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Optimal Campaign in Leptospirosis Epidemic by Multiple Control Variables
Department of Mathematics, University of Malakand, Chakdara, Lower Dir District of Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, University of Malakand, Chakdara, Lower Dir District of Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan
Department of Business Administration and Accounting, Buraimi University College, Al-Buraimi, Oman
- 1 Department of Mathematics, University of Malakand, Chakdara, Lower Dir District of Khyber Pakhtunkhwa, Pakistan
- 2 Department of Mathematics, University of Malakand, Chakdara, Lower Dir District of Khyber Pakhtunkhwa, Pakistan
- 3 Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan
- 4 Department of Business Administration and Accounting, Buraimi University College, Al-Buraimi, Oman
Applied Mathematics·Volume 03 (2012)·Pages 1655–1663·Published 7 November 2012·DOI10.4236/am.2012.311229
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Abstract
In this paper, we consider a leptospirosis epidemic model to implement optimal campaign by using multiple control variables. First, we show the existence of the control problem. Then we derive the conditions under which it is optimal to eradicate the leptospirosis infection and examine the impact of a possible educatioal/vaccinaction campaign using Pontryagin’s Maximum Principle. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method. The results obtained from the numerical simulations of the model show that a possible educational/vaccinaction combined with effective treatment regime would reduce the spread of the leptospirosis infection appreciably.
KeywordsMathematical ModelOptimal ControlPontryagin’s Maximum PrincipleNumerical Results
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