Mathematical Modeling of Typhoid Fever Disease Incorporating Unprotected Humans in the Spread Dynamics
Journal of Advances in Mathematics and Computer Science,
Page 1-11
DOI:
10.9734/jamcs/2019/v32i330144
Abstract
A deterministic mathematical model of typhoid fever incorporating unprotected humans is formulated in this study and employed to study local and global stability of equilibrium points. The model incorporating Susceptible, unprotected, Infectious and Recovered humans which are analyzed mathematically and also result into a system of ordinary differential equations which are used for interpretations and comparison to the qualitative solutions in studying the spread dynamics of typhoid fever. Jacobian matrix was considered in the study of local stability of disease free equilibrium point and Castillo-Chavez approach used to determine global stability of disease free equilibrium point. Lyapunov function was used to study global stability of endemic equilibrium point. Both equilibrium points (DFE and EE) were found to be local and globally asymptotically stable. This means that the disease will be dependent on numbers of unprotected humans and other factors who contributes positively to the transmission dynamics.
Keywords:
- Basic reproduction number
- invariant region
- positivity of solution
- mathematical model
- unprotected humans
- disease free equilibrium
- endemic equilibrium point
- global stability
How to Cite
References
WHO Background paper on vaccination against typhoid fever using new generation vaccines-presented at the SAGE November 2007 meeting. WHO. 2007;11.
Nthiiri JK. Global stability of equilibrium points of typhoid fever model with protection. 2017; 21(5):1-6.
[Article no.BJMSCS.32690] [ISSN:2231-0851]
Nthiiri JK, Lawi GO, Akinyi CO. Mathematical modeling of typhoid fever disease in co-orporating protection against infection. BJMCS 23325. 2016;1-10.
Muhammad AK, Muhammad P, Saeed I. Mathematical analysis of typhoid model with saturated incidence rate 92D25. 2017;7(2):65-78.
Ivanoff BN, Levine MM. Lambert fever: Present statuses Bulletin of the world heal organization. 1994;72(6):957-971.
Adetunde IA. Mathematical model of spread of typhoid fever. World Journal of Applied Science and Technology. 2008;3(2):10-12.
Shaibu Osman, Oluwole Daniel Makinde, David Mwangi Theuri. Stability analysis and modeling of listeriosis dynamics in human and animal population. Global Journal of Pure and Applied Mathematics. 2018c;14(1):115-137.
Oluwole Daniel Makinde. A domain decomposition approach to a sir epidemic model with constant vaccination strategy. Applied Mathematics and Computation. 2007;184(2):842-848.
Shaibu Osman, Oluwale Daniel Makinde, David Mwangi Theuri. Mathematical modeling of transmission dynamics of Anthrax in human and animal population. Mathematical Theory and Modelling; 2018b.
Moffat N. Chamuchi, Johana K. Sigee, Jeconiah A. Okello, James M. Okwoyo. SIICR model and simulation of the effects of carriers on the transmission dynamics of typhoid fever in KISII town Kenya. 2014;2(3).
Peter OJ, Ibrahim MO, Akinduko OB, Rabiu M. Mathematics model for the control of typhoid fever. ISOR Journal of Mathematics (ISOR-JM). 2017;13(4)Ver. II.:60-66.
Stephen Edward, Kitengeso Raymond E, Kiria Gabriel T, Felician N, Mwema G, Mafarasa A. Mathematical model for control and elimination of the transmission dynamics of measles. 2015;4(6): 396-408.
[ISSN 2328-5605]
DOI: 10.11648/j.acm.20150406.12
LaSalle JS. Stability of dynamical systems. CBMS-NS Fregional conference series in applied mathematics. SIAM. 1976;25.
Ochoche JM, Gweryina RI. On mathematical model on measles with vaccination and two phases of infectiousness. 2014;10(1)Ver-V:95-105.
[ISSN 2278-5728,P-ISSN:2319-765X]
Leopard C. Mpande, Damian Kajunguri, Emmanuel A. Mpolya. Modelling and stability analysis for measles meta population model with vaccination. ISSN 2328-5605, 2328-5613. 2015;4(6):431-444.
Kalu A, Agwi IA, Agbanyim Akuagwuon N. Mathematical analysis of the endemic equilibrium dynamics of the transmission dynamics of tuberculosis. International Journal of Scientific and Technology Research. 2013;2(12).
Castillo-Chavez, Feng Z, Hung W. Computation of basic reproductive number and its role. Global Stability. 2002;125:229-250.
Soufiane Elkhaiar, Abdelilah Kaddar. On stability analysis of a SEIR with treatment. Article ID 101266. 2017;1:1-16.
DOI: 10.11131/2017/101266
Hongbin Guo, Michael YLI. Global stability in a mathematical model of tuberculosis. Article in Canadian Applied Mathematics Quarterly. 2006;4(2).
-
Abstract View: 2032 times
PDF Download: 904 times
