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Optimal control and stability analysis of an epidemic model with population dispersal

Author

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  • Jana, Soovoojeet
  • Haldar, Palash
  • Kar, T.K.

Abstract

In the present paper we consider an SEIR type epidemic model with transport related infection between two cities. It is observed that transportation among regions has a strong impact on the dynamic evolution of a disease which can be eradicated in the absence of transportation. Transportation can lead to the incorporation of a positive risk probability. The epidemiological threshold, commonly known as the basic reproduction number, is derived and it is observed that when the basic reproduction number is less than unity the disease dies out, where as if it exceeds unity the disease may persist in the system. A thorough dynamical behavior of the constructed model is studied. We formulate and solve an optimal control problem using vaccination as a control tool. Extensive numerical simulations are carried out based on our analytical results. Finally we try to relate our work with a real world problem.

Suggested Citation

  • Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.
    • Handle: RePEc:eee:chsofr:v:83:y:2016:i:c:p:67-81
    DOI: 10.1016/j.chaos.2015.11.018
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    References listed on IDEAS

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    1. Yao Chen & Mei Yan & Zhongyi Xiang, 2014. "Transmission Dynamics of a Two-City SIR Epidemic Model with Transport-Related Infections," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, January.
    2. Liu, Junli & Zhou, Yicang, 2009. "Global stability of an SIRS epidemic model with transport-related infection," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 145-158.
    3. Julien Arino & P. van den Driessche, 2003. "A multi-city epidemic model," Mathematical Population Studies, Taylor & Francis Journals, vol. 10(3), pages 175-193.
    4. Li, Xue-Zhi & Li, Wen-Sheng & Ghosh, Mini, 2009. "Stability and bifurcation of an SIS epidemic model with treatment," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2822-2832.
    5. Li, Xue-Zhi & Zhou, Lin-Lin, 2009. "Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 874-884.
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    Cited by:

    1. Andrea Di Liddo, 2018. "Price and Treatment Decisions in Epidemics: A Differential Game Approach," Mathematics, MDPI, vol. 6(10), pages 1-19, October.
    2. Feng, Liang & Zhao, Qianchuan & Zhou, Cangqi, 2020. "Epidemic in networked population with recurrent mobility pattern," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Andrea Di Liddo, 2016. "Optimal Control and Treatment of Infectious Diseases. The Case of Huge Treatment Costs," Mathematics, MDPI, vol. 4(2), pages 1-27, April.
    4. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.
    5. Abbasi, Zohreh & Zamani, Iman & Mehra, Amir Hossein Amiri & Shafieirad, Mohsen & Ibeas, Asier, 2020. "Optimal Control Design of Impulsive SQEIAR Epidemic Models with Application to COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.
    7. Mandal, Manotosh & Jana, Soovoojeet & Nandi, Swapan Kumar & Khatua, Anupam & Adak, Sayani & Kar, T.K., 2020. "A model based study on the dynamics of COVID-19: Prediction and control," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).

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