Dynamic Stochastic Model Research Articles

A Stochastic Model for Transmission Dynamics of AIDS with Protection Consciousness and Log-normal Ornstein–Uhlenbeck Process

A Stochastic Model for Transmission Dynamics of AIDS with Protection Consciousness and Log-normal Ornstein–Uhlenbeck Process

Extinction Dynamics and Equilibrium Patterns in Stochastic Epidemic Model for Norovirus: Role of Temporal Immunity and Generalized Incidence Rates

Norovirus is a leading global cause of viral gastroenteritis, significantly affecting mortality, morbidity, and healthcare costs. This paper develops and analyzes a stochastic SEIQR epidemic model for norovirus dynamics, incorporating temporal immunity and a generalized incidence rate. The model is proven to have a unique positive global solution, with extinction conditions explored. Using Khasminskii’s method, the model’s ergodicity and equilibrium distribution are investigated, demonstrating a unique ergodic stationary distribution when R^s>1. Extinction occurs when R0E<1. Computer simulations confirm that noise level significantly influences epidemic spread.

Optimization based data enrichment using stochastic dynamical system models

We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of variations to derive optimality conditions for continuous time functions. We make no prior assumptions on the form of the mapping from measurements to state-estimate or on the distributions of the noise terms, making the framework more general than Kalman filtering/smoothing where this mapping is assumed to be linear and the noises Gaussian. The optimal solution that arises is interpreted as a continuous time spline, the structure and temporal dependency of which is determined by the system dynamics and the distributions of the process and measurement noise. Similar to Kalman smoothing, the optimal spline yields increased data accuracy at instants when measurements are taken, in addition to providing continuous time estimates outside the measurement instances. We demonstrate the utility and generality of our approach via illustrative examples that render both linear and nonlinear data filters depending on the particular system. Application of the proposed approach to a Monte Carlo simulation exhibits significant performance improvement in comparison to a common existing method.

Quantifying random collisions between particles inside and outside a circle

Random collisions of particles occur in various biophysical and physical systems. Inspired by the binding of receptor and ligand on the cell membrane, we devised a method based on stochastic dynamical modeling to quantify the likelihood of two random particles colliding on a circle. We consider the dynamics of a receptor binding to a ligand on the cell membrane, where the receptor and ligand perform different motions and are thus modeled by stochastic differential equations with non-Gaussian noise. We use neural networks based on the Onsager–Machlup function to compute the probability P1 of an unbounded receptor diffusing to the cell membrane. Meanwhile, we compute the probability P2 of the extracellular ligand arriving at the cell membrane by solving the associated nonlocal Fokker–Planck equation. We can then calculate the most probable binding probability by combining P1 and P2. In this way, we conclude with some indication of how the receptors could distribute on the membrane, as well as where the ligand will most probably encounter the receptor, contributing to a better understanding of the cell’s response to external stimuli and communication with other cells.

Learning Joint Topic Representation for Detecting Drift in Social Media Text

Social media texts like tweets and blogs are collaboratively created by human interaction. Rapidly changing trends are leading to topic drift in the social media text. This drift is usually associated with words and hashtags. However, geotags play an essential part in determining topic distribution with location context. The rate of change in the distribution of words, hashtags and geotags cannot be considered uniform and must be handled accordingly. This paper builds a topic model that associates the topic with a mixture of distributions of words, hashtags and geotags. Stochastic gradient Langevin dynamic model with varying mini-batch sizes is used to capture the changes due to the asynchronous distribution of words and tags. Topic representations with co-occurrence and location contexts are specified as hashtag context vector and geotag context vector respectively. These two vectors are jointly learned to yield topical word embedding vectors over time conditioned on hashtags and geotags that can predict location-based topical variations effectively. When evaluated with Chennai and UK geolocated Twitter data, the proposed joint topical word embedding model enhanced by the social tags context, outperforms other methods.

Dynamic Stochastic Model of Atmospheric Drought Forecast in Uzbekistan

The article considers a predictive model of atmospheric dryness with a one-month lead time, developed at the Scientific Research Hydrometeorological Institute. The model is based on a dynamic stochastic approach to constructing a regression predictive equation. From the set of existing methods for constructing regression equations, a method based on the characteristic roots (eigenvalues) of a correlation matrix, including a column of the predicted variable and predictor columns (extended matrix) is applied. The predicted variable is the standardized drought index SPI, and the predictors are the average monthly precipitation for the 3 months preceding the forecast month, the average monthly value of variations in solar activity (Wolf numbers) and the average monthly value of the Southern Oscillation index for the month preceding the forecast. The predictors were selected on the basis of mutual correlation and applied time series analyses between the aridity index SPI and the indicated heliogeophysical values. The performed estimates of the studied dependence of the aridity index SPI on the state of solar activity, the influence of El Niño (La Niña) and precipitation preceding the forecast date showed their high correlation. Estimates of the accuracy of the SPI forecast with a monthly advance lead time for the territory of Uzbekistan, performed on an independent sample, were quite high, which was the basis for the introduction of this model into the operational work of the hydrometeorological service of Uzbekistan (Uzhydromet).

Dynamic-Stochastic Modeling of Long-Term Level Regime of the Caspian Sea during Early Khvalynsk and Late Khvalynsk Transgressions

Dynamic-Stochastic Modeling of Long-Term Level Regime of the Caspian Sea during Early Khvalynsk and Late Khvalynsk Transgressions

Complex dynamics of a magnetic microrobot driven by single deformation soft tail in random environment

This study focuses on exploring the complex dynamical behaviors of a magnetic microrobot in a random environment. The purpose is to reveal the mechanism of influence of random disturbance on microrobot dynamics. This paper establishes stochastic dynamic models for the microrobot before and after deformation, considering the influence of Gaussian white noise. The system responses are analyzed via steady-state probability density functions and first deformation time. The effects of different magnetic field strengths and fluid viscosities on the movement speed and angular velocity of the microrobot are studied. The results indicate that random disturbances can cause deformation of microrobots in advance compared to the deterministic case. This work contributes to the design and motion control of microrobots and enhances the theoretical foundation of microrobots.

Robust Trajectory Planning of Gliding-Guided Projectiles with Weak Maneuverability

Due to constraints in launch platforms and cost, the maneuverability of gliding-guided projectiles is limited, necessitating a rational design of their trajectory schemes. To reduce the sensitivity of trajectory schemes to uncertainties while ensuring compatibility between flight schemes and guidance control systems and fully exploiting the control capability of the projectile, a closed-loop robust trajectory planning method is proposed. Models of major uncertain factors and state deviation at the control start point are established. Based on the NIPCE method, the stochastic dynamic model is transformed into a high-dimensional deterministic model with PCE coefficients as state variables, and the uncertainty propagation law is obtained. A PID algorithm is employed to design a tracking guidance law based on position error feedback, and open-loop and closed-loop robust trajectory planning models are established accordingly. The optimal control problem is solved by transforming it into a nonlinear programming problem using the direct shooting method. Our simulation results indicate that the NIPCE method can significantly improve the computational efficiency of uncertainty propagation while ensuring accuracy; compared with parallel MCS, the computation time is reduced by 96.8%. Open-loop robust planning can effectively mitigate the sensitivity of gliding trajectories to uncertainties (the standard deviations of terminal altitude and lateral deviations are reduced by 23.6% and 35.3%, respectively, compared to deterministic planning) but cannot completely eliminate terminal dispersion. Closed-loop robust planning effectively improves control effort consumption on the basis of open-loop planning.

Random Vibration Analysis of Double Deck Rocking Self-Centering Pier Under Seismic Excitation

This paper investigates nonlinear random vibration of double deck rocking self-centering pier structure subjected to seismic excitation. First of all, a novel type of double deck rocking self-centering pier that offers better resilience is designed. The stochastic dynamical model of the system is then established, in which the seismic excitation is viewed as Kanai–Tajimi filtered white noise and the self-centering restoring force is characterized by classical flag-shaped hysteretic model. Subsequently, the self-centering restoring force is decomposed into equivalent quasi-linear elastic and damping forces by adopting the harmonic balance (HB) scheme. Following this, the stochastic averaging (SA) technique is implemented to derive the averaged Itô equation. The steady-state response probability density with respect to the amplitudes is solved from the averaged Fokker–Planck–Kolmogorov (FPK) equation. Finally, the effects of system parameters on the stochastic response of the double deck rocking self-centering pier structure are performed, and validated by the Monte Carlo simulation (MCS). In addition, with the help of the Laplace transform, the transition function as well as conditional power spectral density are achieved, which are combined with the steady-state probability density to obtain the power spectral density response. This research will contribute to the optimal seismic design of double-deck rocking self-centering piers.

Improved Bayesian Model Updating Method for Frequency Response Function with Metrics Utilizing NHBFT-PCA

To establish a high-fidelity model of engineering structures, this paper introduces an improved Bayesian model updating method for stochastic dynamic models based on frequency response functions (FRFs). A novel validation metric is proposed first within the Bayesian theory by using the normalized half-power bandwidth frequency transformation (NHBFT) and the principal component analysis (PCA) method to process the analytical and experimental frequency response functions. Subsequently, traditional Bayesian and approximate Bayesian computation (ABC) are improved by integrating NHBFT-PCA metrics for different application scenarios. The efficacy of the improved Bayesian model updating method is demonstrated through a numerical case involving a three-degrees-of-freedom system and the experimental case of a bolted joint lap plate structure. Comparative analysis shows that the improved method outperforms conventional methods. The efforts of this study provide an effective and efficient updating method for dynamic model updating based on the FRFs, addressing some of the existing challenges associated with FRF-based model updating.

Inference on spatiotemporal dynamics for coupled biological populations.

Mathematical models in ecology and epidemiology must be consistent with observed data in order to generate reliable knowledge and evidence-based policy. Metapopulation systems, which consist of a network of connected sub-populations, pose technical challenges in statistical inference owing to nonlinear, stochastic interactions. Numerical difficulties encountered in conducting inference can obstruct the core scientific questions concerning the link between the mathematical models and the data. Recently, an algorithm has been proposed that enables computationally tractable likelihood-based inference for high-dimensional partially observed stochastic dynamic models of metapopulation systems. We use this algorithm to build a statistically principled data analysis workflow for metapopulation systems. Via a case study of COVID-19, we show how this workflow addresses the limitations of previous approaches. The COVID-19 pandemic provides a situation where mathematical models and their policy implications are widely visible, and we revisit an influential metapopulation model used to inform basic epidemiological understanding early in the pandemic. Our methods support self-critical data analysis, enabling us to identify and address model weaknesses, leading to a new model with substantially improved statistical fit and parameter identifiability. Our results suggest that the lockdown initiated on 23 January 2020 in China was more effective than previously thought.

A Bibliometric Study: General Equilibrium Models on Energy Economics

General equilibrium (GE) models are commonly used for economic impact analysis. They offer a benchmark for analyzing changes in the overall economy due to new policies, shocks, or technological improvements, using the data from the social accounting matrices and input-output tables. GE models are widely used for analyzing the areas of energy economics, as the focus on energy-related issues has become critical throughout the years. Therefore, a broad literature focuses on the GE models and energy economics. This study uses bibliometric analysis to examine the networks between the existing literature between 1990-2020. No other paper uses this method to focus on the selected literature. The data for the bibliometric analysis is subtracted from the Web of Science. The keywords are "computable general equilibrium, dynamic stochastic general equilibrium, and energy." Dynamic Stochastic Models are added to expand the scope of the dataset. In addition, the paper reviews the ten most cited articles based on the data retrieved from the Web of Science. The main results of the bibliometric analysis show that the GE models were highly used after 2005, with the introduction of international energy agreements. The focus of these models is usually renewable energy and mitigation policies.

Assessing effects of climate and technology uncertainties in large natural resource allocation problems

Abstract. The productivity of the world's natural resources is critically dependent on a variety of highly uncertain factors, which obscure individual investors and governments that seek to make long-term, sometimes irreversible, investments in their exploration and utilization. These dynamic considerations are poorly represented in disaggregated resource models, as incorporating uncertainty into large-dimensional problems presents a challenging computational task. In this paper, we apply the SCEQ algorithm (Cai and Judd, 2023) to solve a large-scale dynamic stochastic global land resource use problem with stochastic crop yields due to adverse climate impacts and limits on further technological progress. For the same model parameters and bounded shocks, the range of land conversion is considerably smaller for the dynamic stochastic model than for deterministic scenario analysis.

A Novel Stochastic Model for Human Norovirus Dynamics: Vaccination Impact with Lévy Noise

The epidemic norovirus causes vomiting and diarrhea and is a highly contagious infection. The disease is affecting human lives in terms of deaths and medical expenses. This study examines the governing dynamics of norovirus by incorporating Lévy noise into a stochastic SIRWF (susceptible, infected, recovered, water contamination, and food contamination) model. The existence of a non-negative solution and its uniqueness are proved after model formulation. Subsequently, the threshold parameter is calculated, and this number is used to explore the conditions under which disease tends to exist in the population. Likewise, additional conditions are derived that ensure the elimination of the disease from the community. It is proved that the norovirus is extinct whenever the threshold parameter is less than one and it persists for Rs>1. The work assumes two working examples to numerically explain the theoretical findings. Simulations of the study are visually presented, and comparisons are made. The results of this study suggest a robust approach for handling complex biological and epidemic phenomena.

Three-dimensional stochastic dynamical modeling for wind farm flow estimation

Modifying turbine blade pitch, generator torque, and nacelle direction (yaw) are conventional approaches for enhancing energy output and alleviating structural loads. However, the efficacy of such methods is challenged by the lag in adjusting such settings after atmospheric variations are detected. Without reliable short-term wind forecasting tools, current practice, which mostly relies on data collected at or just behind turbines, can result in sub-optimal performance. Data-assimilation strategies can achieve real-time wind forecasting capabilities by correcting model-based predictions of the incoming wind using various field measurements. In this paper, we revisit the development of a class of prior models for real-time estimation via Kalman filtering algorithms that track atmospheric variations using ground-level pressure sensors. This class of models is given by the stochastically forced linearized Navier-Stokes equations around the three-dimensional waked velocity profile defined by a curled wake model. The stochastic input to these models is devised using convex optimization to achieve statistical consistency with high-fidelity large-eddy simulations. We demonstrate the ability of such models in reproducing the second-order statistical signatures of the turbulent velocity field. In support of assimilating ground-level pressure measurements with the predictions of said models, we also highlight the significance of the wall-normal dimension in enhancing two-point correlations of the pressure field between the ground and the computational domain.

How to reduce household food waste during and after the COVID‐19 lockdown? Evidence from a structural model

AbstractThe COVID‐19 lockdown precipitated a fundamental shift in consumer food‐related behaviours. Owing to adherence to stay‐at‐home directives and concerns over potential exposure to the coronavirus, consumers engaged in less frequent in‐person shopping, opting for larger quantities of food purchased per trip, a trend with the potential to exacerbate food wastage patterns among bulk food purchasers. Nevertheless, recent empirical data obtained from the United Kingdom have revealed a 34% reduction in household food waste during the nationwide lockdown in April 2020. To gain deeper insights into the underlying mechanisms governing household food waste behaviours, we employ an infinite horizon dynamic stochastic model that operates on a daily cycle, focusing specifically on household food inventory management. Our analysis demonstrates that absent any improvements in food management practices, panic‐stricken consumers who stockpiled food at home during the early phase of the pandemic generated significantly higher levels of food waste. Conversely, consumers who embraced effective food management techniques and transitioned to online grocery shopping managed to reduce household food waste by about 50% during the pandemic. Additionally, we conduct simulations to envision potential post‐pandemic scenarios and conclude the study with a set of recommendations aimed at curbing household food waste in the aftermath of the pandemic.

Route Guidance Model with Limited Overlap on Freeway Network under Traffic Incidents

With the increasing density of the freeway network, frequent traffic incidents on road segments have a significant impact on the operational efficiency of the road network. Therefore, it has become urgent and important to study traffic route guidance strategy on the road network level. The previous traffic route guidance method primarily focused on the congestion on the road segments where incidents occurred, with insufficient attention given to the impact of congestion on the road network level. In this study, a route guidance model with limited overlap is proposed to improve freeway network reliability under traffic incidents. Specifically, in order to explore alternative paths, we conducted a study on the problem of finding k-short paths with limited overlap. The objective is to identify a set of k-paths that are both sufficiently dissimilar and as short as possible. Then, we promptly update the route guidance information using a stochastic dynamic traffic assignment model that aligns with travelers’ path choice psychology. Moreover, we use the reliability of the road network to evaluate the network performance. To illustrate the model, the Jinan freeway network is selected as an experimental study. The effectiveness of this method was validated through SUMO simulations, comparing it with alternative route guidance methods, including Yen’s algorithm, A∗ algorithm, and ant colony algorithm. These results show that the proposed method has proven effective in mitigating traffic congestion arising from incidents and performs well in regard to the reliability of the road network under the impact of incidents.

Deterministic and Stochastic Nonlinear Model for Transmission Dynamics of COVID-19 with Vaccinations Following Bayesian-Type Procedure

We develop a mathematical model for the SARAS-CoV-2 double variant transmission characteristics with variant 1 vaccination to address this novel aspect of the disease. The model is theoretically examined, and adequate requirements are derived for the stability of its equilibrium points. The model includes the single variant 1 and variant 2 endemic equilibria in addition to the endemic and disease-free equilibria. Various approaches are used for the global and local stability of the model. For both strains, we determine the basic reproductive numbers R1 and R2. To investigate the occurrence of the layers (waves), we expand the model to include some analysis based on the second-order derivative. The model is then expanded to its stochastic form, and numerical outcomes are computed. For numerical purposes, we use the nonstandard finite difference method. Some error analysis is also recorded.

Stochastic response and stability analysis of nonlinear vehicle energy-regenerative suspension system with time delay

With the rapid development of new energy vehicles, a novel vehicle energy-regenerative suspension for simultaneous vibration suppression and energy harvesting has become one of the key development directions of the next generation of vehicle design. In order to improve the performance of suspension system, the time-delayed feedback control is applied to the novel suspension system subjected to different external excitation. At the same time, there are few studies related to the stochastic dynamics of nonlinear vehicle energy-regenerative suspension system with time delay. This paper studies stochastic response and stability of nonlinear vehicle energy-regenerative suspension with time-delayed feedback control under the excitation of Gaussian white noise. First of all, a stochastic dynamic model of the nonlinear vehicle energy-regenerative suspension with time delay system is established. Secondly, using the stochastic averaging method based on generalized harmonic function, the steady-state probability density function (PDF) of amplitude is obtained. The accuracy of the presented approach is verified through the comparison of analytical and numerical solutions. In addition, through combining the stochastic averaging method with the Khasminskii method, the top Lyapunov exponent (TLE) of the system is obtained, and then the influence of time delay and system parameters on the asymptotic Lyapunov stability is discussed. Finally, the effects of time delay and system parameters on system performance are also studied.