Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 595487, 21 pages
Research Article

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

1Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, H-12 Campus, Islamabad 44000, Pakistan
2Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea
3Department of Mathematics, Vaal University of Technology, Andries Potgieter Boulevard, Private Bag X021, Vanderbijlpark 1900, South Africa

Received 29 July 2012; Revised 17 September 2012; Accepted 17 September 2012

Academic Editor: M. De la Sen

Copyright © 2012 Muhammad Ozair et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 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.