Article
Mathematical & Computational Biology
Samuel Bronstein, Stefan Engblom, Robin Marin
Summary: This paper qualitatively investigates the convergence of Bayesian parameter inference in disease modeling. The study focuses on the Bayesian model's convergence with increasing amounts of data under measurement limitations. Depending on the informativeness of the disease measurements, a 'best case' and a 'worst case' analysis are provided. These cases consider direct accessibility to prevalence and binary signals corresponding to prevalence detection threshold, respectively. Numerical experiments are conducted to test the adaptability of the results in more realistic scenarios where analytical results are unavailable.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematics, Applied
Aadil Lahrouz, Adel Settati, Mohamed El Fatini, Abdessamad Tridane
Summary: This paper aims to analyze the classical SIS epidemic model with a generalized force of infection perturbed by white noise. Through Feller's test, it is proven that the disease dies out with probability one without any restriction on the model parameters.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Physics, Multidisciplinary
Aziz Laaribi, Brahim Boukanjime, Mohamed El Khalifi, Driss Bouggar, Mohamed El Fatini
Summary: The aim of this study is to analyze a new stochastic SIRS epidemic model incorporating the mean-reverting Ornstein-Uhlenbeck process and a general incidence rate. The global existence and positivity of the solution are proven using Lyapunov functions. The stochastic epidemic threshold (T) over tilde (S)(0), which determines disease extinction or persistence, is analytically determined. Numerical simulations are conducted to validate the theoretical results.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Mathematics
Pece Trajanovski, Petar Jolakoski, Ljupco Kocarev, Trifce Sandev
Summary: This study investigates anomalous transport in a three-dimensional comb structure using the Ornstein-Uhlenbeck (O-U) process with resetting. The three-dimensional comb structure consists of backbones and fingers, with x-axis corresponding to the backbones and y-axis and z-axis corresponding to the fingers. Implementation of the O-U process on the comb structure leads to anomalous (non-Markovian) diffusion. This specific anomalous transport with resetting results in non-equilibrium stationary states. Analytical expressions for the mean values and mean squared displacements along all three directions of the comb are obtained and numerically verified. The marginal probability density functions for each direction are obtained through Monte Carlo simulation of a random transport described by a system of coupled Langevin equations for the comb geometry.
Article
Mathematics, Applied
Yaxin Zhou, Daqing Jiang
Summary: This study considers the dynamical behaviors of a stochastic SIQR epidemic model with mean-reverting Ornstein-Uhlenbeck process and standard incidence under the continuous interference of environmental white noise. After dimensionality reduction, several conclusions are derived, including the existence and uniqueness of positive solution, a sufficient condition for extinction of the diseases, and the stationary distribution of the model. Furthermore, an exact local expression of the density function of the random model near the unique endemic equilibrium is proposed, and numerical simulations are performed to validate the theoretical results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Multidisciplinary Sciences
Peter J. Dodd, Debebe Shaweno, Chu-Chang Ku, Philippe Glaziou, Carel Pretorius, Richard J. Hayes, Peter MacPherson, Ted Cohen, Helen Ayles
Summary: Accurately estimating the burden of tuberculosis in high HIV prevalence areas is challenging. The authors developed a new age-structured TB transmission model that incorporates evolving demographic, HIV and antiretroviral therapy effects. By including Bayesian methods and accounting for uncertainty, they estimated age-specific annual risks of TB infection and the proportion resulting from recent infection.
NATURE COMMUNICATIONS
(2023)
Article
Mathematics, Applied
Tan Su, Xinhong Zhang
Summary: In this paper, a stochastic SEI epidemic model with general transmission rates following a log-normal Ornstein-Uhlenbeck process is proposed. The existence of a unique positive global solution is theoretically proved. By constructing suitable Lyapunov functions, the condition Rs0 > 1 for the existence of a stationary distribution is established. The extinction of the disease is also investigated, and it is found that the disease will die out at an exponential rate when RE0 < 1.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Engineering, Mechanical
Osmo Kaleva, Heikki Orelma
Summary: This paper is a continuation of the study on the continuum approach to high-cycle fatigue model. It models stress history as a stochastic process to simulate fatigue evolution and lifetime distribution.
INTERNATIONAL JOURNAL OF FATIGUE
(2021)
Article
Statistics & Probability
Soren Wengel Mogensen, Niels Richard Hansen
Summary: We examine a class of graphs that represent local independence structures in stochastic processes with correlated noise. We classify graphs that encode the same local independencies and show that determining Markov equivalence for this class of graphs is a complex task. Additionally, we prove the global Markov property for a specific multivariate process.
Article
Mathematics, Applied
Hidekazu Yoshioka, Motoh Tsujimura, Tomohiro Tanaka, Yumi Yoshioka, Ayumi Hashiguchi
Summary: In this study, we propose a linear-quadratic control method for optimizing streamflow discharge using an infinite-dimensional jump-driven stochastic differential equation. Our model utilizes a superposition of Ornstein-Uhlenbeck processes to generate the observed sub-exponential autocorrelation function in real data, and the optimal control is determined through an integral operator Riccati equation. By parameterizing the process based on actual data and conducting computational experiments, we analyze the convergence of the numerical scheme and demonstrate the application of the proposed model to realistic problems, evaluating the performance of the controls using the Kolmogorov backward equation.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Engineering, Mechanical
Xiaojie Mu, Daqing Jiang, Tasawar Hayat, Ahmed Alsaedi, Yunhui Liao
Summary: This paper investigates the Ornstein-Uhlenbeck process in turbidostat systems and studies the dynamic behavior of the stochastic model, including the existence and uniqueness of globally positive equilibrium, conditions for extinction, the existence of a unique stationary distribution, and the expression of density function for quasi-stationary distribution. The results indicate that weaker volatility intensity ensures the existence and uniqueness of the stationary distribution, while stronger reversion speed leads to the extinction of microorganisms.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Wenxu Ning, Zhijun Liu, Lianwen Wang, Ronghua Tan
Summary: This paper presents a stochastic mutualism model with saturation effect and pulse toxicant input, and derives a set of sufficient conditions. Analysis results are supported by numerical simulations, and the effects of various factors on the survival of species are investigated.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Review
Physics, Multidisciplinary
Tan Su, Qing Yang, Xinhong Zhang, Daqing Jiang
Summary: In this paper, a stochastic SEIV epidemic model with mean-reversion Ornstein-Uhlenbeck process and general incidence rate is investigated. The unique global solution of the stochastic model is theoretically proved. By constructing suitable Lyapunov functions, a sufficient criterion Rs0> 1 for the existence of stationary distribution and a sufficient condition for the extinction of the infectious disease are obtained. An exact expression of probability density function near the quasi-endemic equilibrium is also derived. Numerical simulations are conducted to illustrate the theoretical results.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Physics, Multidisciplinary
Frank Aurzada, Volker Betz, Mikhail Lifshits
Summary: This study demonstrates that a properly scaled stretched long Brownian chain converges to a two-parametric stochastic process, which is the sum of an explicit deterministic continuous function and the solution of the stochastic heat equation with zero boundary conditions.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Mathematics, Applied
Xinhong Zhang, Tan Su, Daqing Jiang
Summary: Considering the effects of environmental perturbations on disease transmission, this paper studies a stochastic SVEIR epidemic model in which the transmission rate follows a log-normal Ornstein-Uhlenbeck process and the incidence rate is general. The dynamics of the stochastic model are analyzed by establishing the existence of a unique positive global solution, deriving conditions for the existence of stationary distribution, and determining the conditions for disease extinction. The asymptotic stability of equilibria for the deterministic model and the probability density function of the stationary distribution for the stochastic model are also investigated.
JOURNAL OF NONLINEAR SCIENCE
(2023)
