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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
Journal of the Franklin Institute, ISSN 0016-0032, 11/2017, Volume 354, Issue 16, pp. 7410 - 7428
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 06/2019, Volume 524, pp. 601 - 613
In this paper, a stochastic multimolecular biochemical reaction model with lévy jumps is investigated. Firstly, we prove the existence and uniqueness of the... 
Positive recurrence | Stochastic biochemical reaction model | lévy jumps | Lyapunov function | SYSTEM | THRESHOLD | SIRS EPIDEMIC MODEL | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | Stochastic biochemical reaction model levy jumps | DYNAMICS | DRIVEN | SIS MODEL | Petroleum mining | Models | Numerical analysis | Analysis
Journal Article
Journal of Applied Analysis and Computation, ISSN 2156-907X, 08/2018, Volume 8, Issue 4, pp. 1108 - 1121
A stochastic mathematical model with both horizontal and vertical transmission is proposed to investigate the dynamical behavior of SIR disease. By employing... 
Persistence | Vertical transmission | Stochastic SIR epidemic model | Extinction | Threshold | SYSTEM | MATHEMATICS, APPLIED | extinction | BEHAVIOR | STABILITY | EPIDEMIC MODEL | vertical transmission | persistence | threshold | INFECTION | PULSE VACCINATION
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 01/2019, Volume 513, pp. 273 - 287
In this paper, we study a stochastic predator–prey model with distributed delay and general functional response. We transform the model with weak kernel case... 
Stochastic predator–prey model | Markov semigroups | General functional response | Distributed delay | Stationary distribution | Stochastic predator-prey model | SYSTEM | SIRS EPIDEMIC MODEL | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | PERTURBATION | DYNAMICS
Journal Article
Mathematical Biosciences, ISSN 0025-5564, 2007, Volume 208, Issue 1, pp. 76 - 97
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2018, Volume 510, pp. 522 - 537
Brucellosis is a kind of zoonotic disease caused by Gram-negative bacteria of the genus Brucella. In this paper, we propose a stochastic periodic brucellosis... 
White noise | Transmission dynamic | Periodic brucellosis model | Stochastic periodic solution | Lyapunov function | SIRS EPIDEMIC MODEL | PHYSICS, MULTIDISCIPLINARY | LEVY JUMPS | STATIONARY DISTRIBUTION | TRANSMISSION DYNAMICS | NONLINEAR INCIDENCE RATE | INNER-MONGOLIA | Medical colleges | Brucellosis | Models | Numerical analysis | Biomedical engineering | Zoonoses
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 07/2018, Volume 501, pp. 276 - 292
A stochastic HIV viral model with both logistic target cell growth and nonlinear immune response function is formulated to investigate the effect of white... 
Immune response | HIV model | Logistic growth | Stochastic differential equation | Stationary distribution | SYSTEM | GLOBAL STABILITY | VIRUS | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | NOISE | VIRAL-INFECTION MODEL | SIRS EPIDEMIC MODEL | POPULATION-DYNAMICS | INTRACELLULAR DELAYS | T-CELLS
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 06/2013, Volume 14, Issue 3, pp. 1286 - 1299
In this paper, we obtain sufficient criteria for the existence of periodic solutions to deterministic SIR and SEIR epidemic models with modified saturation... 
Stochastic Lyapunov function | Itô’s formula | Coincidence degree | Epidemiological model | Asymptotic behavior | Itô's formula | EXISTENCE | PERIODIC-SOLUTIONS | DELAYED SIR | MATHEMATICS, APPLIED | GLOBAL STABILITY | Ito's formula | Epidemics | Models
Journal Article
Acta Biotheoretica, ISSN 0001-5342, 06/2017, Volume 65, Issue 2, pp. 151 - 165
We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination.... 
Basic reproduction number | Stochastic SIR model | Exponential stability | Vaccination | SYSTEM | PERTURBATIONS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | INFLUENZA | Models, Theoretical | Epidemics | Humans | Population Density | Models | Disease transmission | Analysis | Differential equations | Immunization | Population number | Mathematical models | Infections | Stochasticity | Equilibrium
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 07/2019, Volume 93, pp. 15 - 21
In this paper, based on the existing literature, we further study an important statistical character of a stochastic delayed chemostat model. By constructing... 
Lyapunov functional | Stochastic chemostat model | Delay | Stationary distribution | BREAK-EVEN CONCENTRATION | POPULATION | MATHEMATICS, APPLIED | THRESHOLD | COMPETITION | GLOBAL ASYMPTOTIC-BEHAVIOR | SIR EPIDEMIC MODEL
Journal Article
Mathematical biosciences and engineering : MBE, ISSN 1547-1063, 12/2018, Volume 15, Issue 6, pp. 1401 - 1423
This paper investigates the complex dynamics of a Harrison-type predator-prey model that incorporating: (1) A constant time delay in the functional response... 
stochastic perturbations | time delay | Hopf bifurcation | stability | Prey-predator model | SIRS EPIDEMIC MODEL | PREY SYSTEM | BEHAVIOR | COMPLEXITY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | NOISE
Journal Article
Theoretical Population Biology, ISSN 0040-5809, 04/2019, Volume 126, pp. 1 - 18
In-host mutation of a cross-species infectious disease to a form that is transmissible between humans has resulted with devastating global pandemics in the... 
Epidemic | Mathematical models | Mutation | Stochastic process | Asymptotic analysis | Differential equations | AVIAN INFLUENZA | STABILITY | SIR EPIDEMIC MODEL | EVOLUTIONARY BIOLOGY | GENETICS & HEREDITY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | ECOLOGY | SPREAD
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 03/2017, Volume 469, pp. 706 - 717
This paper is concerned with a stochastic HIV-1 infection model with logistic growth. Firstly, by constructing suitable stochastic Lyapunov functions, we... 
Stochastic HIV-1 infection model | Extinction | Stationary distribution | Lyapunov function | MATHEMATICAL-ANALYSIS | VIVO | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | PERTURBATION | VIRUS DYNAMICS | SIR EPIDEMIC MODEL | HTLV-I INFECTION | T-CELLS | Models | HIV (Viruses) | Growth | Health aspects | Analysis
Journal Article
International Journal of Biomathematics, ISSN 1793-5245, 11/2018, Volume 11, Issue 8
A susceptible-infected-vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We... 
Stochastic epidemic model | delay | extinction | persistence in the mean | THRESHOLD | PERSISTENCE | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SIR EPIDEMIC MODEL
Journal Article