Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies
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Date
2017
Authors
Tilahun, Getachew Teshome
Oluwole, Daniel Makinde
Malonza, David
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi Publishing Corporation
Abstract
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.
Description
Research Article
Keywords
Citation
Computational and Mathematical Methods in Medicine Volume 2017, Article ID 2324518, 16 pages