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G. Zaman, Y. H. Kang and I. H. Jung, “Optimal Treatment of an SIR Epedemic Model with Time Delay,” Biosystems, Vol. 98, No. 1, 2009, pp. 43-50. doi:10.1016/j.biosystems.2009.05.006

has been cited by the following article:

• TITLE: Optimal Campaign in Leptospirosis Epidemic by Multiple Control Variables

  AUTHORS: Muhammad Altaf Khan, Gul Zaman, Saeed Islam, Muhammad Ikhlaq Chohan

  KEYWORDS: Mathematical Model; Optimal Control; Pontryagin’s Maximum Principle; Numerical Results

  JOURNAL NAME: Applied Mathematics, Vol.3 No.11, November 20, 2012

  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.