Article
Materials Science, Multidisciplinary
Zakia Hammouch, Mudhafar F. Hama, Rando R. Q. Rasul, Kawa A. H. Rasul, Jaouad Danane
Summary: In this study, we analyze and investigate the behavior of an SEIS stochastic model performed by a Levy process and demonstrate that the model has a unique global positive bounded solution. We prove that the disease-free equilibrium point is stable under certain conditions using a suitable Lyapunov function. We also provide sufficient conditions for the stability of the model around the disease-free and endemic equilibrium points. Through simulation studies, we demonstrate our theoretical results and show that the virus can be extinguished under certain conditions if the basic reproductive number is more than one.
RESULTS IN PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Ting Cui, Anwarud Din, Peijiang Liu, Amir Khan
Summary: In this article, the dynamics of Norovirus infection is studied using a stochastic epidemic model with Levy noise. The study shows that Levy noise and informative interventions have a greater influence on the dynamics.
COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING
(2023)
Article
Mathematics, Interdisciplinary Applications
Xiao-Ping Li, Anwarud Din, Anwar Zeb, Sunil Kumar, Tareq Saeed
Summary: The main focus of this paper is to analyze the Levy noise-driven Hepatitis B virus (HBV) infectious disease, considering the vaccination effect on the epidemic's dynamical behavior. Through theoretical analysis and numerical simulations, it has been found that the fractional-order system has a good extinction effect, providing a strong theoretical basis for understanding and controlling epidemics.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
R. Bobryk
Summary: This paper focuses on an SIR model with random additive perturbations of the transmission rate in the spread of an epidemic. Three models of random perturbation are considered, with two models maintaining the condition of positivity of the transmission rate. An efficient numerical procedure is proposed for stability charts in the presence of bounded noise, and the impact of random perturbations on the stability behavior of disease-free equilibrium is discussed.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Chemistry, Multidisciplinary
Hari M. Srivastava, Jaouad Danane
Summary: We propose a new SICR epidemic model and study its properties, considering the strong fluctuations in the dynamics by incorporating Brownian motion and jump Levy noise as driving forces. We establish the existence and uniqueness of a global positive solution and investigate the extinction and persistence of the infection. We also introduce a new numerical method to validate our theoretical findings.
APPLIED SCIENCES-BASEL
(2022)
Article
Mathematics, Applied
Mengling Li, Zhengyong Ouyang, Feiqi Deng, Ze-Hao Wu
Summary: This paper focuses on the stochastic dissipativity theory and applications for nonlinear stochastic systems with Markov jump and Levy noise. The theory is established based on the dissipation inequality, multi supply rates, multi storage functions and stochastic analysis tools, and utilized to obtain sufficient conditions for system stability. The effectiveness of the results is validated through examples.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Materials Science, Multidisciplinary
Qi Liu, Aeshah A. Raezah, Anwarud Din
Summary: This manuscript investigates the security challenges faced by wireless sensor networks (WSNs) due to worm infiltration. A stochastic system based on Levy noise is proposed to explain the spread of worms in WSNs. A unique positive global solution for the proposed model is established. The results show that the proposed model outperforms existing models in mitigating worm transmission in WSNs.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Abdulwasea Alkhazzan, Jungang Wang, Yufeng Nie, Hasib Khan, Jehad Alzabut
Summary: This study proposes a novel epidemic model that considers the impact of transport-related infection, media coverage, and Levy noise. The researchers investigate the existence of a positive global solution and derive sufficient conditions for disease extinction and persistence. By analyzing the influence of various parameters on the model's dynamics, the study provides important insights into the science of epidemiology and lays the groundwork for improved methods of disease prevention.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
Sanae El Attouga, Driss Bouggar, Mohamed El Fatini, Astrid Hilbert, Roger Pettersson
Summary: In this paper, a stochastic SIRS epidemic model with generalized nonlinear incidence and Levy noise is studied. The existence and uniqueness of a global positive solution are shown. Sufficient conditions for the extinction and persistence of the disease are established. The main results are proved under weak assumptions regarding the incidence function, and under a Levy-type perturbation without requiring the finiteness of its activity. Numerical simulations are performed to illustrate the main results.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Mathematics
Xueyong Zhou
Summary: This paper establishes and investigates a stochastic infectious disease model for cholera. The dynamics of the model are discussed and the existence and uniqueness of the positive solution, as well as the asymptotic stability of the disease-free equilibrium and endemic equilibrium, are proven. The theoretical results are verified through numerical simulations, and the optimal control problem is considered as the theoretical basis for cholera control. The results indicate that random perturbations can make the model more realistic and provide theoretical assessment for cholera transmission control.
Article
Materials Science, Multidisciplinary
Anwarud Din, Tahir Khan, Yongjin Li, Hassan Tahir, Asaf Khan, Wajahat Ali Khan
Summary: In this study, a stochastic Markovian dynamics approach was used to model the transmission of dengue fever and the threshold of the disease. The basic stochastic reproduction number R-0(s) was calculated as a threshold for determining the extinction or persistence of the disease. Results showed that R-0(s) can determine the fate of the disease.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Ali Raza, Jan Awrejcewicz, Muhammad Rafiq, Nauman Ahmed, Muhammad Sarwar Ehsan, Muhammad Mohsin
Summary: This article presents the dynamical analysis of a stochastic leprosy epidemic model using the Euler Maruyama method. The proposed stochastic non-standard finite difference (NSFD) method is found to be more efficient, cost-effective, and accommodates all desired feasible properties compared to traditional computational methods. The article highlights the novelty of the proposed approach through a comparison with existing schemes.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematical & Computational Biology
Tingting Cai, Yuqian Wang, Liang Wang, Zongying Tang, Jun Zhou
Summary: This paper discusses a stochastic epidemic model with logistic growth. Based on stochastic differential equation theory and stochastic control method, the properties of the model's solution near the epidemic equilibrium of the original deterministic system are investigated. The paper establishes sufficient conditions for the stability of the disease-free equilibrium and constructs two event-triggered controllers to drive the disease from endemic to extinction. Numerical examples illustrate the effectiveness of the results.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Automation & Control Systems
Qianqian Sun, Dejun Tan, Shuwen Zhang
Summary: In this study, the impacts of Gaussian white noise and semi-Markovian switching on the propagation dynamics of COVID-19 were investigated using a stochastic SIQR model. It was found that the fate of COVID-19 is determined by the basic reproduction number R0, and the effect of quarantine rate on R0 is more significant than transmission rate. The presence of Gaussian white noise reduces R0 but poses challenges for prediction and control, and the conditional holding time distribution significantly affects the kinetics of COVID-19. Semi-Markov switching and Gaussian white noise support irregular recurrence of COVID-19 outbreaks.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Ecology
Peijiang Liu, Lifang Huang, Anwarud Din, Xiangxiang Huang
Summary: This paper considers a stochastic coronavirus epidemic model with information intervention and Levy noise, proving the existence and uniqueness of positive solutions, establishing a stochastic threshold for disease extinction and persistence, estimating model parameters based on COVID-19 data, fitting the model with real statistics, and presenting numerical simulations to support theoretical results.
JOURNAL OF BIOLOGICAL DYNAMICS
(2022)
