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Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables

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  • Muhammad Altaf Khan
  • Saeed Islam
  • Sher Afzal Khan
  • Ilyas Khan
  • Sharidan Shafie
  • Taza Gul

Abstract

Leptospirosis is an infectious disease that damages the liver and kidneys, found mainly in dogs and farm animals and caused by bacteria. In this paper, we present the optimal control problem applied to a dynamical leptospirosis infected vector and human population by using multiple control variables. First, we show the existence of the control problem and then use analytical and numerical techniques to investigate the existence cost effective control efforts for prevention of indirect and direct transmission of this disease. In order to do this, we consider three control functions two for human and one for vector population. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method.

Suggested Citation

  • Muhammad Altaf Khan & Saeed Islam & Sher Afzal Khan & Ilyas Khan & Sharidan Shafie & Taza Gul, 2014. "Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, November.
    • Handle: RePEc:hin:jnlaaa:619035
    DOI: 10.1155/2014/619035
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    Cited by:

    1. Fauzi Mohamed Yusof & Farah Aini Abdullah & Ahmad Izani Md. Ismail, 2019. "Modeling and Optimal Control on the Spread of Hantavirus Infection," Mathematics, MDPI, vol. 7(12), pages 1-11, December.
    2. Khan, Muhammad Altaf & Khan, Rizwan & Khan, Yasir & Islam, Saeed, 2018. "A mathematical analysis of Pine Wilt disease with variable population size and optimal control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 205-217.

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