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Nonlinear dynamics in an SIR model with ratio-dependent incidence and holling type III treatment rate functions

Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics: Selected Works from the BIOMAT Consortium Lectures, Rio de Janeiro, Brazil, 2022, Page: 57-72
2023
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Book Chapter Description

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 R > 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.

Bibliographic Details

Akriti Srivastava; Prashant K. Srivastava

Springer Science and Business Media LLC

Mathematics; Medicine; Agricultural and Biological Sciences; Environmental Science; Biochemistry, Genetics and Molecular Biology

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