever Disease

S  Rekha; Balaganesan Palanivelu; P Mercy

S Rekha Research Scholar, Department of Mathematics, AMET University, Chennai, India.
Balaganesan Palanivelu Associate Professor, Department of Mathematics, AMET University, Chennai, India.
P Mercy Professor and Head St.Joseph University Dimapur, Nagaland, India.

Keywords: Typhoid Modeling, Bacteria Populations, Human Population, Analytical Solution, Homotopy Perturbation Method, and Numerical Simulation

Abstract

To analyze the optimal control of the Typhoid fever virus a mathematical modeling was developed by Getachew Teshome Tilahun. We have approached a Homotopy Perturbation Method to solve a linear differential equation. An analytical solution of Susceptible People(S), Infected People (I), Carrier People (C), Recovered People (R), and
Bacteria People ( is obtained and compared with simulation results. A significant agreement is produced when approximate analytical results are compared to numerical simulation. The treatment rate of infectious disease (, Natural death rate (and typhoid-induced death rates (Î±) are discussed.

How to cite this article:
S Rekha, Palanivelu B, Mercy P. Semi - Analytical Solution of Modelled Typhoid Fever Disease. Chettinad Health City Med J. 2022;11(3):30-35.

DOI: https://doi.org/10.24321/2278.2044.202226

Author Biographies

S Rekha, Research Scholar, Department of Mathematics, AMET University, Chennai, India.

Research Scholar (Full time)

Department of Mathematics

AMET University

P Mercy, Professor and Head St.Joseph University Dimapur, Nagaland, India.

Professor and Head

St.Joseph University

Dimapur, Nagaland - 797 115

References

W.H.O. Background paper onvaccination against typhoid fever using New-Generation Vaccines - presented at

the SAGE 2007.

Cook GC, Zumla A. Mansonâ€™s tropical diseases. Elsevier Health Sciences; 2008 Dec 16. [Google Scholar]

WHO:Immunization Vaccines and Biologicals. Available from: https://www.who.int/teams/immunizationvaccines-and-biologicals/diseases/typhoid. Accessed

Nov 2020.

Simiyu K, Leslie J. Typhoid in a Kenyan village: its impact, its prevention. Am J Trop Med Hygien. 2018;95(5):1112-3.[PubMed] [Google Scholar]

Nthiiri JK. Mathematical modelling of typhoid fever disease incorporating protection against infection. Br

J Math Comput Sci. 2016;14(1):1â€“10. [Google Scholar]

Stephen E, Nyerere N. Modelling typhoid fever with education, vaccination and treatment and applied

mathematics. Am J Trop Med Hyg. 2016;2:156-64. [Google Scholar]

Ogunlade TO, Ogunmiloro OM, Ogunyebi SN, Fatoyinbo GE, Okoro JO, Akindutire OR, Halid OY, Olubiyi AO. On

the effect of vaccination, screening and treatment in controlling typhoid fever spread dynamics: deterministic

and stochastic applications. Math Stat. 2020;8(6):621-30. [Google Scholar]

He JH, El-Dib YO. Homotopy perturbation method for Fangzhu oscillator. J Math Chem. 2020 Nov;58(10):2245-

[Google Scholar]

Anjum N, He JH. Nonlinear dynamic analysis of vibratory behavior of a graphene nano/microelectromechanical

system. Math Meth Appl Sci. 2020; pp.1-16.[Google Scholar]

Wu Y, He JH. Homotopy perturbation method for nonlinear oscillators with coordinate dependent mass.

Results Phys. 2018 Sep;10:270-1. [Google Scholar]

Tilahun GT, Makinde OD, Malonza D. Modelling and optimal control of typhoid fever disease with cost-effective strategies. Comput Math Methods Med. 2017;2017:2324518. [PubMed] [Google Scholar]