Demographic stochasticity in the SDE SIS epidemic model

DOI10.3934/dcdsb.2015.20.2859zbMath1326.34081OpenAlexW1752556915MaRDI QIDQ500140

David Greenhalgh, Xuerong Mao, Yanfeng Liang

Publication date: 1 October 2015

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2015.20.2859

zbMATH Keywords

Brownian motionstochastic differential equationsextinctionSIS epidemic modeldemographic stochasticityFeller test

Mathematics Subject Classification ID

Epidemiology (92D30) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Ordinary differential equations and systems with randomness (34F05) Stochastic systems in control theory (general) (93E03) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (5)

A stochastic differential equation SIS epidemic model with two independent Brownian motions ⋮ Estimation of anthracnose dynamics by nonlinear filtering ⋮ Effects of stochastic perturbation on the SIS epidemic system ⋮ A stochastic differential equation SIS epidemic model with two correlated Brownian motions ⋮ The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients

Cites Work

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• The SIS epidemic model with Markovian switching
• Extinction and quasi-stationarity in the stochastic logistic SIS model.
• Dynamical behavior of Lotka-Volterra competition systems: non-autonomous bistable case and the effect of telegraph noise
• A stochastic SIS epidemic with demography: Initial stages and time to extinction
• Workshop on branching processes and their applications. Selected papers based on the presentations at the workshop WBPA 09, April 20--23, 2009, Badajoz, Spain.
• A comparison of three different stochastic population models with regard to persistence time
• Stochastic orders
• A stochastic model of AIDS and condom use
• Stochastic epidemic models: a survey
• Qualitative analyses of communicable disease models
• Stochastic models of some endemic infections
• On the quasi-stationary distribution of the stochastic logistic epidemic
• Comparison of deterministic and stochastic SIS and SIR models in discrete time
• A mathematical model for the spread of \textit{Streptococcus pneumoniae} with transmission due to sequence type
• An analysis of stability of Milstein method for stochastic differential equations with delay
• On the asymptotic behavior of the stochastic and deterministic models of an epidemic
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• A Stochastic Differential Equation SIS Epidemic Model
• Modeling with Itô Stochastic Differential Equations
• An Introduction to Stochastic Epidemic Models
• On the distribution of the time to extinction in the stochastic logistic population model
• Quasi-stationary distributions of birth-and-death processes
• On the Extinction of theS–I–Sstochastic logistic epidemic
• On the Time to Extinction in Recurrent Epidemics
• A note on quasi-stationary distributions of birth–death processes and the SIS logistic epidemic
• The quasistationary distribution of the stochastic logistic model
• The quasi-stationary distribution of the closed endemic sis model
• Some Stochastic Models for Small Epidemics in Large Populations

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