Discontinuity, Nonlinearity, and Complexity
Complex Dynamics of an Epidemic Model With Optimal Vaccination and Treatment in the Presence of Population Dispersal
Discontinuity, Nonlinearity, and Complexity 10(3) (2021) 471497  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,
Howrah711103, West Bengal, India
$^3$ Department of Mathematics, Ramsaday College, Amta711401, Howrah, West Bengal, India
$^4$ Department of Mathematics, Nayabasat P.M.Sikshaniketan, Paschim Medinipur721253, West Bengal, India
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Abstract
In this article, we describe an SEIR type epidemic model with a transportrelated 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 realworld problem to establish that our model can be used in some practical cases if the parameters are known.
Acknowledgments
The authors are grateful to the anonymous reviewers and Prof. Dimitri Volchenkov,
EditorinChief 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/16G12/2018 dt 19022019).
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