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Article
Multidisciplinary Sciences
Konstantinos Mamis et al.
Summary: Compartmental models are important in epidemiology for predicting the course of communicable diseases. A common stochastic model treating uncertainties as white noise is flawed as it incorrectly suggests that greater uncertainties will lead to disease eradication. Our principled modelling of uncertainties based on reasonable assumptions introduces the correlated Ornstein-Uhlenbeck (OU) process as the appropriate tool. We apply our findings to a compartmental model of COVID-19 and demonstrate that the white noise model underestimates the severity of the Omicron variant, while the OU model accurately forecasts its course. Our results support the need for temporal correlations in compartmental models of infectious diseases.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Computer Science, Interdisciplinary Applications
Yiping Tan et al.
Summary: This paper investigates a stochastic SIS epidemic model with a general transmission function and media coverage, establishing two thresholds to govern the stochastic dynamics of the model. Based on these thresholds, the disease can either die out or persist, with the intensity of random disturbances affecting the dynamics of the disease.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics
Zhaohua Wu et al.
Summary: In this paper, a new fractional order SIS model is established using continuous time random walk. The value of this study lies in two aspects: mathematically, a framework for the global stability of the frSIS model is provided, and it is proven that the basic reproduction number R0 can govern the dynamics of the model; epidemiologically, it is found that decreasing the death rate and the average infectious period can control the spread of the disease and provide useful control strategies to regulate disease dynamics.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Biology
Xiaojie Jing et al.
Summary: In this study, a stochastic SIS pairwise model is derived by considering the changes in the system variables caused by events. A low-dimensional deterministic system is constructed based on approximations to describe the epidemic spread on a regular network. Comparisons between the stochastic pairwise model and the stochastic mean-field SIS model reveal that the variances of infection prevalence in both models are almost equal when the number of individual neighbors is large. The study also provides approximations for the quasi-stationary distribution of infected individuals and the expected time to extinction, as well as analyzes the critical number of neighbors and the persistence threshold based on the stochastic model.
JOURNAL OF MATHEMATICAL BIOLOGY
(2022)
Article
Automation & Control Systems
Zhenfeng Shi et al.
Summary: In this paper, we propose a stochastic virus infection model with multitarget cells and exposed state, and theoretically prove the positivity and globality of the solution. We also obtain the existence and uniqueness of the ergodic stationary distribution of the stochastic system, as well as the exact expression of the probability density function around the quasi-endemic equilibrium.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Baoquan Zhou et al.
Summary: This paper investigates a stochastic epidemic model with media coverage and biologically reasonable stochastic effects. The introduction of Ornstein-Uhlenbeck processes as stochastic effects is explained and mathematically justified. The paper proves the uniqueness and global existence of the solution to the stochastic model and the existence of an ergodic stationary distribution. The results are verified through numerical simulations, and the impact of stochastic noises and media coverage on epidemic transmission is studied.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Yunquan Song et al.
Summary: In this paper, a new stochastic SVEIS model is proposed by assuming that the parameter in the SVEIS epidemic model satisfies the mean-reverting Ornstein-Uhlenbeck process. It is proven through constructing suitable Lyapunov function that this stochastic model has a stationary distribution when the critical value R-0(s) is greater than 1. Additionally, the sufficient condition for exponential extinction, R-0(e) being less than 1, is established.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Interdisciplinary Applications
Shengnan Zhao et al.
Summary: This paper investigates the impact of environmental fluctuations on plankton populations by developing and analyzing a stochastic model. The research reveals that environmental noise increases the vulnerability of zooplankton populations, benefiting phytoplankton.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Zhenfeng Shi et al.
Summary: In this study, a HTLV-I infection model with general infection form is developed by considering the Ornstein-Uhlenbeck process. By constructing suitable functions and sets, and using mathematical theorems and lemmas, the existence and uniqueness of the model are obtained. The results show that HTLV-I infection has longterm persistence in a biological sense, and sufficient conditions for the extinction of the infection are established. Numerical simulations are used to support the results.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Bingtao Han et al.
Summary: This paper studies a stochastic SEI epidemic model with general distributed delay, proving the existence and uniqueness of a global positive solution and verifying the existence of a stationary distribution under a stochastic criterion. The study also obtains exact probability density functions around the quasi-stable equilibrium and establishes conditions for disease extinction. Numerical simulations are provided to reveal the impact of stochastic perturbations on disease transmission.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics
Shengnan Zhao et al.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2020)
Article
Mathematics, Applied
Zhenfeng Shi et al.
APPLIED MATHEMATICS AND COMPUTATION
(2019)
Article
Physics, Multidisciplinary
S. P. Rajasekar et al.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2019)
Article
Mathematics, Applied
Nguyen Thanh Dieu
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2018)
Article
Mathematics, Applied
Yongli Cai et al.
APPLIED MATHEMATICS AND COMPUTATION
(2018)
Article
Mathematics, Interdisciplinary Applications
Xuejin Lv et al.
CHAOS SOLITONS & FRACTALS
(2018)
Article
Mathematics, Applied
Edward Allen
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2016)
Article
Statistics & Probability
Nguyen Huu Du et al.
JOURNAL OF APPLIED PROBABILITY
(2016)
Article
Physics, Multidisciplinary
Zhidong Teng et al.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2016)
Article
Mathematics
Yongli Cai et al.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2015)
Article
Mathematics, Applied
A. Gray et al.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2011)
Article
Biology
Tom Britton
MATHEMATICAL BIOSCIENCES
(2010)
Article
Mathematics, Applied
DJ Higham
