scholarly journals Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mei Yan ◽  
Zhongyi Xiang
Keyword(s):  
Differential Equations ◽  
Disease Control ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Floquet Theory ◽  
Impulsive Differential Equations ◽  
Threshold Parameter ◽  
Pulse Vaccination ◽  
Periodic Environment ◽  
Theoretical Results

We consider a nonautonomous SEIR endemic model with saturation incidence concerning pulse vaccination. By applying Floquet theory and the comparison theorem of impulsive differential equations, a threshold parameter which determines the extinction or persistence of the disease is presented. Finally, numerical simulations are given to illustrate the main theoretical results and it shows that pulse vaccination plays a key role in the disease control.

scholarly journals Unpredictable Solutions of Linear Impulsive Systems

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1798
Author(s):  
Marat Akhmet ◽  
Madina Tleubergenova ◽  
Mehmet Onur Fen ◽  
Zakhira Nugayeva
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Random Process ◽  
Logistic Map ◽  
Impulsive Differential Equations ◽  
Impulsive Systems ◽  
New Type ◽  
Piecewise Continuous ◽  
Definition Of ◽  
Theoretical Results

We consider a new type of oscillations of discontinuous unpredictable solutions for linear impulsive nonhomogeneous systems. The models under investigation are with unpredictable perturbations. The definition of a piecewise continuous unpredictable function is provided. The moments of impulses constitute a newly determined unpredictable discrete set. Theoretical results on the existence, uniqueness, and stability of discontinuous unpredictable solutions for linear impulsive differential equations are provided. We benefit from the B-topology in the space of discontinuous functions on the purpose of proving the presence of unpredictable solutions. For constructive definitions of unpredictable components in examples, randomly determined unpredictable sequences are newly utilized. Namely, the construction of a discontinuous unpredictable function is based on an unpredictable sequence determined by a discrete random process, and the set of discontinuity moments is realized by the logistic map. Examples with numerical simulations are presented to illustrate the theoretical results.

scholarly journals Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xiongwei Liu ◽  
Junjun Xu ◽  
Xiao Wang ◽  
Lizhi Cheng
Keyword(s):  
Theoretical Analysis ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Dynamic Models ◽  
Reproduction Number ◽  
Threshold Parameter ◽  
Endemic Disease ◽  
Target Field ◽  
Transgenic Mosquitoes

The release of transgenic mosquitoes to interact with wild ones is a promising method for controlling malaria. How to effectively release transgenic mosquitoes to prevent malaria is always a concern for researchers. This paper investigates two methods of releasing transgenic mosquitoes and proposes two epidemic models involving malaria patients, anopheles, wild mosquitoes, and transgenic mosquitoes based on system of continuous differential equations. A basic reproduction numberR0is defined for the models and it serves as a threshold parameter that predicts whether malaria will spread. By theoretical analysis of the dynamic behaviors of the models and numerical simulations, it is verified that malaria can be effectively controlled by the opportune release of transgenic mosquitoes; that is, whenR0≤1, malaria will disappear; whenR0>1, malaria will become an endemic disease in the target field.

scholarly journals Analysis of COVID-19 based on SEIR epidemic models in a multi-patch environment

2021 ◽  
Author(s):  
Lan Meng ◽  
Wei Zhu
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behavior ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Migration Rate ◽  
Reproduction Number ◽  
Population Migration ◽  
Theoretical Results ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstract In this paper, an n-patch SEIR epidemic model for the coronavirus disease 2019 (COVID-19) is presented. It is shown that there is unique disease-free equilibrium for this model. Then, the dynamic behavior is studied by the basic reproduction number. Some numerical simulations with three patches are given to validate the effectiveness of the theoretical results. The influence of quarantined rate and population migration rate on the basic reproduction number is also discussed by simulation.

Dynamics of a stochastic rabies epidemic model with markovian switching

2021 ◽  
pp. 2150032
Author(s):  
Hao Peng ◽  
Xinhong Zhang ◽  
Daqing Jiang
Keyword(s):  
Lyapunov Function ◽  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Telegraph Noise ◽  
Global Positive Solution ◽  
Theoretical Results

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

scholarly journals Modeling the Parasitic Filariasis Spread by Mosquito in Periodic Environment

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yan Cheng ◽  
Xiaoyun Wang ◽  
Qiuhui Pan ◽  
Mingfeng He
Keyword(s):  
Sensitivity Analysis ◽  
Periodic Solution ◽  
Numerical Simulations ◽  
Parasitic Infection ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Threshold Parameter ◽  
Globally Asymptotically Stable ◽  
Periodic Environment ◽  
Disease Free

In this paper a mosquito-borne parasitic infection model in periodic environment is considered. Threshold parameterR0is given by linear next infection operator, which determined the dynamic behaviors of system. We obtain that whenR0<1, the disease-free periodic solution is globally asymptotically stable and whenR0>1by Poincaré map we obtain that disease is uniformly persistent. Numerical simulations support the results and sensitivity analysis shows effects of parameters onR0, which provided references to seek optimal measures to control the transmission of lymphatic filariasis.

scholarly journals Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 745 ◽  
Author(s):  
Tongqian Zhang ◽  
Tingting Ding ◽  
Ning Gao ◽  
Yi Song
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Influenza A ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Stochastic Lyapunov Function

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

scholarly journals Stability Results for a Coupled System of Impulsive Fractional Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 927 ◽  
Author(s):  
Akbar Zada ◽  
Shaheen Fatima ◽  
Zeeshan Ali ◽  
Jiafa Xu ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Stability Results ◽  
Theoretical Results

In this paper, we establish sufficient conditions for the existence, uniqueness and Ulam–Hyers stability of the solutions of a coupled system of nonlinear fractional impulsive differential equations. The existence and uniqueness results are carried out via Banach contraction principle and Schauder’s fixed point theorem. The main theoretical results are well illustrated with the help of an example.

scholarly journals Ergodicity of a Nonlinear Stochastic SIRS Epidemic Model with Regime-Switching Diffusions

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongxia Liu ◽  
Juan Li ◽  
Mengnan Chi ◽  
Jinlei Liu ◽  
Wencai Zhao
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Threshold Parameter ◽  
Sirs Epidemic Model ◽  
Switching Diffusions ◽  
White Noises ◽  
Stochastic Sirs Epidemic Model

In this paper, taking both white noises and colored noises into consideration, a nonlinear stochastic SIRS epidemic model with regime switching is explored. The threshold parameter R s is found, and we investigate sufficient conditions for the existence of the ergodic stationary distribution of the positive solution. Finally, some numerical simulations are also carried out to demonstrate the analytical results.

scholarly journals The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yanan Jiang ◽  
Liangjian Hu ◽  
Jianqiu Lu
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Stochastic Differential Equations ◽  
Stationary Distribution ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Markovian Switching ◽  
Theoretical Results

AbstractIn this paper, stationary distribution of stochastic differential equations (SDEs) with Markovian switching is approximated by numerical solutions generated by the stochastic θ method. We prove the existence and uniqueness of stationary distribution of the numerical solutions firstly. Then, the convergence of numerical stationary distribution to the underlying one is discussed. Numerical simulations are conducted to support the theoretical results.

MIXED VACCINATION STRATEGY IN SIRS EPIDEMIC MODEL WITH SEASONAL VARIABILITY ON INFECTION

2011 ◽  
Vol 04 (04) ◽  
pp. 473-491 ◽  
Author(s):  
SHUJING GAO ◽  
HONGSHUI OUYANG ◽  
JUAN J. NIETO
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Epidemic Model ◽  
Vaccination Strategy ◽  
Contact Rate ◽  
Seasonal Fluctuations ◽  
Pulse Vaccination ◽  
Sirs Epidemic Model ◽  
Theoretical Results ◽  
Disease Free

In many diseases seasonal fluctuations are observed. SIRS epidemic model with seasonal varying contact rate and mixed vaccination strategy (including first vaccination and pulse vaccination strategy) is investigated. The effects of the variation of dependent on the season of the contact rate and the vaccination strategy to eradicate infectious diseases are studied and discussed. A threshold for a disease to be extinct or endemic is established. The existence and global asymptotic stability of disease-free periodic solution and the permanence of the disease are illustrated. Finally, our theoretical results are confirmed by numerical simulations.

Sign in / Sign up

Export Citation Format

Share Document