Deterministic Model Research Articles

A Bayesian model calibration framework for stochastic compartmental models with both time-varying and time-invariant parameters

We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. In this manuscript, we first detail a general Bayesian computational framework as a continuation of our previous work. Subsequently, this framework is specifically tailored to the susceptible-infectious-removed (SIR) model which describes a basic mechanism for the spread of infectious diseases through a system of coupled nonlinear differential equations. The SIR model consists of three states, namely, the susceptible, infectious, and removed compartments. The coupling among these states is controlled by two parameters, the infection rate and the recovery rate. The simplicity of the SIR model and similar compartmental models make them applicable to many classes of infectious diseases. However, the combined assumption of a deterministic model and time-invariance among the model parameters are two significant impediments which critically limit their use for long-term predictions. The tendency of certain model parameters to vary in time due to seasonal trends, non-pharmaceutical interventions, and other random effects necessitates a model that structurally permits the incorporation of such time-varying effects. Complementary to this, is the need for a robust mechanism for the estimation of the parameters of the resulting model from data. To this end, we consider an augmented state vector, which appends the time-varying parameters to the original system states whereby the time evolution of the time-varying parameters are driven by an artificial noise process in a standard manner. Distinguishing between time-varying and time-invariant parameters in this fashion limits the introduction of artificial dynamics into the system, and provides a robust, fully Bayesian approach for estimating the time-invariant system parameters as well as the elements of the process noise covariance matrix. This computational framework is implemented by leveraging the robustness of the Markov chain Monte Carlo algorithm permits the estimation of time-invariant parameters while nested nonlinear filters concurrently perform the joint estimation of the system states and time-varying parameters. We demonstrate performance of the framework by first considering a series of examples using synthetic data, followed by an exposition on public health data collected in the province of Ontario.

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.

Statistical methods for the computation and parameter estimation of a fractional SIRC model with Salmonella infection

This study analyzes the fractional order SIRC epidemic model under stochastic fractional differential equations in the Caputo sense. This article describes Salmonella infection in animal herds. For the deterministic system, we explain solution positivity and boundness. We also prove that the fractional stochastic solution exists and is unique. Other criteria considered include non-negativity of solutions, local and global stability analyses, Hyers-Ulam stability analysis, and sensitivity analysis for the deterministic system. Furthermore, according to the truncated Ito-Taylor expansion, we apply a numerical method to solve the stochastic fractional SIRC epidemic model, namely the Milstein method, to solve the stochastic fractional SIRC epidemic model. A comparison of the approximation solution and the corresponding deterministic model for different sample paths shows the efficiency of the numerical method. In addition, graphs and error tables provide insight into numerical experiments' results. The stochastic nature of the model allows random fluctuations in Salmonella infection spread. By incorporating uncertainty into the model, we gain a more realistic understanding of the epidemic dynamics and can better evaluate the effectiveness of control measures. Additionally, the numerical method used to solve the stochastic fractional SIRC epidemic model provides valuable insights into the variability of the results. This enhances our ability to make informed decisions about managing and preventing bacterial infections in animal herds.

Multi-objective robust optimization of staff scheduling for emergency under stochastic demand

Large-scale centralized emergency rescue staff scheduling under emergencies has always been a challenge. With a specific focus on nucleic acid testing amid the COVID-19 pandemic, this study introduces a model that considers dynamic changes in staff supply at rescue points, the varying demand at sampling points over time, and their impact on the spread of the epidemic. We quantified the emergency weight of sampling points by the demand and the regional risk degree and adopted robust optimization with base constraint. With the objectives of minimum comprehensive service distance, maximum weighted value of demand satisfaction rate, and minimum loss caused by unmet demand, a multi-stage, multi-medical rescue point medical staff scheduling model for nucleic acid sampling points with the influence caused by uncertain demand disturbance was built, and an improved NSGA-II-HC algorithm was designed to solve the optimization problem under the influence of demand disturbances. The testing results proved that the NSGA-II-HC algorithm can tackle the issue of insufficient uniformity and diversity in the solution set of NSGA-II while Multi-Objective Particle Swarm Optimization (MOPSO) failed to do so. Taking the epidemic data of Guangzhou city in May 2021 as a case study, our model and algorithm are verified to be feasible. We offer a scheme selection strategy according to the loss degree of two conflicting objectives, the comprehensive service distance and shortage loss. The results suggest that, compared with the demand deterministic model, the decision mechanism under the robust model can reduce the deviation from the optimization objective due to the demand disruption

Prediction and control of cholera outbreak: Study case of Cameroon

This paper deals with the problem of the prediction and control of cholera outbreak using real data of Cameroon. We first develop and analyze a deterministic model with seasonality for the cholera, the novelty of which lies in the incorporation of undetected cases. We present the basic properties of the model and compute two explicit threshold parameters R¯0 and R̲0 that bound the effective reproduction number R0, from below and above, that is R̲0≤R0≤R¯0. We prove that cholera tends to disappear when R¯0≤1, while when R̲0>1, cholera persists uniformly within the population. After, assuming that the cholera transmission rates and the proportions of newly symptomatic are unknown, we develop the EnKf approach to estimate unmeasurable state variables and these unknown parameters using real data of cholera from 2014 to 2022 in Cameroon. We use this result to estimate the upper and lower bound of the effective reproduction number and reconstructed active asymptomatic and symptomatic cholera cases in Cameroon, and give a short-term forecasts of cholera in Cameroon until 2024. Numerical simulations show that (i) the transmission rate from free Vibrio cholerae in the environment is more important than the human transmission and begin to be high few week after May and in October, (ii) 90% of newly cholera infected cases that present the symptoms of cholera are not diagnosed and (iii) 60.36% of asymptomatic are detected at 14% and 86% of them recover naturally. The future trends reveals that an outbreak appeared from July to November 2023 with the number of cases reported monthly peaked in October 2023. An impulsive control strategy is incorporated in the model with the aim to avoid or prevent the cholera outbreak. In the first year of monitoring, we observed a reduction of more than 75% of incidences and the disappearance of the peaks when no control are available in Cameroon. A second monitoring of control led to a further reduction of around 60% of incidences the following year, showing how impulse control could be an effective means of eradicating cholera.

Response analysis of asymmetric monostable energy harvester with an uncertain parameter

The nonlinear piezoelectric vibration energy harvesting system offers a solution to the power supply challenge for low-power sensors. However, In practical engineering, structural parameter uncertainties arise from manufacturing errors, environmental temperature fluctuations, and changes in material properties. Besides, due to inherent flaws in the structure and materials, asymmetry may occur in the potential well, which leads to the complexity of the dynamic behavior exhibited in energy harvesting system. In this paper, in order to investigate the dynamics of the asymmetric monostable piezoelectric energy harvesting system under an uncertain parameter, the orthogonal polynomial approximation method is applied to transform the stochastic system into an equivalent deterministic system. Then, the responses of the equivalent deterministic system are used to reveal the stochastic behavior of the uncertainty system. The results indicate that, when the uncertainty intensity of the cubic nonlinear coefficient is 0, an increase in the asymmetry level of the potential well leads to an increase in the output voltage. Increasing the other parameters, the output voltage is reduced. In addition, as the uncertainty intensity increases, the parameter intervals of chaotic response become wider and the energy harvesting efficiency decreases. Moreover, as the potential well asymmetry increases, the sensitivity of energy harvesting system to uncertain parameter increases.

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.

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.