Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies
Joint Authors
Malonza, D. M.
Tilahun, Getachew Teshome
Makinde, Oluwole Daniel
Source
Computational and Mathematical Methods in Medicine
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-09-10
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population.
The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix.
Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined.
The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed.
The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers.
The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted.
Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.
American Psychological Association (APA)
Tilahun, Getachew Teshome& Makinde, Oluwole Daniel& Malonza, D. M.. 2017. Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies. Computational and Mathematical Methods in Medicine،Vol. 2017, no. 2017, pp.1-16.
https://search.emarefa.net/detail/BIM-1141995
Modern Language Association (MLA)
Tilahun, Getachew Teshome…[et al.]. Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies. Computational and Mathematical Methods in Medicine No. 2017 (2017), pp.1-16.
https://search.emarefa.net/detail/BIM-1141995
American Medical Association (AMA)
Tilahun, Getachew Teshome& Makinde, Oluwole Daniel& Malonza, D. M.. Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies. Computational and Mathematical Methods in Medicine. 2017. Vol. 2017, no. 2017, pp.1-16.
https://search.emarefa.net/detail/BIM-1141995
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1141995