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Mathematical Biosciences, ISSN 0025-5564, 2011, Volume 232, Issue 1, pp. 31 - 41
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2019, Volume 351, pp. 260 - 269
In this paper, we investigate a stochastic heroin epidemic model. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions... 
Sensitivity analysis | Extinction | Stochastic heroin epidemic model | Stationary distribution | ERGODICITY | MATHEMATICS, APPLIED | STABILITY | BEHAVIOR | NOISE | THRESHOLD | LOTKA-VOLTERRA MODEL | SYSTEMS | SEIR
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 9/2008, Volume 20, Issue 3, pp. 699 - 717
Journal Article
Journal of Theoretical Biology, ISSN 0022-5193, 07/2014, Volume 352, pp. 71 - 81
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2012, Volume 388, Issue 1, pp. 248 - 271
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2019, p. 123361
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 10/2013, Volume 392, Issue 20, pp. 4928 - 4936
For an epidemic model of the type mentioned, we prove a theorem on almost sure exponential stability of the disease-free equilibrium. For small values of the... 
SEIR model | Basic reproduction number | Almost sure exponential stability | Stochastic differential equation | MULTI-GROUP SEIR | TRANSMISSION | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | DYNAMICS | AIDS | SIR | EXTINCTION | Epidemics | Analysis | Models
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 08/2012, Volume 13, Issue 4, pp. 1581 - 1592
The dynamics of multi-group SEIR epidemic models with distributed and infinite delay and nonlinear transmission are investigated. We derive the basic... 
Multi-group | Lyapunov functional | Distributed delays | Global stability | SEIR | POPULATION | MATHEMATICS, APPLIED | SUBPOPULATIONS | DYNAMICS | FUNCTIONAL-DIFFERENTIAL EQUATIONS | ENDEMIC EQUILIBRIUM | Epidemics | Analysis | Nonlinear dynamics | Dynamic tests | Reproduction | Stability | Asymptotic properties | Nonlinearity | Delay
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 06/2016, Volume 451, pp. 507 - 518
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 12/2018, Volume 338, pp. 249 - 259
•Nonlinear dynamics of Zika virus is addressed.•SEIR–SEI epidemic model is employed to model Zika virus outbreak in Brazil.•An inverse problem is solved to... 
Zika virus dynamics | Nonlinear dynamics | Mathematical biology | SEIR epidemic model | Model calibration | Inverse problem | MATHEMATICS, APPLIED | TRANSMISSION | AMERICA | ISLAND | DYNAMICS | REGION | Life Sciences | Dynamical Systems | Quantitative Methods | Santé publique et épidémiologie | Nonlinear Sciences | Mathematics | Statistics
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2016, Volume 462, pp. 870 - 882
This paper is concerned with a stochastic delayed SEIR epidemic model with nonlinear incidence. Firstly we verify that there exists a unique global positive... 
Stochastic SEIR epidemic model | Time delays | Nonlinear incidence | Lyapunov function | MULTI-GROUP SEIR | GLOBAL STABILITY | PHYSICS, MULTIDISCIPLINARY | NONMONOTONIC INCIDENCE RATE | VACCINATION | TIME-DELAY | RANDOM PERTURBATION | INFECTIOUS-DISEASES | SIR | EXTINCTION | Epidemics | Analysis | Models
Journal Article
Vaccine, ISSN 0264-410X, 2006, Volume 24, Issue 35, pp. 6037 - 6045
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 03/2018, Volume 493, pp. 210 - 227
In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical... 
Basic reproduction number | Global stability | Backward bifurcation | Numerical simulation | SEIR epidemic model | Optimal treatment control | Epidemiology | PROBABILISTIC SOLUTION | PHYSICS, MULTIDISCIPLINARY | TUBERCULOSIS | INCLUDES | IMPACT | VACCINATION MODEL | GLOBAL-STABILITY | DISEASE | Epidemics | Models | Numerical analysis | Analysis
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 16
For an SEIRS epidemic model with stochastic perturbations on transmission from the susceptible class to the latent and infectious classes, we prove the... 
SEIRS model | stochastic transmission | almost sure exponential stability | MATHEMATICS | MULTI-GROUP SEIR | MATHEMATICS, APPLIED | PERTURBATIONS | STABILITY | Usage | Disease transmission | Research | Perturbation (Mathematics) | Differential equations | Epidemics | Pathogens | Biological effects | Stability | Perturbation methods | Texts | Mathematical models | Stochasticity
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 06/2017, Volume 476, pp. 58 - 69
In this paper, we consider a stochastic SEIR epidemic model with standard incidence. By constructing suitable stochastic Lyapunov functions, we establish... 
Stochastic SEIR epidemic model | Extinction | Stationary distribution | Lyapunov function | SYSTEM | PHYSICS, MULTIDISCIPLINARY | STABILITY | BEHAVIOR | VACCINATION | THRESHOLD | SATURATED INCIDENCE | DYNAMICS | NONLINEAR INCIDENCE | SIR | Epidemics | Models | Big data | Analysis
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 08/2015, Volume 24, pp. 18 - 35
In this paper, an SEIR epidemic model for a disease with age-dependent latency and relapse is proposed. Such a model is very appropriate for tuberculosis and... 
Age-dependent relapse | Lyapunov functional | SEIR epidemic model | Global stability | Age-dependent latency | MATHEMATICS, APPLIED | DISEASES | LYAPUNOV FUNCTIONS | INFECTION-AGE | PERSISTENCE | DYNAMICS | SYSTEMS | Epidemics | Analysis | Reproduction | Tuberculosis | Stability | Asymptotic properties | Mathematical analysis | Constants | Mathematical models | Volterra integral equations
Journal Article