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

Author

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  • Muhammad Ozair
  • Abid Ali Lashari
  • Il Hyo Jung
  • Kazeem Oare Okosun

Abstract

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.

Suggested Citation

  • Muhammad Ozair & Abid Ali Lashari & Il Hyo Jung & Kazeem Oare Okosun, 2012. "Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-21, November.
    • Handle: RePEc:hin:jnddns:595487
    DOI: 10.1155/2012/595487
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    Cited by:

    1. Pang, Liuyong & Zhao, Zhong & Song, Xinyu, 2016. "Cost-effectiveness analysis of optimal strategy for tumor treatment," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 293-301.
    2. Cai, Li-Ming & Li, Xue-Zhi & Li, Zhaoqiang, 2013. "Dynamical behavior of an epidemic model for a vector-borne disease with direct transmission," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 54-64.
    3. Kumari, Sangeeta & Upadhyay, Ranjit Kumar, 2021. "Exploring the behavior of malware propagation on mobile wireless sensor networks: Stability and control analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 246-269.
    4. Liu, Li & Luo, Xiaofeng & Chang, Lili, 2017. "Vaccination strategies of an SIR pair approximation model with demographics on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 282-290.
    5. Upadhyay, Ranjit Kumar & Singh, Prerna, 2020. "Modeling and control of computer virus attack on a targeted network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    6. Avila-Vales, Eric & Pérez, Ángel G.C., 2019. "Dynamics of a time-delayed SIR epidemic model with logistic growth and saturated treatment," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 55-69.

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