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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Complex Dynamics of an Epidemic Model With Optimal Vaccination and Treatment in the Presence of Population Dispersal

Discontinuity, Nonlinearity, and Complexity 10(3) (2021) 471--497 | DOI:10.5890/DNC.2021.09.010

Manotosh Mandal$^{1,2}$, Soovoojeet Jana$^3$ , Swapan Kumar Nandi$^4$, T. K. Kar$^2$

$^{1}$ Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk -721636 , West Bengal, India

$^2$ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India

$^3$ Department of Mathematics, Ramsaday College, Amta-711401, Howrah, West Bengal, India

$^4$ Department of Mathematics, Nayabasat P.M.Sikshaniketan, Paschim Medinipur-721253, West Bengal, India

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In this article, we describe an SEIR type epidemic model with a transport-related infection between two cities in the presence of vaccination and treatment control. The epidemiological threshold, commonly known as basic reproduction number is derived and its impact on the dynamical behaviour of the disease has been established. The optimal control problem is constructed with the objective of minimizing the effect of infection in the system and then it is solved. We compare the result of the model to a real-world problem to establish that our model can be used in some practical cases if the parameters are known.


The authors are grateful to the anonymous reviewers and Prof. Dimitri Volchenkov, Editor-in-Chief of the journal for their valuable suggestions to improve both the quality and presentation of the manuscript significantly. The work of Soovoojeet Jana is financially supported by Dept of Science \& Technology Biotechnology, Govt. of West Bengal (vide memo no. 201 (Sanc.)/ST/P/S\&T/16G-12/2018 dt 19-02-2019).


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