Deterministic Model Research Articles

The Significance of Stochastic CTMC Over Deterministic Model in Understanding the Dynamics of Lymphatic Filariasis With Asymptomatic Carriers

Lymphatic filariasis is a leading cause of chronic and irreversible damage to human immunity. This paper presents deterministic and continuous-time Markov chain (CTMC) stochastic models regarding lymphatic filariasis dynamics. To account for randomness and uncertainties in dynamics, the CTMC model was formulated based on deterministic model possible events. A deterministic model’s outputs suggest that disease extinction is feasible when the secondary threshold infection number is below one, while persistence becomes likely when the opposite holds true. Furthermore, the significant contribution of asymptomatic carriers was identified. Results indicate that persistence is more likely to occur when the infection results from asymptomatic, acutely infected, or infectious mosquitoes. Consequently, the CTMC stochastic model is essential in capturing variabilities, randomness, associated probabilities, and validity across different scales, whereas oversimplification and unpredictability of inherent may not be featured in a deterministic model.

Effects of stochastic perturbations on a phytoplankton allelopathy competitive system

In this paper, we investigate stochastic models of two species competitive phytoplankton system with allelopathic interaction. We construct stochastic models from deterministic models by introducing three different stochastic perturbations to the equations. For the first model, we prove that this model is asymptotically stable in probability at three different equilibrium points. It is also shown that the system is positively recurrent under some conditions. For the second model, we study the extinction, existence of positive recurrence and global asymptotic stability under some sufficient conditions. For the last system, almost sufficient and necessary conditions for global asymptotic stability, the existence of positive recurrence and extinction of each population are established. In addition, using a suitable stochastic Lyapunov method, we prove that there is a unique solution to three models, we also discuss the ultimate boundedness of the three stochastic systems. Moreover, some numerical simulations are introduced to illustrate our mathematical results. We show that stochastic models still retain the desirable stability of their deterministic counterparts if stochastic perturbations are relatively small.

Modeling the Transmission Dynamics of Tuberculosis in Humans

Tuberculosis (TB) is a major threat to human health particularly in most of developing countries. In this article, we formulate and analyze a deterministic model for the transmission dynamics of pulmonary and extra-pulmonary tuberculosis. The next generation method is employed to find the basic reproduction number R0 which helps to determine whether TB clears or persists in the human population. Global stability of model equilibria is done through Lyapunov functions whereas the normalized forward sensitivity index method is adopted to determine parameters that drive tuberculosis. Analysis shows that both TB free and endemic equilibria exist. The TB free equilibrium is globally asymptotically stable whenever the basic reproduction number R0 < 1 whereas the endemic equilibrium is globally asymptotically stable whenever R0 > 1. Sensitivity analysis shows that the TB infection rate, the fraction of individuals who progress to pulmonary tuberculosis and its induced death drive TB. Numerical results indicate that when there are no interventions, susceptible humans decline significantly with time until when they are attracted to the steady state whereas latently infected, pulmonary and extra-pulmonary TB individuals increase until when they settle at the equilibrium states supporting the analytical results for existence of the endemic equilibrium. In light of these findings, we recommend treating humans infected with pulmonary TB who are carriers of the disease.

Causes of Backward Bifurcation in a Tuberculosis-Schistosomiasis Co-infection Dynamics

Causes of Backward Bifurcation in a Tuberculosis-Schistosomiasis Co-infection Dynamics

Impact of screening and doxycycline prevention on the syphilis epidemic among men who have sex with men in British Columbia: a mathematical modelling study

Men who have sex with men (MSM) in British Columbia (BC) are disproportionately affected by infectious syphilis and HIV. In this study, we developed a co-interaction model and evaluated the impact and effectiveness of possible interventions among different MSM subgroups on the syphilis epidemic. We designed a deterministic compartmental model, which stratified MSM by HIV status and HIV pre-exposure prophylaxis (HIV-PrEP) usage into (1) HIV-negative/unaware MSM (HIV-PrEP not recommended, noton HIV-PrEP), (2) HIV-negative/unaware MSM with HIV-PrEP recommended (not on HIV-PrEP), (3)HIV-negative/unaware MSM actively on HIV-PrEP, and (4) MSM diagnosed with HIV. We estimated the effect of scaling up syphilis testing frequency from Status Quo to six-, four-, and three-months, increasing the percentage of MSM using doxycycline prevention (Doxy-P) to 25%, 50%, and 100% of the target level, and a combination of both among subgroups (2)-(4). We also assessed the impact of these interventions on the syphilis incidence rates from 2020 to 2034 in comparison to the Status Quo scenario where no intervention was introduced. Under the Status Quo scenario, with the expansion of the HIV-PrEP program to improve syphilis testing, the syphilis incidence rate was estimated to peak at 16.1 [Credible Interval (CI):14.2-17.9] per 1,000 person-years (PYs) in 2023 and decrease to 6.7 (CI:3.8-10.9) per 1,000 PYs by 2034. The syphilis incidence rate in 2034 was estimated at 0.7 (0.3-1.3) per 1,000 PYs if MSM diagnosed with HIV could be tested every four months, and at 1.5 (0.7-3.0) per 1,000 PYs if HIV-negative/unaware MSM actively on HIV-PrEP could be tested every three months. By achieving 100% of the target coverage of Doxy-P, the syphilis incidence rate was estimated at 1.4 (0.5-3.4) if focusing on MSM diagnosed with HIV, and 2.6 (1.2-5.1) per 1,000 PYs if focusing on HIV-negative/unaware MSM actively on HIV-PrEP. Under the combined interventions, the syphilis incidence rate could be as low as 0.0 (0.0-0.1) and 0.8 (0.3-1.8) per 1,000 PYs, respectively. The HIV-PrEP program in BC plays a crucial role in increasing syphilis testing frequency among high-risk MSM and reducing syphilis transmission among this group. In addition, introducing Doxy-P can be an effective complementary strategy to minimize syphilis incidence, especially among MSM diagnosed with HIV. This work was funded by the Canadian Institutes of Health Research.

Model and Analysis of the Maximum Upstream Latency of a Deterministic Industrial PON System Applying Frame-Based Dense Burst Allocation Method

Model and Analysis of the Maximum Upstream Latency of a Deterministic Industrial PON System Applying Frame-Based Dense Burst Allocation Method

Impact of simplified HCV diagnostic strategies on the HCV epidemic among men who have sex with men in the era of HIV oral pre-exposure prophylaxis in Taiwan: a modelling study.

Simplified hepatitis C virus (HCV) diagnostic strategies have the potential to improve HCV diagnoses and treatment. We aimed to investigate the impact of simplified HCV diagnostic strategies on HCV incidence and its effect on HCV diagnosis and treatment among men who have sex with men (MSM) regardless of HIV status and use of HIV pre-exposure prophylaxis (PrEP) in Taiwan. A compartmental deterministic model was developed to describe the natural history of HCV disease progression, the HCV care cascade and the HIV status and PrEP using among MSM. The model was calibrated to available data for HCV and HIV epidemiology and population demographics in Taiwan. We simulated the epidemic from 2004 and projected the impact of simplified testing strategies on the HCV epidemic among MSM over 2022-2030. Under the current testing approach in Taiwan, total HCV incidence would increase to 12.6 per 1000 person-years among MSM by 2030. Single-visit point-of-care RNA testing had the largest impact on reducing the number of new HCV infections over 2022-2030, with a 31.1% reduction (interquartile range: 24.9%-32.8%). By 2030, single-visit point-of-care HCV testing improved HCV diagnosis to 90.9%, HCV treatment to 87.7% and HCV cure to 81.5% among MSM living with HCV. Compared to status quo, prioritized simplified HCV testing for PrEP users and MSM living with diagnosed HIV had considerable impact on the broader HCV epidemic among MSM. A sensitivity analysis suggests that reinfection risk would have a large impact on the effectiveness of each point-of-care testing scenario. Simplified HCV diagnostic strategies could control the ongoing HCV epidemic and improve HCV testing and treatment among Taiwanese MSM. Single-visit point-of-care RNA testing would result in large reductions in HCV incidence and prevalence among MSM. Efficient risk-reduction strategies will need to be implemented alongside point-of-care testing to achieve HCV elimination among MSM in Taiwan.

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.

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.

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.

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.

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.

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.

High‐rate Dissolution Mechanism of Ti‐48Al‐2Cr‐2Nb Alloy in Electrochemical Machining from a Nonlinear Dynamic PeWen Yuan Lirspective

The high‐rate dissolution process of Ti‐48Al‐2Cr‐2Nb alloy in electrochemical machining exhibits strong nonlinear dynamic characteristics, but the quantitative relationship between these nonlinear characteristics and surface topography, as well as the electro‐dissolution mechanism, is unknown. Therefore, the fractal and recursive features of dissolution behavior was investigated, and the dissolved surface topography was quantitatively characterized. Additionally, an electro‐dissolution mechanism model in electrochemical machining process was presented. Applying a moderate extraction potential of 8 V instead of 11 V can enhance the stability of the electrochemical system, resulting in a smoother and uniform surface. At 11 V, the saturation correlation dimension, surface roughness, and integral area of lacunarity initially decrease before increasing with higher electrolytic pressure, while laminarity (𝐿𝐴𝑀) and determinism (𝐷𝐸𝑇) show an initial increase followed by a decrease. These five characteristic parameters reach their optimal values at an electrolyte pressure of 0.4 MPa, indicating that achieving a stable and deterministic electrochemical system is crucial for obtaining a uniform smooth surface. These nonlinear dynamic characteristic parameters can be considered as in‐situ monitoring parameters for surface quality in ECM. The anodic dissolution process comprises three stages: initial passive film dissolution and breakdown, rapid dissolving with surface coarsening, and stable dissolving with polishing.This article is protected by copyright. All rights reserved.

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 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.