Title: An SEIR epidemic model's global analysis that incorporates the bi-linear incidence rate with treatment function

Authors: S.K. Tiwari; Pradeep Porwal; Neha Mangal

Addresses: School of Studies in Mathematics, Vikram University, Ujjain, M.P., India ' School of Studies in Mathematics, Vikram University, Ujjain, M.P., India ' School of Studies in Mathematics, Vikram University, Ujjain, M.P., India

Abstract: In this paper, the bi-linear incidence rate and saturated treatment function of the SEIR epidemic model are examined, with a particular emphasis on the impact of inadequate treatment on the infectious disease's transmissibility. The basic reproductive number, which determines the potential for disease extinction or persistence, is evaluated. The determination of threshold requirements for all types of equilibrium points is examined. We prove that the equilibrium is locally asymptotically stable by calculating the eigenvalues and using the Routh-Hurwitz criterion. The autonomous convergence theorem and the Lyapunov function are also used to investigate the disease-free and endemic equilibrium's global asymptotical stability. The research carried out suggested that the commencement of treatment is a highly relevant element in infection control. The results of the numerical simulations are used to support and verify the theoretical findings.

Keywords: mathematical models; epidemiology; treatment; basic reproduction number; stability analysis.

DOI: 10.1504/IJANS.2024.141345

International Journal of Applied Nonlinear Science, 2024 Vol.4 No.3, pp.175 - 190

Received: 24 Jul 2023
Accepted: 01 Dec 2023
Published online: 09 Sep 2024 *

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