Time-continuous and time-discrete SIR models revisited: theory and applications

DOI10.1186/s13662-020-02995-1zbMath1486.92291OpenAlexW3091889883WikidataQ100518641 ScholiaQ100518641MaRDI QIDQ2125802

Jan Schlüter, Benjamin Wacker

Publication date: 14 April 2022

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-020-02995-1

zbMATH Keywords

well-posednessdifference equationsexistence and uniquenessnonlinear ordinary differential equationsnumerical analysisSIR modelmathematical epidemiologyCOVID-19

Mathematics Subject Classification ID

Epidemiology (92D30) Dynamical systems in biology (37N25)

Related Items (4)

A cubic nonlinear population growth model for single species: theory, an explicit-implicit solution algorithm and applications ⋮ Qualitative analysis of two systems of nonlinear first‐order ordinary differential equations for biological systems ⋮ Framework for solving dynamics of Ca²⁺ ion concentrations in liver cells numerically: Analysis of a non‐negativity‐preserving non‐standard finite‐difference method ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exact analytical solutions of the susceptible-infected-recovered (SIR) epidemic model and of the SIR model with equal death and birth rates
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Inequalities for differential and integral equations
• Some discrete-time SI, SIR, and SIS epidemic models
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• The parameter identification problem for SIR epidemic models: identifying unreported cases
• Numerical data fitting in dynamical systems. A practical introduction with applications and software. With CD-ROM
• A time delay dynamical model for outbreak of 2019-nCov and the parameter identification
• Inverse problem for coefficient identification in SIR epidemic models
• A discrete stochastic model of the COVID-19 outbreak: forecast and control
• An age- and sex-structured SIR model: theory and an explicit-implicit numerical solution algorithm
• Existence of solution and stability for the fractional order novel coronavirus (nCoV-2019) model
• Analysis and forecast of COVID-19 spreading in China, Italy and France
• The role of power decay, exponential decay and Mittag-Leffler function's waiting time distribution: application of cancer spread
• Exact solution to a dynamic SIR model
• The inverse problem in mathematical biology
• The basic approach to age-structured population dynamics. Models, methods and numerics
• Some simple epidemic models
• The Kermack--McKendrick epidemic model revisited
• Forecasting seasonal influenza with a state-space SIR model
• The Mathematics of Infectious Diseases
• Ordinary Differential Equations: Basics and Beyond
• A Stochastic Differential Equation SIS Epidemic Model
• Mathematical Models in Population Biology and Epidemiology
• Contributions to the mathematical theory of epidemics. II. —The problem of endemicity
• Inverse Problem Theory and Methods for Model Parameter Estimation
• The concept of R_o in epidemic theory
• Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China
• Numerical Methods for Fractional Differentiation
• An Introduction to Mathematical Epidemiology

This page was built for publication: Time-continuous and time-discrete SIR models revisited: theory and applications