Periodic solution and ergodic stationary distribution of stochastic SIRI epidemic systems with nonlinear perturbations

DOI10.1007/s11424-018-7348-9zbMath1418.92209OpenAlexW2909849241MaRDI QIDQ2320623

Yulin Dong, Wei-Wei Zhang, Xin-Zhu Meng

Publication date: 23 August 2019

Published in: Journal of Systems Science and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11424-018-7348-9

zbMATH Keywords

periodic solutionMarkov chainstationary distribution and ergodicitystochastic SIRI epidemic modelextinction and stochastic permanence

Mathematics Subject Classification ID

Epidemiology (92D30) Periodic solutions to ordinary differential equations (34C25) Stochastic systems in control theory (general) (93E03) Dynamical systems and their relations with probability theory and stochastic processes (37A50)

Related Items

Dynamical behavior of a higher order stochastically perturbed SIRI epidemic model with relapse and media coverage, Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth, Dynamics analysis of a delayed virus model with two different transmission methods and treatments, Qualitative analysis of an HIV/AIDS model with treatment and nonlinear perturbation, Markovian switching for near-optimal control of a stochastic SIV epidemic model, Dynamical properties of a herbivore-plankton impulsive semidynamic system with eating behavior, The threshold of a stochastic SIRS epidemic model with general incidence rate under regime-switching, Analysis on dynamical behavior of a stochastic phytoplankton‐zooplankton model with nonlinear perturbation, A stochastic switched SIRS epidemic model with nonlinear incidence and vaccination: Stationary distribution and extinction, Higher order stochastically perturbed SIRS epidemic model with relapse and media impact, Unnamed Item, Dynamic analysis of stochastic Lotka-Volterra predator-prey model with discrete delays and feedback control, Dynamic analysis of Beddington-DeAngelis predator-prey system with nonlinear impulse feedback control, Dynamics analysis of a stochastic Leslie-Gower predator-prey model with feedback controls, Periodicity and stationary distribution of two novel stochastic epidemic models with infectivity in the latent period and household quarantine, ANALYSIS OF A STOCHASTIC RECOVERY-RELAPSE EPIDEMIC MODEL WITH PERIODIC PARAMETERS AND MEDIA COVERAGE, A ratio-dependent impulsive control of an SIQS epidemic model with non-linear incidence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lyapunov functions and global stability for \(SIR\) and \(SIRS\) epidemiological models with non-linear transmission
• The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence
• Global dynamics for a new high-dimensional SIR model with distributed delay
• Stability analysis of a delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure
• Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis
• Stability and bifurcation of an SIS epidemic model with treatment
• Stability of a novel stochastic epidemic model with double epidemic hypothesis
• Global analysis on a class of multi-group SEIR model with latency and relapse
• Dynamics of a stochastic Lotka-Volterra model perturbed by white noise
• Stability analysis for stochastic differential equations with infinite Markovian switchings
• Modeling the spread of seasonal epidemiological diseases: Theory and applications
• Statistical inference for ergodic diffusion processes.
• The threshold of a stochastic delayed SIR epidemic model with vaccination
• Optimal harvesting control and dynamics of two-species stochastic model with delays
• Dynamical analysis of a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis
• The extinction and persistence of the stochastic SIS epidemic model with vaccination
• A diffusive HIV infection model with nonlocal delayed transmission
• Dynamics analysis and numerical simulations of a stochastic non-autonomous predator-prey system with impulsive effects
• Threshold dynamics of a stochastic \(S I R\) model with vertical transmission and vaccination
• Extinction and persistence in mean of a novel delay impulsive stochastic infected predator-prey system with jumps
• Stochastic stability and instability of an epidemic model with relapse
• The asymptotic behaviour of a logistic epidemic model with stochastic disease transmission
• Stability analysis of an SEIQV epidemic model with saturated incidence rate
• Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence
• Nontrivial periodic solution of a stochastic epidemic model with seasonal variation
• The Mathematics of Infectious Diseases
• Evolutionary dynamics in a Lotka-Volterra competition model with impulsive periodic disturbance
• A Deterministic Model for Herpes Infections in Human and Animal Populations
• A Stochastic Differential Equation SIS Epidemic Model
• Asymptotic Properties of Hybrid Diffusion Systems
• Stationary distribution and extinction of a stochastic SIRI epidemic model with relapse
• GLOBAL DYNAMICS ANALYSIS OF A NONLINEAR IMPULSIVE STOCHASTIC CHEMOSTAT SYSTEM IN A POLLUTED ENVIRONMENT