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Journal of Applied Mathematics
Volume 2012, Article ID 294275, 14 pages
Research Article

Prevention of Influenza Pandemic by Multiple Control Strategies

1Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa 23200, Pakistan
2Department of Mathematics, University of Malakand, Chakdara, Lower Dir, Khyber Pakhtunkhwa 23101, Pakistan

Received 4 October 2012; Accepted 25 November 2012

Academic Editor: Junjie Wei

Copyright © 2012 Roman Ullah 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.


We present the prevention of influenza pandemic by using multiple control functions. First, we adjust the control functions in the pandemic model, then we show the existence of the optimal control problem, and, by using both analytical and numerical techniques, we investigate cost-effective control effects for the prevention of transmission of disease. To do this, we use four control functions, the first one for increasing the effect of vaccination, the second one for the strategies to isolate infected individuals, and the last two for the antiviral treatment to control clinically infectious and hospitalization cases, respectively. We completely characterized the optimal control and compute the numerical solution of the optimality system by using an iterative method.