Deterministic Model Research Articles

Dynamical analysis of HIV-TB co-infection transmission model in the presence of treatment for TB

The immense disease burden of tuberculosis (TB) infection is well-documented, particularly among those co-infected with HIV and TB. To better understand the transmission dynamics of HIV-TB co-infection in the absence of readily available HIV treatment, we develop a deterministic compartmental co-infection model. Our model helps to identify the effects of TB infection on the co-infection dynamics of the two diseases, especially when treatment for TB is readily available. We find that susceptibility to TB reinfection after a previous infection leads to backward bifurcation in the TB-only model when the associated reproduction number (R_0) is less than unity. However, when we make the susceptibility to TB re-infection insignificant in the model, the disease-free equilibrium of the TB-only model is locally asymptotically stable when the associated R_0 is less than unity. We conduct sensitivity and uncertainty analyses to identify the key parameters driving TB infection dynamics, using the R_0 as the response function. We discover that the transmission rate for TB, the modification parameters accounting for the infectiousness of infected individuals with TB-only, and the treatment rates for singly infected individuals with latently infected TB are the top drivers of TB infection in the given population. Our numerical simulations suggest that concentrating treatment on TB-infected individuals in the diagnosed latently infected stage (singly or dually infected with HIV) could effectively reduce the co-infection disease burden and HIV incidence in the population under study.

Network-level pavement maintenance and rehabilitation planning considering uncertainties using chance-constrained programming

ABSTRACT In practice, given limited funds, to consider multiple strategic goals/objectives that different stakeholders concern, pavement network-level maintenance and rehabilitation (M&R) planning becomes a multi-objective optimisation (MOO) based project selection and budget allocation problem. In an attempt to solve this problem, most agencies established MOO models under the deterministic situation without appropriate consideration of uncertainties. However, ignoring performance uncertainties often leads to unreasonable decisions. To provide more convincing and reliable pavement M&R decisions, this paper proposes a Chance-Constrained Programming (CCP) based MOO method to incorporate performance uncertainties in network-level single period pavement M&R planning. First, a general deterministic MOO model with budget and network performance constraints is established. Then, three commonly-used statistical forms of network-level performance measures are introduced. To incorporate uncertainties, the probability distribution of each form of performance measure is derived. Based on the CCP method, the MOO model is transformed to an equivalent deterministic formulation as a mixed non-linear integer programming (MNLIP) problem. To demonstrate the proposed method, a case study using real data is conducted. The results show that the proposed method can effectively help decision-makers to appropriately incorporate performance uncertainties in conducting network-level pavement M&R planning.

Mathematical modeling for the transmission dynamics of cholera with an optimal control strategy

Cholera is an acute diarrheal disease caused by Vibrio cholera, its prevalence occurs in almost all the continents of the world, annually there are about 1.3 to 4.0 million cases of cholera and 21,000 to 143,000 deaths worldwide. In this paper, we propose a deterministic model for the transmission dynamics of cholera to assess the impact of vaccines in decreasing the spread of cholera infection in Nigeria. Moreover, we develop an optimal control strategy, in which we consider personal hygiene a control strategy on infection class, with u(t) as the control function. The best values of the fitting parameters have been obtained using least square minimization to validate the model with the help of experimental data obtained from Nigeria. We perform sensitivity analysis to determine the key parameters that have impacts on the control of the spread of cholera infections in the population. In addition, the numerical simulation of the model reveals that the use of vaccines and personal hygiene will effectively control the spread of cholera infection.

Deterministic and Stochastic Surrogate Models for a Slowly Driven Fast Oscillator

Deterministic and Stochastic Surrogate Models for a Slowly Driven Fast Oscillator

The effects of additional food and environmental stochasticity on the asymptotic properties of a nutrient–phytoplankton model

In this paper, we investigate the deterministic and stochastic features of an additional food provided nutrient–phytoplankton model, and discuss the effects of additional food and environmental stochasticity (noise) on its asymptotic properties. A detailed global dynamics analysis of the deterministic model is firstly provided, and then the critical conditions for persistence and extinction of phytoplankton is found. For the stochastic model, we establish some sufficient conditions for the exponential extinction of phytoplankton and the existence of stationary distribution. By solving the Fokker–Planck equation, the explicit expression of local probability density of the stochastic model is further derived. With the help of probability density, we obtain the mean, variance, skewness and kurtosis of the biomass of phytoplankton, and numerically find the additional food and stochasticity have complex effects on these statistical properties. Both theoretical and numerical findings indicate that the additional food source is favorable for the growth of phytoplankton, whereas the stochasticity is adverse to its growth. Moreover, the additional food source and stochasticity play important roles in the formation of phytoplankton bloom.

Prediction of COVID-19 spread with models in different patterns: A case study of Russia

Abstract This study deals with a mathematical model that examines the spread of Coronavirus disease (COVID-19). This model has been handled with different processes such as deterministic, stochastic, and deterministic–stochastic. First of all, a detailed analysis is presented for the deterministic model, which includes the positivity of the solution, the basic reproduction number, the disease, and endemic equilibrium points. Then, for the stochastic model, we investigate under which conditions, the solution exists and is unique. Later, model is reconsidered with the help of the piecewise derivative, which can combine deterministic and stochastic processes. Numerical simulations are presented for all these processes. Finally, the model has been modified with the rate indicator function. The model presenting these four different situations is compared with the real data in Russia. According to the results obtained from these situations, the model that is obtained by adding the rate indicator function predicts the COVID-19 outbreak in Russia more accurately. Thus, it is concluded that the model with the rate indicator function presents more realistic approach than the previous ones.

Deterministic mathematical modeling, sensitivity analysis, and dynamic optimization of cross-flow ultrafiltration systems for concentration of monoclonal antibody solutions

This manuscript proposes a general new framework for mathematical modeling, extended sensitivity analysis and dynamic optimization of tangential flow filtration (TFF) systems for concentration of monoclonal antibody (mAb) products and, potentially, other biologics. This framework is comprised of four major components: (I) a new first-principles-inspired TFF model; (II) dedicated parameter estimation strategies for automated model training; (III) new extended sensitivity analysis techniques for enhancing TFF phenomenological understanding and providing general guidance on TFF process development; and (IV) novel mono-objective and multi-objective dynamic optimization strategies for optimal TFF design and operation. The application of this framework to Bovine immunoglobulin γ (IgG) – a mAb analog in terms of physicochemical properties – shows the potential benefits it may offer in terms of overall TFF performance and rapid TFF development for new mAb candidates, compared to the current state of the art.

Dynamics of an [formula omitted] epidemic model with stochastic optimal control and awareness programs

An unaware susceptible-aware susceptible-vaccinated-infected-recovered (SuSaV IR) epidemic disease model has been developed and extensively examined to better understand the intricate dynamics of the disease transmission with saturated recovery function. A non-linear, monotonically increasing awareness function has been incorporated and its application is contingent upon the number of infected individuals. The spreading threshold R0 and its sensitivity indices are computed to determine both the prevalence and the potential decline of the spread of disease. Contour plots have been generated to explain how alterations in key parameters affect the evolution of infected individuals. In deterministic model, the condition R0<1 ensures the global stability of a disease-free state while R0>1 indicates the presence of a globally stable prevailing state. A numerical approach has been employed to pinpoint the stability switches for R0 which indicates transcritical bifurcation. Subsequently, a corresponding stochastic model is developed to investigate the impact of random external factors represented as white noise. In addition, the global existence and uniqueness of solutions, and the asymptotic behavior of solutions in the vicinity of steady-states are exhibited in the stochastic model. In the stochastic model, the extinction threshold Res is consistently below R0 due to noise intensity, leading to quicker disease extinction. In order to elucidate the influence of parameters and noise intensities on persistence threshold Rps and extinction threshold Res, a comprehensive sensitivity analysis and the variation of each noise intensity have been performed. This study shows that treatment can be used as an effective tool for controlling the spread of disease by lowering R0 and Rps. It has been empirically observed that high environmental fluctuations can serve as a suppressive factor for disease spread in stochastic model with R0,Rps>1 and the higher noise intensities lead to a faster disappearance of the disease. It is noticed that randomness in susceptible and infected individuals can exert a more significant influence on disease mitigation. The spread of infection exhibits a noteworthy dependence on environmental fluctuations. Additionally, to combat and mitigate the spread of disease, we have executed stochastic optimal control measures. Consequently, the control strategy has emerged as a potent tools for effectively managing the propagation of disease.

Mathematical simulation of duration and frequency of water consumption by various water dispensers

Water flow rates calculated by using deterministic models and methods do not describe the real variability in the water supply operation. This problem can be solved by mathematical simulation. The stochastic nature of the water consumption process implies involves random variables with certain distribution laws describing the main process components, namely intensity, duration and frequency.This paper discusses the mathematical simulation of the duration and frequency of water consumption by the most common types of water dispensers (kitchen sink and bathtub faucets (shower cubicle), toilet bowl with flush tank, washing machine and dishwasher).Purpose: The aim of this work is to evaluate and substantiate theoretical laws of the water consumption by the most common types of water dispensers as well as the frequency (probability) of their daily use.Research findings: The duration and frequency are determined for water consumed by various water dispensers using water supply systems of buildings. The empirical data are analyzed. Mathematical simulation method is proposed and justified for the water consumption process.

A Survey on Software Vulnerability Exploitability Assessment

Knowing the exploitability and severity of software vulnerabilities helps practitioners prioritize vulnerability mitigation efforts. Researchers have proposed and evaluated many different exploitability assessment methods. The goal of this research is to assist practitioners and researchers in understanding existing methods for assessing vulnerability exploitability through a survey of exploitability assessment literature. We identify three exploitability assessment approaches: assessments based on original, manual Common Vulnerability Scoring System, automated Deterministic assessments, and automated Probabilistic assessments. Other than the original Common Vulnerability Scoring System, the two most common sub-categories are Deterministic, Program State based, and Probabilistic learning model assessments.

ИССЛЕДОВАНИЕ ПОЖАРНОЙ ОПАСНОСТИ ЭЛЕКТРИЧЕСКОЙ СИСТЕМЫ АВТОТРАНСПОРТНОГО СРЕДСТВА

The article examines the change of the probability of an emergency mode (failure) of the vehicle's electrical wiring depending on the time of its operation. We revealed necessity of establishing the wear and operation time of electrical wiring in a vehicle. Emergency modes in the vehicle electrical network have been identified and analyzed. The behavior of some contact connections of a vehicle was studied for an increase in contact resistance. It is concluded that it is necessary to develop deterministic and stochastic mathematical models that describe the state of the vehicle’s electrical network in order to assess its fire hazard.

A New Model Making the Transition From Oil to Solar Energy

Today, the use of renewable energy sources such as sun, wind and hot water to generate electricity is increasingly becoming a global priority. In this paper, we propose a deterministic dynamical system reporting the transition from oil to solar energy, in which we then add the randomness of this phenomenon. First, we study the positivity of the deterministic oil-solar model and show that there is a maximum solution of the deterministic model and that the system is controllable at any time T &gt; 0 from an initial point. We also prove the existence of an equilibrium state, study its nature and prove that there is no limit cycle between the quantity of oil available and the solar production capacity installed. Secondly, we formulate the stochastic solar energy model from the deterministic model, for which we proved the existence of a unique solution. Finally, using a model extracted from the model performed and examining the transition from the amount of available oil to the installed solar generation capacity, we associate a linear optimal control problem, from which we prove that the optimal control components are of bang-bang type, and we characterize them.

Cost-based distributionally robust tourist attraction recommendation with demand uncertainty

Tourist attraction recommendation (TAR) problem has gained attention due to its potential to enhance tourist services. Existing studies focus on meeting tourists’ individual needs, but overlook the tour operator’s interests as the TAR service provider. The TAR problem is more challenging due to the high variability of customer demand, which is difficult to predict accurately beforehand. This paper examines TAR in response to random changes in tourist demand, aiming to minimize transportation costs, cooperation expenses between tour operators and attractions, ticket booking fees, and promotion costs, where ambiguity set is defined by means, mean absolute deviations, and the support set. Firstly a distributionally robust model is proposed to identify suitable attractions for cooperation, along with determining the associated costs of ticket booking, promotion, and tourist transportation, while considering chance constraint on the service level. Subsequently, the model is reformulated into a tractable mixed integer linear programming model using duality theory. Numerical experiments illustrate that the proposed model outperforms both the stochastic programming model and the deterministic model in terms of risk level by out-of-sample test. In particularly, considering uncertainty and distributional ambiguity can make the model more accurate and credible.

Nonparametric approach for structural dynamics of high-voltage cables

High-voltage cables, as applied in the electro-mobility, are highly complex structures regarding their vibration behaviour. The high complexity leads to considerable uncertainty in models for a finite element method (FEM) simulation, which is shown, for example, in the contact modelling between the strands of the cable. To handle this uncertainty and model the structural dynamic, a nonparametric probabilistic approach (NPPA) with random matrices is used for the first time on high-voltage cables. This novel application of NPPA has an advantage over typical FEM analysis by using a more manageable simulation model and eliminating the need for a complex deterministic simulation model. Initially, the NPPA is analysed and enhanced, with an optimization for the dispersion parameter and a frequency shift introduced as methodological improvements. These enhancements result in a comparable scatter band of the frequency response. Following preliminary studies, the cable's dynamic behaviour is examined through experimental modal analysis, after which the dispersion parameters are computed. The NPPA is then applied to the simplified deterministic model with the calculated dispersion parameters, and a Monte Carlo simulation is done. As a result of this simulation, a scatter band is given. The results from the simulation are then compared to the results of an experiment. It is shown that the frequency response from the experiment is almost always in the inner area of the scatter band. Consequently, this innovative method can be used for a risk evaluation according to the path of the frequency response function and an evaluation of the structural behaviour.

A Critical Review of the Modelling Tools for the Reactive Transport of Organic Contaminants

The pollution of groundwater and soil by hydrocarbons is a significant and growing global problem. Efforts to mitigate and minimise pollution risks are often based on modelling. Modelling-based solutions for prediction and control play a critical role in preserving dwindling water resources and facilitating remediation. The objectives of this article are to: (i) to provide a concise overview of the mechanisms that influence the migration of hydrocarbons in groundwater and to improve the understanding of the processes that affect contamination levels, (ii) to compile the most commonly used models to simulate the migration and fate of hydrocarbons in the subsurface; and (iii) to evaluate these solutions in terms of their functionality, limitations, and requirements. The aim of this article is to enable potential users to make an informed decision regarding the modelling approaches (deterministic, stochastic, and hybrid) and to match their expectations with the characteristics of the models. The review of 11 1D screening models, 18 deterministic models, 7 stochastic tools, and machine learning experiments aimed at modelling hydrocarbon migration in the subsurface should provide a solid basis for understanding the capabilities of each method and their potential applications.

AGENT-BASED MODELING OF UP DILIMAN INTRACAMPUS PEDESTRIAN MOBILITY USING NETLOGO AND GIS

Abstract. In the Philippines, campus mobility studies remain underexplored. Since small-scale models help in policy making that may also be applied in a large spatiotemporal context, intracampus mobility modeling and simulation offer support for future mobility research. In this study, we designed a NetLogo model to apply ABM and GIS in understanding intracampus student pedestrian mobility. We created a deterministic model using discrete student schedule and a probabilistic model using the multinomial logistic (MNL) regression model derived from the student demographics data to analyze student movement. To provide a realistic representation of student pedestrians and campus environment, GIS spatiotemporal data was proven crucial to the pedestrian mobility models. The generated pedestrian count heatmaps show a significant increase in student count from online learning switching to face–to–face instruction. The overall campus building occupancy served as the key factor influencing the changes in agent behaviors such as walking speed and student tardiness. Moreover, the probabilistic model showed erratic movements of students. The model evaluation depends on the heavily imbalanced datasets and its multiclass nature with relatively higher model performance (F1 score &gt; 0.8) is observed during morning, noon, and end schedule times, whereas suboptimal performance (F1 score &lt; 0.6) where the dataset has a higher number of classes. The simulations demonstrate that ABM is a useful tool for examining pedestrian and transport patterns and can be enhanced further to allow multimodal and multiagent systems.

A framework for the in silico assessment of the robustness of an MPC in a CDC line in function of process variability

The shift from batch manufacturing towards continuous manufacturing for the production of oral solid dosages requires the development and implementation of process models and process control. Previous work focused mainly on developing deterministic models for the investigated system. Furthermore, the in silico tuning and analysis of a control strategy are mostly done based on deterministic models. This deterministic approach could lead to wrong actions in diversion strategies and poor transferability of the controller performance if the system behaves differently than the deterministic model. This work introduces a framework that explicitly includes the process variability which is characteristic of powder handling processes and tests it on a novel continuous feeding–blending unit (i.e., the FE continuous processing system (CPS)), followed by a tablet press (i.e., the FE 55). It employs a stochastic model by allowing the model parameters to have a probability distribution. The performance of a model predictive control (MPC), steering the feed rate of the main excipient feeder to compensate for the feed rate deviations of the active pharmaceutical ingredient (API) feeder to keep the API concentration close to the desired value, is evaluated and the impact of process variability is assessed in a Monte Carlo (MC) analysis. Next to the process variability, a model for the prediction error of the chemometric model and realistic feed rate disturbances were included to increase the transferability of the results to the real system. The obtained results show that process variability is inherently present and that wrong conclusions can be drawn if it is not taken into account in the in silico analysis.

Optimizing with Attractor: A Tutorial

This tutorial presents a novel search system—the Attractor-Based Search System (ABSS)—that can solve the Traveling Salesman Problem very efficiently with optimality guarantee. From the perspective of dynamical systems, a heuristic local search algorithm for an NP-complete combinatorial problem is a discrete dynamical system. In a local search system, an attractor drives the search trajectories into the vicinity of a globally optimal point in the solution space, and the convergence of local search trajectories makes the search system become a global and deterministic system. The attractor contains a small set of the most promising solutions to the problem. The attractor can reduce the problem size exponentially, and thus make the exhaustive search feasible. Therefore, this new search paradigm is called optimizing with attractor. The ABSS consists of two search phases: local search phase and exhaustive search phase. The local search process is used to quickly construct the attractor in the solution space, and the exhaustive search process is used to completely search the attractor to identify the optimal solution. Therefore, the exact optimal solution can be found quickly by combining local search and exhaustive search. This tutorial introduces the concept of an attractor in a local search system, and describes the process of optimizing with the attractor, using the Traveling Salesman Problem as the study platform.

Generative probabilistic prediction of precipitation induced landslide deformation with variational autoencoder and gated recurrent unit

Landslides, prevalent in mountainous areas, are typically triggered by tectonic movements, climatic changes, and human activities. They pose catastrophic risks, especially when occurring near settlements and infrastructure. Therefore, detecting, monitoring, and predicting landslide deformations is essential for geo-risk mitigation. The mainstream of the previous studies have often focused on deterministic models for immediate landslide prediction. However, in most of them, the aspect of prediction uncertainties are not sufficiently addressed. This paper introduces an innovative probabilistic prediction method using a Variational Autoencoder (VAE) combined with Gated Recurrent Unit (GRU) to forecast landslide deformations from a generative standpoint. Our approach consists of two main elements: firstly, training the VAE-GRU model to maximize the variational lower bound on the likelihood of historical precipitation data; secondly, using the learned approximated posterior distribution to predict imminent deformations from a generative angle. To assess the prediction quality, we use four widely-used metrics: Prediction Interval Coverage Probability (PICP), Prediction Interval Normalized Average Width (PINAW), Coverage Width-Based Criterion (CWC), and Prediction Interval Normalized Root Mean Square Width (PINRW). The results demonstrate that our proposed VAE-GRU framework surpasses traditional state-of-the-art (SOTA) probabilistic deformation prediction algorithms in terms of accuracy and reliability.

Uniform propagation of chaos for a dollar exchange econophysics model

Abstract We study the poor-biased model for money exchange introduced in Cao &amp; Motsch ((2023) Kinet. Relat. Models 16(5), 764–794.): agents are being randomly picked at a rate proportional to their current wealth, and then the selected agent gives a dollar to another agent picked uniformly at random. Simulations of a stochastic system of finitely many agents as well as a rigorous analysis carried out in Cao &amp; Motsch ((2023) Kinet. Relat. Models 16(5), 764–794.), Lanchier ((2017) J. Stat. Phys. 167(1), 160–172.) suggest that, when both the number of agents and time become large enough, the distribution of money among the agents converges to a Poisson distribution. In this manuscript, we establish a uniform-in-time propagation of chaos result as the number of agents goes to infinity, which justifies the validity of the mean-field deterministic infinite system of ordinary differential equations as an approximation of the underlying stochastic agent-based dynamics.