Analytical features of the SIR model and their applications to COVID-19

DOI10.1016/j.apm.2020.08.057zbMath1481.92146OpenAlexW3088403292WikidataQ100434073 ScholiaQ100434073MaRDI QIDQ2241766

Nikolay A. Kudryashov, Mikhail A. Chmykhov, Michael V. Vigdorowitsch

Publication date: 9 November 2021

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2020.08.057

zbMATH Keywords

coronavirussolutionnonlinear differential equationfirst integralinfectionSIR-model

Mathematics Subject Classification ID

Epidemiology (92D30) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (16)

Community-distributed compartmental models ⋮ Nonlinear control of infection spread based on a deterministic SEIR model ⋮ A restricted epidemic SIR model with elementary solutions ⋮ Toward an efficient approximate analytical solution for 4-compartment COVID-19 fractional mathematical model ⋮ Basic reproduction number for the SIR epidemic in degree correlated networks ⋮ Bayesian computational methods for state-space models with application to SIR model ⋮ Analytical and numerical investigation of the SIR mathematical model ⋮ Novel class of susceptible-infectious-recovered models involving power-law interactions ⋮ Computational aspects of the approximate analytic solutions of the SIR model: applications to modelling of COVID-19 outbreaks ⋮ Stochastic Modeling of a Measles Outbreak in Brazil ⋮ Network-based uncertainty quantification for mathematical models in epidemiology ⋮ Analytical properties and solutions of a modified Lindemann mechanism with three reaction rate constants ⋮ Two critical times for the SIR model ⋮ Comments on some analytical and numerical aspects of the SIR model ⋮ Asymptotic analysis of the SIR model and the Gompertz distribution ⋮ The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: new framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case

Uses Software

• GitHub

Cites Work

• Exact analytical solutions of the susceptible-infected-recovered (SIR) epidemic model and of the SIR model with equal death and birth rates
• On the Lambert \(w\) function
• Accurate closed-form solution of the SIR epidemic model
• Analysis and forecast of COVID-19 spreading in China, Italy and France
• Dynamics and density function analysis of a stochastic SVI epidemic model with half saturated incidence rate
• Insights into the dynamics and control of COVID-19 infection rates
• Painlevé analysis and exact solutions of the fourth-order equation for description of nonlinear waves
• Global dynamics of SIR model with switched transmission rate
• Painlevé analysis and exact solutions of the Korteweg-de Vries equation with a source
• Simplest equation method to look for exact solutions of nonlinear differential equations
• The Mathematics of Infectious Diseases
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I

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