Mathematical analysis of a delayed epidemic model with nonlinear incidence and treatment rates

DOI10.1007/s10665-019-09989-3zbMath1425.34095OpenAlexW2921941578WikidataQ128268977 ScholiaQ128268977MaRDI QIDQ2324448

Abhishek Kumar, Murray E. Alexander Nilam

Publication date: 11 September 2019

Published in: Journal of Engineering Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10665-019-09989-3

zbMATH Keywords

time delayHopf bifurcationlocal and global stabilitySIR modelHolling type III treatment rateMonod-Haldane incidence rate

Mathematics Subject Classification ID

Epidemiology (92D30) Stability theory of functional-differential equations (34K20) Periodic solutions to functional-differential equations (34K13) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Stationary solutions of functional-differential equations (34K21)

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Cites Work

• Unnamed Item
• Unnamed Item
• Persistence and global stability of Bazykin predator-prey model with Beddington-DeAngelis response function
• Dynamics of an SIR epidemic model with limited medical resources revisited
• Quantitative analysis of time delays of glucose-insulin dynamics using artificial pancreas
• Analysis of a stage-structured predator-prey model with Crowley-Martin function
• Stability of a delayed SIRS epidemic model with a nonlinear incidence rate
• Qualitative analysis of a SIR epidemic model with saturated treatment rate
• Some epidemiological models with nonlinear incidence
• Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
• Dynamical behavior of epidemiological models with nonlinear incidence rates
• A generalization of the Kermack-McKendrick deterministic epidemic model
• Nonlinear systems. Analysis, stability, and control
• Introduction to functional differential equations
• Bifurcations in an epidemic model with constant removal rate of the infectives
• Dynamical models of tuberculosis and their applications
• A disease transmission model in a nonconstant population
• Global dynamics of a SEIR model with varying total population size
• Global behavior of an SEIRS epidemic model with time delays
• Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
• Global analysis of an epidemic model with nonmonotone incidence rate
• An SVEIR model for assessing potential impact of an imperfect anti-SARS vaccine
• Periodicity in an epidemic model with a generalized non-linear incidence
• The Mathematics of Infectious Diseases
• MODELING AND ANALYSIS OF AN SEIR MODEL WITH DIFFERENT TYPES OF NONLINEAR TREATMENT RATES
• A Simple Proof of Descartes's Rule of Signs
• Stability of a Time Delayed SIR Epidemic Model Along with Nonlinear Incidence Rate and Holling Type-II Treatment Rate
• An SIR Model with Nonlinear Incidence Rate and Holling Type III Treatment Rate
• A delayed SIR epidemic model with a general incidence rate

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