Nonlinear Dynamics in an SIR Model with Ratio-Dependent Incidence and Holling Type III Treatment Rate Functions

Akriti Srivastava and Prashant K. Srivastava ()
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Akriti Srivastava: Indian Institute of Technology Patna, Department of Mathematics
Prashant K. Srivastava: Indian Institute of Technology Patna, Department of Mathematics

A chapter in Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics, 2023, pp 57-72 from Springer

Abstract: Abstract This article proposes and analyzes a Susceptible-Infective-Recovered (SIR) infectious disease model. Here we consider a ratio-dependent incidence rate and Holling type III treatment rate functions. We observe that there is a possibility of existence of multiple endemic steady states when ℛ0 > 1. A geometric approach is used to establish the global asymptotic stability of the unique endemic steady state under certain condition. Bi-stable steady states, transcritical bifurcation, and hysteresis are some of the nonlinear dynamical phenomena which are observed in this model system. Numerical examples are provided to demonstrate and validate our analytical results.

Keywords: Holling type III treatment; Nonlinear incidence; Stability analysis; Bifurcation analysis (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-33050-6_4

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DOI: 10.1007/978-3-031-33050-6_4

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