Study of fractional order SIR model with M-H type treatment rate and its stability analysis

Subrata Paul; Animesh Mahata; Supriya Mukherjee; Meghadri Das; Prakash Chandra Mali; Banamali Roy; Poulami Mukherjee; Pramodh Bharati

doi:10.59292/bulletinbiomath.2024004

Authors

Subrata Paul Department of Mathematics, Arambagh Govt. Polytechnic, Arambagh-712602, West Bengal, India https://orcid.org/0000-0002-5886-4341
Animesh Mahata Department of Mathematics, Sri Ramkrishna Sarada Vidya Mahapitha, Kamarpukur, Hooghly-712612, India https://orcid.org/0000-0002-4261-0611
Supriya Mukherjee Department of Mathematics, Gurudas College, 1/1 Suren Sarkar Road, Kolkata-700054, West Bengal, India https://orcid.org/0000-0001-5586-8358
Meghadri Das Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India https://orcid.org/0000-0001-6512-9700
Prakash Chandra Mali Department of Mathematics, Jadavpur University, 188 Raja S.C. Mallik Road, Kolkata-700032, West Bengal, India https://orcid.org/0009-0004-5342-2001
Banamali Roy Department of Mathematics, Bangabasi Evening College, Kolkata-700009, West Bengal, India https://orcid.org/0000-0001-5231-1474
Poulami Mukherjee Department of Mathematics, Calcutta Girls’ B.T. College, Ballygunge, Kolkata-700019, West Bengal, India https://orcid.org/0009-0007-7910-5583
Pramodh Bharati Department of Mathematics, Ramnagar College, Purba Medinipur-721453, West Bengal, India https://orcid.org/0009-0008-0627-7234

DOI:

https://doi.org/10.59292/bulletinbiomath.2024004

Keywords:

SIR model, Monod-Haldane type treatment rate, optimal control, Caputo derivative

Abstract

In this manuscript, we analyze a fractional-order susceptible-infected-recovered (SIR) mathematical model with a nonlinear incidence rate and nonlinear treatment rate for the control of infectious illness. The incidence rate of infection is considered as Holling type II and the treatment rate is considered as Monod-Haldane (MH) type. The existence and uniqueness criteria for the new model, as well as the non-negativity and boundedness, have been established. We also provide an ideal control strategy for the SIR model using the treatment rate as a control parameter. The solution of the suggested model is approximated using the fractional-order Taylor's method. With the help of MATLAB (2018a), we perform numerical simulations and illustrate the results through graphical representations.

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