Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence

The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the se...

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Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2012-01, Vol.2012 (2012), p.646-666-145
Main Authors: Ozair, Muhammad, Lashari, Abid Ali, Jung, Il Hyo, Okosun, Kazeem Oare
Format: Article
Language:English
Subjects:
Control theory
Disease control
Disease transmission
Epidemiology
Human
Mathematical analysis
Mathematical models
Mortality
Mosquitoes
Nonlinear dynamics
Nonlinearity
Optimal control
Sensitivity analysis
Studies
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Summary:The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the sensitivity analysis of the basic reproductive number R0 and the endemic proportions with respect to epidemiological and demographic parameters are provided. From the results of the sensitivity analysis, the model is modified to assess the impact of three control measures; the preventive control to minimize vector human contacts, the treatment control to the infected human, and the insecticide control to the vector. Analytically the existence of the optimal control is established by the use of an optimal control technique and numerically it is solved by an iterative method. Numerical simulations and optimal analysis of the model show that restricted and proper use of control measures might considerably decrease the number of infected humans in a viable way.
ISSN:1026-0226
1607-887X
DOI:10.1155/2012/595487