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Applied Mathematical Modelling, ISSN 0307-904X, 11/2014, Volume 38, Issue 21-22, pp. 5067 - 5079
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 06/2016, Volume 452, pp. 86 - 93
Fractional-order SIR models have become increasingly popular in the literature in recent years, however unlike the standard SIR model, they often lack a... 
SIR models | Epidemiological models | Fractional order differential equations | Continuous time random walk | PHYSICS, MULTIDISCIPLINARY | RANDOM-WALKS | MATHEMATICAL-THEORY | Stochastic processes | Analysis | Models | Differential equations | Mathematical analysis | Compartments | Derivation | Mathematical models | Derivatives | Standards
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 04/2019, Volume 520, pp. 489 - 506
Sudden environmental perturbations may affect population dynamics. Parameters of mathematical models can also be imprecise due to uncertainties and unknown... 
Persistence | Stochastic SIRS epidemic model | Extinction | Interval number | Lévy jumps | Levy jumps | SYSTEM | THRESHOLD | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | SIS EPIDEMIC MODEL | Epidemics | Models | Noise pollution | Numerical analysis | Analysis | Population biology
Journal Article
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, ISSN 1531-3492, 09/2019, Volume 24, Issue 9, pp. 4827 - 4849
Many studies of mathematical epidemiology assume that model parameters are precisely known. However, they can be imprecise due to various uncertainties.... 
information intervention | SYSTEM | extinction and persistence | MATHEMATICS, APPLIED | stochastic basic reproduction number | interval parameter | STABILITY | SEIR EPIDEMIC MODELS | VACCINATION | Stochastic SIRS model | EXTINCTION
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 02/2013, Volume 14, Issue 1, pp. 352 - 364
We propose a new stochastic SIRS model under regime switching in which both white and color environmental noises are taken into account. We show that white... 
Markov chain | Stochastic SIRS model | Itô formula | Moment average in time | Boundedness | SYSTEM | MATHEMATICS, APPLIED | Ito formula | STABILITY | BEHAVIOR | EPIDEMIC MODEL | PERTURBATION | POPULATION-DYNAMICS | Asymptotic properties | Probability theory | Color | Randomness | Mathematical models | Explosions | Stochasticity | Switching
Journal Article
Journal of Applied Mathematics and Computing, ISSN 1598-5865, 10/2016, Volume 52, Issue 1, pp. 101 - 123
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 360, Issue 1, pp. 235 - 244
In this paper, we discuss the two-group SIR model introduced by Guo, Li and Shuai [H.B. Guo, M.Y. Li, Z. Shuai, Global stability of the endemic equilibrium of... 
Brownian motion | Itô's formula | Stochastic multigroup SIR model | Stochastic asymptotically stable in the large | Lyapunov function | POPULATION | MATHEMATICS, APPLIED | BEHAVIOR | PERSISTENCE | EPIDEMIC MODEL | TIME-DELAY | Ito's formula | STOCHASTIC-MODEL | MATHEMATICS | TRANSMISSION | LOTKA-VOLTERRA MODEL | DISEASE | DYNAMICS
Journal Article
Journal of the Franklin Institute, ISSN 0016-0032, 12/2019, Volume 356, Issue 18, pp. 11385 - 11413
Parameters of mathematical models are often imprecise due to various uncertainties. How parameter imprecision and sudden environmental changes influence the... 
SYSTEM | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | STABILITY | EPIDEMIC MODEL | STOCHASTIC SIS MODEL | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
Bulletin of Mathematical Biology, ISSN 0092-8240, 03/2016, Volume 78, Issue 3, pp. 468 - 499
Journal Article
Nonlinear Analysis: Hybrid Systems, ISSN 1751-570X, 11/2019, Volume 34, pp. 121 - 130
In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold... 
SIRS | Epidemic models | Permanence | Extinction | POPULATION | COEXISTENCE | MATHEMATICS, APPLIED | STABILITY | EPIDEMIC MODEL | DYNAMIC-BEHAVIOR | AUTOMATION & CONTROL SYSTEMS | MATHEMATICAL-THEORY | Epidemics | Vietnam | Models | Research | Mathematical research | Stochastic processes
Journal Article
Advances in Difference Equations, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 20
Journal Article
Mathematical and Computer Modelling, ISSN 0895-7177, 2011, Volume 54, Issue 1, pp. 221 - 232
In this paper, we explore a stochastic SIR model and show that this model has a unique global positive solution. Furthermore, we investigate the asymptotic... 
Brownian motion | Stochastic SIR model | It [formula omitted]’s formula | Global positive solution | Asymptotic behavior | Itô's formula | MATHEMATICS, APPLIED | Ito's formula
Journal Article
PLoS ONE, ISSN 1932-6203, 04/2016, Volume 11, Issue 4, p. e0152950
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2018, Volume 505, pp. 385 - 397
In this paper, we consider an impulsive SIR model with incidence rate stochastically perturbed. First, we prove the existence and uniqueness of the global... 
SIR epidemic model | Periodic solution | Impulsive effect | Global attraction | Stochastic perturbation | SYSTEM | PHYSICS, MULTIDISCIPLINARY | STABILITY | MEASLES | SEIR EPIDEMIC MODEL | THRESHOLD | PULSE VACCINATION STRATEGY | ERADICATION | VERTICAL TRANSMISSION | EQUATION | Epidemics | Vaccination | Models
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 11/2017, Volume 73, pp. 8 - 15
In this paper, we analyze a stochastic SIR model with nonlinear perturbation. By the Lyapunov function method, we establish sufficient conditions for the... 
Nonlinear perturbation | Ergodicity | Stochastic SIR model | Extinction | Stationary distribution | MATHEMATICS, APPLIED | PERSISTENCE | EPIDEMIC MODEL | Analysis | Big data | Models
Journal Article
Statistics in Medicine, ISSN 0277-6715, 12/2018, Volume 37, Issue 29, pp. 4490 - 4506
Journal Article
Nonlinear Functional Analysis and Applications, ISSN 1229-1595, 03/2018, Volume 23, Issue 1, pp. 31 - 48
Journal Article
Stochastic Analysis and Applications, ISSN 0736-2994, 11/2018, Volume 36, Issue 5, pp. 895 - 908
In this article, a stochastic version of a SIR nonautonomous model previously introduced in Kloeden and Kozyakin (2011) is considered. The noise considered is... 
epidemiology | 92D30 | 60H10 | fractional Brownian motion | SIR model | 34D20 | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | Random walk theory | Stochastic models | Brownian movements | Dependence
Journal Article