Dynamic Stochastic Model Research Articles

Neural network approach for cholera dynamics: Integrating deterministic and stochastic insights

In this article, a comprehensive qualitative analysis framework is presented that integrates stochastic and deterministic models to explore the transmission dynamics of Cholera disease. The significance of the reproduction number in understanding the spread of the disease and in formulating effective control strategies is emphasized. The sensitivity analysis of model parameters is conducted to identify those that critically influence transmission. By converting the deterministic model into a stochastic form, Brownian motion and stochastic parameters are incorporated to capture the inherent randomness in disease dynamics. This approach is further enriched by the application of neural networks (NN) to simulate and validate the complex interactions involved in Cholera transmission. The analysis extends to the global positive solution, stochastic reproduction number, and virus-free stochastic dynamics, providing an improved understanding of the disease's behavior. The critical conditions necessary for the extinction and long-term elimination of the virus are also addressed, highlighting the importance of controlling its spread. The stationary distribution of the disease is examined through the lens of a regular Markov process, enhancing the understanding of the stochastic model's dynamics. The results verified by neural networks, compared with those obtained from conventional numerical methods, underscore the accuracy and versatility of neural networks in epidemiological research, offering new perspectives and methodologies for tackling this global health challenge.

Conjunctive surface water and groundwater management in a multiple user environment

The conjunctive use of surface water and groundwater is practiced worldwide as a measure to address water supply uncertainty. This paper focuses on a scenario in which an aquifer is open to multiple users and examines the impact of such an open-access environment on the stabilization function of conjunctive management. We construct a non-cooperative stochastic dynamic game model where multiple users utilize groundwater intake from a common aquifer as a complement to fluctuating surface water. We also propose a simpler baseline applicable to dynamic environments to compute the benefits of the stabilization function when users are unable to adjust groundwater intake to surface water uncertainties. We then apply the model to the real-world case of the water supply environment of the Cao’e River in China. Simulation results show that open access leads to diminishing stabilization values as higher pumping costs due to declining stocks lead to a weakening of users’ incentive to utilize groundwater flexibly. Furthermore, the stabilization function itself is destabilized as the number of users increases. This is because greater groundwater intake and a decline in stocks amplify variations in pumping costs caused by different patterns of surface-water fluctuation.

Effects of extending dairy cow longevity by adjusted reproduction management decisions on partial net return and greenhouse gas emissions: A dynamic stochastic herd simulation study

Prolonging dairy cattle longevity is regarded as one of the options to contribute to more sustainable milk production. Because failure to conceive is one of the main reasons for culling, this study investigates how adjustments in reproduction management affect partial net return at herd level and greenhouse gas emissions per unit of milk, using a dynamic stochastic simulation model. The effects of reproduction decisions that extend cattle longevity on milk yield, calving interval and pregnancy rate were derived from actual performance of Dutch commercial dairy cows over multiple lactations. The model simulated lactations, calving, and health status events of individual cows for herds of 100 cows. Scenarios evaluated differed in the maximum number of consecutive AI attempts (4, 5, or 6 services), or the production threshold (20, 15, or 10 kg of milk/d) at which cows that failed to conceive are culled (reproductive culling). Annual partial net return was computed from revenues of sold milk, calves, and slaughtered cows, and the costs from feed consumption, rearing replacement heifers, AI services, and treatment for clinical mastitis and lameness. Greenhouse gas emissions were computed for feed production, enteric fermentation, and manure management, and were expressed as total CO2 equivalents (CO2-eq). Average age at culling increased with an increased maximum number of AI services. This increase was larger when going from a maximum of 4 to 5 AI attempts (108 d) than from a maximum of 5 to 6 attempts (47 d). Similarly, the average age at culling increased from 1,968 to 2,040 and 2,132 d when the threshold for reproductive culling decreased from 20, to 15 and 10 kg of milk/d, respectively. Average annual partial net return increased by 1.1% from €165,850 per 100 cows at a maximum of 4 AI to €167,670 per 100 cows at a maximum of 6 AI, and increased by 4.3% from €161,210 per 100 cows at a reproductive culling threshold of 10 kg/d to €168,190 per 100 cows at a threshold of 20 kg/d. Greenhouse gas emissions decreased by 1.2% from 0.926 to 0.915 kg CO2-eq per kg of fat- and protein-corrected milk (FPCM) with an increase in a maximum number of AI from 4 to 6 AI. Conversely, greenhouse gas emissions increased by 0.2% from 0.926 kg at a threshold of reproductive culling of 20 kg/d to 0.928 kg CO2-eq/kg FPCM at a threshold of 10 kg/d. Although lowering the threshold for reproductive culling has the potential to extend cattle longevity more than increasing the maximum number of AI services, only the increase in AI services benefits a farm's partial net return, while reducing greenhouse gas emissions.

Controllability of Mild Solution to Hilfer Fuzzy Fractional Differential Inclusion with Infinite Continuous Delay

This work investigates the solvability of the generalized Hilfer fractional inclusion associated with the solution set of a controlled system of minty type–fuzzy mixed quasi-hemivariational inequality (FMQHI). We explore the assumed inclusion via the infinite delay and the semi-group arguments in the area of solid continuity that sculpts the compactness area. The conformable Hilfer fractional time derivative, the theory of fuzzy sets, and the infinite delay arguments support the solution set’s controllability. We explain the existence due to the convergence properties of Mittage–Leffler functions (Eα,β), that is, hatching the existing arguments according to FMQHI and the continuity of infinite delay, which has not been presented before. To prove the main results, we apply the Leray–Schauder nonlinear alternative thereom in the interpolation of Banach spaces. This problem seems to draw new extents on the controllability field of stochastic dynamic models.

Adaptive network traffic control with approximate dynamic programming based on a non-homogeneous Poisson demand model

ABSTRACT In this study, we develop a stochastic dynamic traffic-flow model subject to practical restrictions under the non-homogeneous Poisson vehicle arrival process. Using the cell transmission strategy, we establish traffic dynamics between two intersections. We also discuss simulating the random demand of source links from an estimated intensity function. Additionally, we propose an algorithm to optimize time interval division for aggregated data, aiming to enhance estimation performance. We explore applying our traffic flow model to the adaptive traffic network management problem, which is formulated as a Markov decision process. Leveraging approximate dynamic programming with recursive least squares-temporal difference learning, we achieve adaptive optimal policies. To validate our approach, we conduct a series of numerical experiments with random demands. The results of non-homogeneous Poisson demand conducted using random numbers and a real-word dataset indicate high efficiency with the piecewise constant, I-SMOOTH, and MNO-PQRS estimators. Compared to the Webster and Max-pressure control systems, our proposed approximate dynamic programming-based model exhibits superior stability and applicability.

Financial literacy, uncertainty and costs of education

This paper studies how uncertainty and costs of financial education affect spending on financial literacy. To explore the issue a dynamic stochastic model is employed. We show that the marginal value of financial literacy increases with market volatility, but is hampered by the cost of financial education. A solution is derived for the case of reversible investment. Reversibility increases the fundamental value of financial literacy because of education-related rents.

Stochastic dynamics mass spectrometric structural analysis of poly(methyl methacrylate)

Polymers such as poly(methyl methacrylate), comprising of all-carbon backbones are regarded as ubiquitous functional materials mainly due to their low cost, unique physical properties, and impressive robustness. The latter properties are results from relative chemical inertness of the polymer backbone carbon–carbon bonds. The highlighted stability crucially challenges not only innovations to plastic recycling polymer materials, but also developments of reliable analytical protocols for determining both quantitatively and structurally polymers. Despite, the fact that there are numerous applications of mass spectrometric methods to polymer science, the analysis involves chiefly annotation of monomers of polymers and additives, owing to the fact that the additives are low molecular weight analytes. The exact structural determining of end-chain groups, particularly highlighting chemically substituted end carbon–carbon bond represents significant challenge even utilizing the superior features of the analytical mass spectrometric instrumentation. This study, in the latter context, illustrates innovative stochastic dynamics approach and model equations capable of not only determining unambiguously substituted carbon–carbon end chain of the entitled polymer but also to predict mass spectra of its derivatives: thus, extending crucially the applicability of the method to many fields of the fundamental scientific and industrial research. The latter claim is argued still at the beginning of the study with the achieved method performances showing |r|=0.99998. The study utilizes experimental and theoretical mass spectrometric data on high resolution electrospray ionization mass spectrometry; high accuracy quantum chemical static methods, molecular dynamics; and chemometrics.

Simulation of Full HIV Cluster Networks in a Nationally Representative Model Indicates Intervention Opportunities.

Clusters of rapid HIV transmission in the United States are increasingly recognized through analysis of HIV molecular sequence data reported to the National HIV Surveillance System. Understanding the full extent of cluster networks is important to assess intervention opportunities. However, full cluster networks include undiagnosed and other infections that cannot be systematically observed in real life. We replicated HIV molecular cluster networks during 2015-2017 in the United States using a stochastic dynamic network simulation model of sexual transmission of HIV. Clusters were defined at the 0.5% genetic distance threshold. Ongoing priority clusters had growth of ≥3 diagnoses/year in multiple years; new priority clusters first had ≥3 diagnoses/year in 2017. We assessed the full extent, composition, and transmission rates of new and ongoing priority clusters. Full clusters were 3-9 times larger than detected clusters, with median detected cluster sizes in new and ongoing priority clusters of 4 (range 3-9) and 11 (range 3-33), respectively, corresponding to full cluster sizes with a median of 14 (3-74) and 94 (7-318), respectively. A median of 36.3% (range 11.1%-72.6%) of infections in the full new priority clusters were undiagnosed. HIV transmission rates in these clusters were >4 times the overall rate observed in the entire simulation. Priority clusters reflect networks with rapid HIV transmission. The substantially larger full extent of these clusters, high proportion of undiagnosed infections, and high transmission rates indicate opportunities for public health intervention and impact.

A stochastic model for neural progenitor dynamics in the mouse cerebral cortex

We have designed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, using the formalism of compound Poisson processes. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations.

SVD-Based Parameter Identification of Discrete-Time Stochastic Systems with Unknown Exogenous Inputs

This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it is not possible to make any assumptions about the evolution of the unknown input signal or its statistical properties. The main purpose of this paper is to construct a new SVD-based modification of the existing Gillijns and De Moor filtering algorithm for linear discrete-time stochastic systems with unknown exogenous inputs. Using the theoretical results obtained, we demonstrate how this modified algorithm can be applied to solve the problem of parameter identification. The results of our numerical experiments conducted in MATLAB confirm the effectiveness of the SVD-based parameter identification method that was developed, under conditions of unknown exogenous inputs, compared to maximum likelihood parameter identification when exogenous inputs are known.

Socioeconomic inequalities in accumulation of multimorbidity in England from 2019 to 2049: a microsimulation projection study

There are socioeconomic inequalities in the prevalence of multimorbidity and its accumulation across the life course. Estimates of multimorbidity prevalence in English primary care increased by more than two-thirds from 2004 to 2019. We developed a microsimulation model to quantify current and projected multimorbidity inequalities in the English adult population. We used primary care data for adults in England from the Clinical Practice Research Datalink Aurum database between 2004 and 2019, linked to the 2015 English Index of Multiple Deprivation (IMD), to model time individuals spent in four health states (healthy, one chronic condition, basic multimorbidity [two or more chronic conditions], and complex multimorbidity [three or more chronic conditions affecting three or more body systems]) by sex, age, IMD quintile, birth cohort, and region. We applied these transition times in a stochastic dynamic continuous-time microsimulation model to Office for National Statistics population estimates for adults aged 30-90 years. We calculated projected prevalence and cumulative incident cases from 2019 to 2049 by IMD quintile, age group (younger than 65 years vs 65 years and older), and years to be lived without multimorbidity at age 30 years. Under the assumption that all chronic conditions were lifelong, and that once diagnosed there was no recovery, we projected prevalence of multimorbidity (basic or complex) increases by 34% from 53·8% in 2019 to 71·9% (95% uncertainty interval 71·8-72·0) in 2049. This rise equates to an 84% increase in the number of people with multimorbidity: from 19·2 million in 2019 to 35·3 million in 2049 (35·3 million to 35·4 million). This projected increase is greatest in the most deprived quintile, with an excess 1·07 million (1·04 million to 1·10 million) cumulative incident basic multimorbidity cases and 0·70 million (0·67 million to 0·74 million) complex multimorbidity cases over and above the projected cases for the least deprived quintile, largely driven by inequalities in those younger than 65 years. The median expected number of years to be lived without multimorbidity at age 30 years in 2019 is 15·12 years (14·62-16·01) in the least deprived IMD quintile and 12·15 years (11·61-12·60) in the most deprived IMD quintile. The number of people living with multimorbidity will probably increase substantially in the next 30 years, a continuation of past observed increases partly driven by changing population size and age structure. Inequalities in the multimorbidity burden increase at each stage of disease accumulation, and are projected to widen, particularly among the working-age population. Substantial action is needed now to address population health and to prepare health-care and social-care systems for coming decades. University of Liverpool and National Institute for Health and Care Research School for Public Health Research.

Sequential coordination of power generation and network investments: the role of renewable incentives

The paper addresses the issue of coordinating renewable and network investments in a context of unstable subsidies. It contributes to the literature by developing a three-stage analytical model to address the network operator investment strategies being either proactive or reactive and considering the sensitivity of investments to future renewable incentives, being uncertain and variable. A dynamic stochastic modeling is used to formalize actors' choices. The study's major results show that proactive operator may cause a loss of welfare compared to reactive operator. This depends on network investment costs and network investments delays, the intensity of support measures of renewable energy and the maturity of renewable technologies. While network operator needs to be proactive, especially if moderate new network investments are expected, our results demonstrate that there exists a threshold level of network investment beyond it being reactive is economically preferable. An assessment of some countries cases confirms our theoretical predictions.

Do adjustment costs constrain public healthcare providers' technical efficiency? Evidence from the New Zealand Public Healthcare System.

Efficiency analysis is crucial in healthcare to optimise resource allocation and enhance patient outcomes. However, the prompt adaptation of inputs can be hindered by adjustment costs, which impact Long-Run Technical Efficiency (LRTE). To bridge this gap in healthcare literature, this research employs a Bayesian Dynamic Stochastic Frontier Model to estimate parameters and explore healthcare efficiency dynamics over time. The study reveals the LRTE for New Zealand District Health Boards (DHBs) as 0.76, indicating around 32% more input utilisation due to adjustment costs. Most DHBs exhibit consistent short-run operational efficiency, with the national Short-Run Technical Efficiency (SRTE) very close to the LRTE. Among the tertiary providers, Auckland and Capital & Coast DHBs operate below the LRTE level, setting them apart from other tertiary providers. Similarly, Tairawhiti and West Coast DHBs also fall below the LRTE level, as indicated by their SRTE scores, potentially influenced by their unique healthcare settings and resource challenges. This research brings a new perspective to policy discussions by incorporating the temporal dynamics of decision-making and considering adjustment costs. It underscores the need to balance short-term and long-term technical efficiency, underlining their collective significance in fostering a sustainable and efficient healthcare system in New Zealand.

Study of the stochastic dynamics of particles in the coal screening based on the Markov process

The model of the stochastic dynamics for the screening and screen-penetration processes was developed based on the Markov process to reveal the mechanism of the coal screening effect. As a partial differential equation, the model of the stochastic dynamics describes the relationship between particle position in the y direction, screening time, and particle screen-penetration probability. The obtained model for stochastic dynamics can calculate the screen-penetration probability of a specific particle size at any given time. Moreover, two coefficients, a1 and a2, are defined where a1 represents the average velocity of particles, and a2 represents the combined effect of orderly segregation and mixing of particles in chaotic motion. These coefficients of the stochastic dynamics model were obtained by regression analysis. Additionally, the statistical analysis showed that the fitting errors were all <1. The proposed statistical dynamics model works for all particle sizes. A necessary coefficient, a1, was calculated based on screen-penetration coefficients k, a, and b. A large value of a1 means a high average velocity of particles and a greater screen-penetration probability. The value of a1 for particles smaller than 6 mm declines as the feed mass increases. Moreover, it initially decreases, followed by an increase, in response to a rising proportion of particles <6 mm. In contrast, the a1 value for particles ranging between 6 mm and 13 mm undergoes minimal changes when subjected to variations in feed mass and the proportion of particles <6 mm.

Dysregulated Salience Network Control over Default-Mode and Central-Executive Networks in Schizophrenia Revealed Using Stochastic Dynamical Causal Modeling.

Introduction: Neuroimaging studies suggest that the human brain consists of intrinsically organized, large-scale neural networks. Among these networks, the interplay among the default-mode network (DMN), salience network (SN), and central-executive network (CEN) has been widely used to understand the functional interaction patterns in health and disease. This triple network model suggests that the SN causally controls over the DMN and CEN in healthy individuals. This interaction is often referred to as SN's dynamic regulating mechanism. However, such interactions are not well understood in individuals with schizophrenia. Methods: In this study, we leveraged resting-state functional magnetic resonance imaging data from schizophrenia (n = 67) and healthy controls (n = 81) and evaluated the directional functional interactions among DMN, SN, and CEN using stochastic dynamical causal modeling methodology. Results: In healthy controls, our analyses replicated previous findings that SN regulates DMN and CEN activities (Mann-Whitney U test; p < 10-8). In schizophrenia, however, our analyses revealed a disrupted SN-based controlling mechanism over the DMN and CEN (Mann-Whitney U test; p < 10-16). Conclusions: These results indicate that the disrupted controlling mechanism of SN over the other two neural networks may be a candidate neuroimaging phenotype in schizophrenia.

On the exponential stability of a stochastic model for transmission dynamics of antimicrobial‐resistant infections

In this research, a comprehensive stochastic model was developed to analyze the transmission dynamics of methicillin‐resistant Staphylococcus aureus (MRSA) in both hospital‐acquired and community‐acquired contexts. The study explored the existence and uniqueness of solutions and established the presence of a global solution. The investigation focused on assessing the boundedness, extinction, and persistence of MRSA strains in terms of their means. The analysis of the model revealed a noteworthy phenomenon known as competitive exclusion, where the community‐acquired MRSA strain gradually out‐competes the hospital‐acquired strain within hospital settings. In conclusion, effective interventions and preventive measures, such as improving hand hygiene compliance, implementing decolonization strategies, and enhancing disinfection rates, emerge as critical factors in controlling the transmission of these strains within hospital environments.

Forecasting Coal Price Using Static and Dynamic Stochastic Model as Based for Indonesia’s Mining Project Valuation with Real Option Method

Indonesia's coal mining company is not only a capital-incentive business that needs high investment at the start of the project but also a cost-incentive business that needs high operational costs along the project. The most important parameter needed to determine the project value is assuming uncertainty of coal price in the future. This condition forces mining entrepreneurs to forecast future coal prices with the assumption. One of the approaches is using the Stochastic Model to predict price fluctuation in the future. There are two models: the static model, which uses 50 percentiles of historical data, and the dynamic model, which uses Monte Carlo simulation with normal distribution as the fluctuation of the percentile. Using the Real Options Method, this approach could make a difference in project valuation. This difference could give insight into the mining project valuation.

Optimal Incentives in a Limit Order Book: A SPDE Control Approach

With the fragmentation of electronic markets, exchanges are now competing in order to attract trading activity on their platform. Consequently, they developed several regulatory tools to control liquidity provision/consumption on their liquidity pool. In this paper, we study the problem of an exchange using incentives in order to increase market liquidity. We model the limit order book as the solution of a stochastic partial differential equation (SPDE) as in [R. Cont and M. S. Müller, 2021, A stochastic partial differential equation model for limit order book dynamics, SIAM Journal on Financial Mathematics 12(2), 744–787]. The incentives proposed to the market participants are functions of the time and the distance of their limit order to the mid-price. We formulate the control problem of the exchange who wishes to modify the shape of the order book by increasing the volume at specific limits. Due to the particular nature of the SPDE control problem, we are able to characterize the solution with a classic Feynman–Kac representation theorem. Moreover, when studying the asymptotic behavior of the solution, a specific penalty function enables the exchange to obtain closed-form incentives at each limit of the order book. We study numerically the form of the incentives and their impact on the shape of the order book, and analyze the sensitivity of the incentives to the market parameters.

Resource discoveries and the political survival of dictators

We study the effect of resource discoveries on dictator failure. We extend existing conflict literature by developing a dynamic stochastic model where timing of attack and probability of success are endogenous. Incumbent and opposition invest in military arsenals which determine success probability, while opposition also chooses when to stage a coup. A resource discovery delays the attack and reduces the probability of overthrow. We test these hypotheses using duration models and timing of giant oil and gas discoveries, finding that large discoveries more than double remaining time until failure and reduce hazard faced by an autocrat by 30%–50%.

Individual dynamics and local heterogeneity provide a microscopic view of the epidemic spreading

The COVID-19 pandemic has caused severe global disasters, highlighting the importance of understanding the details and trends of epidemic transmission in order to introduce efficient intervention measures. While the widely used deterministic compartmental models have qualitatively presented continuous “analytical” insight and captured some transmission features, their treatment usually lacks spatiotemporal variation. Here, we propose a stochastic individual dynamical (SID) model to mimic the random and heterogeneous nature of epidemic propagation. The SID model provides a unifying framework for representing the spatiotemporal variations of epidemic development by tracking the movements of each individual. Using this model, we reproduce the infection curves for COVID-19 cases in different areas globally and find the local dynamics and heterogeneity at the individual level that affect the disease outbreak. The macroscopic trend of virus spreading is clearly illustrated from the microscopic perspective, enabling a quantitative assessment of different interventions. Seemingly, this model is also applicable to studying stochastic processes at the “meter scale”, e.g., human society’s collective dynamics.