Article ID: MTJPAM-D-24-00155

Title: Stability analysis of SIRI epidemic model with reintroduced susceptibles under incorporated time delay on susceptible individuals

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00155; Volume 6 / Issue 3 / Year 2024, Pages 558-578

Document Type: Research Paper

Author(s): Kanaka Maha Lakshmi Emandi ^a, Kalesha Vali Shaik ^b, Appa Rao Dokala ^c, Salma Umme ^d,

^aDepartment of Engineering Mathematics, Andhra University, 530003 Visakhapatnam, India

^bDepartment of Engineering Mathematics, Andhra University, 530003 Visakhapatnam, India

^cDepartment of Mathematics, Indian Institutes of Information Technology (IIIT), Rajiv Gandhi University of Knowledge Technologies (RGUKT), 532402 Srikakulam, India

^dDepartment of Electrical Electronics and Communication Engineering (EECE), Gandhi Institute of Technology and Management (GITAM) University, 530045 Visakhapatnam, India

Received: 25 September 2024, Accepted: 14 February 2025, Published: 12 August 2025

Corresponding Author: Kanaka Maha Lakshmi Emandi (Email address: kanakamahalakshmmi.rs@andhrauniversity.edu.in)

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Abstract

In this paper, a three-compartment SIRI epidemic model with reintroduced susceptibles under incorporated time delay on susceptible individuals is considered. Determined disease free, endemic equilibrium points and discussed local stability at endemic equilibrium point. Identified the point where the system stabilizes by means of Hopf bifurcation. Ascertained the results by numerical simulation using MATLAB. Observed that the system becomes unstable in both the cases of increase in the transmission rate and additional transaction rate respectively at a fixed critical time delay parameter using numerical examples.

Keywords: Re-infection rate, additional transaction rate, disease free equilibrium point, endemic equilibrium point, time delay, critical time delay parameter, Hopf-bifurcation

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