Deterministic Model Research Articles

Deterministic Mathematical Model of Energy Demand of Single-Family Building with Different Parameters and Orientation of Windows in Climatic Conditions of Poland

Deterministic Mathematical Model of Energy Demand of Single-Family Building with Different Parameters and Orientation of Windows in Climatic Conditions of Poland

New sexually transmitted HIV infections from 2016 to 2050 in Guangdong Province, China: a study based on a dynamic compartmental model

BackgroundIn Guangdong Province, China, there is lack of information on the HIV epidemic among high-risk groups and the general population, particularly in relation to sexual transmission, which is a predominant route. The new HIV infections each year is also uncertain owing to HIV transmission from men who have sex with men (MSM) to women, as a substantial proportion of MSM also have female sexual partnerships to comply with social demands in China.MethodsA deterministic compartmental model was developed to predict new HIV infections in four risk groups, including heterosexual men and women and low- and high-risk MSM, in Guangdong Province from 2016 to 2050, considering HIV transmission from MSM to women. The new HIV infections and its 95% credible interval (CrI) were predicted. An adaptive sequential Monte Carlo method for approximate Bayesian computation (ABC-SMC) was used to estimate the unknown parameter, a mixing index. We calibrated our results based on new HIV diagnoses and proportions of late diagnoses. The Morris and Sobol methods were applied in the sensitivity analysis.ResultsNew HIV infections increased during and 2 years after the COVID-19 pandemic, then declined until 2050. New infections rose from 8,828 [95% credible interval (CrI): 6,435–10,451] in 2016 to 9,652 (95% CrI: 7,027–11,434) in 2019, peaking at 11,152 (95% CrI: 8,337–13,062) in 2024 before declining to 7,084 (95% CrI: 5,165–8,385) in 2035 and 4,849 (95% CrI: 3,524–5,747) in 2050. Women accounted for approximately 25.0% of new HIV infections, MSM accounted for 40.0% (approximately 55.0% of men), and high-risk MSM accounted for approximately 25.0% of the total. The ABC-SMC mixing index was 0.504 (95% CrI: 0.239–0.894).ConclusionsGiven that new HIV infections and the proportion of women were relatively high in our calibrated model, to some extent, the HIV epidemic in Guangdong Province remains serious, and services for HIV prevention and control are urgently needed to return to the levels before the COVID-19 epidemic, especially in promoting condom-based safe sex and increasing awareness of HIV prevention to general population.

Comprehensive Analysis of Deterministic and Stochastic Eco-Epidemic Models Incorporating Fear, Refuge, Supplementary Resources, and Selective Predation Effects

Comprehensive Analysis of Deterministic and Stochastic Eco-Epidemic Models Incorporating Fear, Refuge, Supplementary Resources, and Selective Predation Effects

Corruption dynamics: a mathematical model and analysis

This study proposes and analyzes a deterministic mathematical model to describe the dynamics of corruption transmission. We began by proving that the solution to the model is bounded and positive. The next-generation matrix approach is used to compute the basic reproduction number (R0) in relation to corruption-free equilibrium. The Jacobian and Lyapunov functions are used to show that corruption-free equilibrium is asymptotically stable in both locally and globally when R0<1, and otherwise, an endemic corruption equilibrium develops. Furthermore, the sensitivity of the model's parameters was investigated. The findings demonstrate that religious precepts govern public education. The two sectors most susceptible to corruption control are education and corrections. The study recommends investing more in the provision of public education to citizens by creating awareness among all and including it in the education curriculum and religious leaders to teach their followers seriously about the impact of corruption as well as the use of jail as punishment. The numerical simulation results agreed with the analytical results.

A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism

A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism

A model for the control of transmission dynamics of human monkeypox disease in Sub-Saharan Africa

The Human Monkeypox virus has received significant research interest in recent times. While few researchers have studied the effects of vaccination on human-to-animal or animal-to-human Monkeypox transmission, others just studied the effects of treatment on human Monkeypox. In this article, we made the proposition of a deterministic vaccine model that deals with the dynamics of the effects of vaccination and treatment on human Monkeypox in sub-Saharan Africa. We investigated the effects of vaccination on the various epidemiological classes qualitatively. The findings from the analysis of the model are that the model possesses two equilibria, locally asymptotically stable disease-free equilibrium (DFE) when an epidemiological threshold - the effective reproductive number is less than unity, and locally asymptotically stable endemic equilibrium when the number is greater than unity. We then corroborated the theoretical findings with numerical simulations, which reveal that when the rate of vaccination is increased resulting in many newly born persons in the populace being vaccinated, the prevalence of the deadly scourge is significantly reduced, while newly born individuals that miss vaccination experience a drastic torment of the deadly disease that often occasion death. Further revelation from the simulations is that when greater efforts

Uncertainty quantification and global sensitivity analysis of bearing capacity of push-out specimen considering randomness in bond-slip behaviour

As an artificial composite material, the uncertainty in mechanical property of concrete significantly impacts the bond-slip behaviour of the shaped steel concrete structure. To investigate the effect of the uncertainty of concrete mechanical properties on the bearing capacity of push-out specimens, based on the data of a small number of push-out test with identical design parameters, the improved Bootstrap method is utilized to execute sample augmentation for the bond stress-slip curves, and the stochastic bond slip constitutive model is established after considering five parameters (K1, …, K5) in the deterministic bond-slip model as random variables. Simultaneously, considering the randomness in elastic modulus of concrete (Ec), uncertainty quantification (UQ) of the bearing capacities of the push-out specimens is conducted using the arbitrary polynomial chaos (aPC) method. Subsequently, the global sensitivity analysis of the ultimate and residual bearing capacities is accomplished through the aPC surrogate model. The results indicate that the probability distribution types of the parameters in the stochastic bond-slip constitutive model can be arbitrary when considering the randomness of concrete material, and the aPC method with at least a third-order expansion is recommended to execute UQ for the push-out test due to the strong nonlinearty between the bearing capacities and the random parameters. The ultimate bearing capacity is primarily affected by the parameter K2, followed by K4, K3, and K5. Whereas the residual bearing capacity is predominantly influenced by the parameter K4, followed by K5, the remaining parameters exhibit negligible influence. In contrast, K1 and Ec have the greatest influence on equivalent plastic strain of the concrete near the loading end of the push-out specimen.

Geomorphic risk maps for river migration using probabilistic modeling – a framework

Abstract. Lateral migration of meandering rivers poses erosional risks to human settlements, roads, and infrastructure in alluvial floodplains. While there is a large body of scientific literature on the dominant mechanisms driving river migration, it is still not possible to accurately predict river meander evolution over multiple years. This is in part because we do not fully understand the relative contribution of each mechanism and because deterministic mathematical models are not equipped to account for stochasticity in the system. Besides, uncertainty due to model structure deficits and unknown parameter values remains. For a more reliable assessment of risks, we therefore need probabilistic forecasts. Here, we present a workflow to generate geomorphic risk maps for river migration using probabilistic modeling. We start with a simple geometric model for river migration, where nominal migration rates increase with local and upstream curvature. We then account for model structure deficits using smooth random functions. Probabilistic forecasts for river channel position over time are generated by Monte Carlo runs using a distribution of model parameter values inferred from satellite data. We provide a recipe for parameter inference within the Bayesian framework. We demonstrate that such risk maps are relatively more informative in avoiding false negatives, which can be both detrimental and costly, in the context of assessing erosional hazards due to river migration. Our results show that with longer prediction time horizons, the spatial uncertainty of erosional hazard within the entire channel belt increases – with more geographical area falling within 25 % < probability < 75 %. However, forecasts also become more confident about erosion for regions immediately in the vicinity of the river, especially on its cut-bank side. Probabilistic modeling thus allows us to quantify our degree of confidence – which is spatially and temporally variable – in river migration forecasts. We also note that to increase the reliability of these risk maps, we need to describe the first-order dynamics in our model to a reasonable degree of accuracy, and simple geometric models do not always possess such accuracy.

Cyclic behavior of laminated bio-based connections with slotted-in steel plates: Genetic algorithm, deterministic neural network-based model parameter identification, and uncertainty quantification

To support more sustainable construction, this paper experimentally investigates the cyclic behavior of laminated timber (Laminated Veneer Lumber (LVL)) and glubam (Glue Laminated Bamboo) connections with slotted-in steel plates in terms of experimental test, numerical simulations and parameter identification. Experimental tests included eight different configurations: two materials (LVL and glubam), two bolt diameters (8 and 10 mm), and one or two bolts. Two different cyclic-loading protocols were applied for each type of connection: only tension and tension/compression. The observed behavior is then compared to a finite element model developed in OpenSeesPy, which takes into account factors such as sliding, contact, pinching, cyclic stiffness, and strength degradation. To identify the best set of parameters for the model, three different approaches are considered: genetic algorithm, fast deterministic neural network, and probabilistic Bayesian method. First, the model identification is carried out by means of a genetic algorithm-based optimization. The parameter-identification results are evaluated in terms of elastic stiffness, yielding point, and ductility. Next, a sensitivity analysis is performed to determine the significance of the parameters, and an innovative approach combining neural network and sensitivity analysis is proposed for fast and preliminary parameter identification. Then, probabilistic Bayesian identification is employed to calculate the posterior distribution of the model parameters identified and the confidence bounds of the estimated response. Finally, different model identification parameters are compared and suggestions for algorithm selection are provided.

Global stability analysis and modelling onchocerciasis transmission dynamics with control measures

ABSTRACT Background: Onchocerciasis infection is one of the neglected tropical diseases targeted for eradication by 2030. The disease is usually transmitted to humans through the bites of black flies. These black flies mostly breed near well-oxygenated fast-running water bodies. The disease is common in mostly remote agricultural villages near rivers and streams. Objective: In this study, a deterministic model describing the infection dynamics of human onchocerciasis disease with control measures is presented. Methods: We derived the model’s reproductive number and used a stability theorem of a Metzler matrix to show that disease-free equilibrium is both locally and globally asymptotically stable whenever the reproductive number is less than one. Parameter contribution was conducted using sensitivity analysis. The model endemic equation is shown to be a cubic polynomial in the presence of infected immigrants and a quadratic form in their absence. Results: When the inflow of infected immigrants is null, the model endemic equation may admit a unique equilibrium if the reproductive number is greater than one, or admits multiple endemic equilibria if the reproductive number is less than unity. We carried out a sensitivity analysis to identify the significant parameters that contribute to onchocerciasis spread. Conclusion: Onchocerciasis disease can be eradicated if the importation of infected immigrants is properly monitored. The integration of the One Health concept in the public health system is key in tackling the emergence and spread of diseases.

A multi-objective planning and scheduling model for elective and emergency cases in the operating room under uncertainty

Hospitals are paramount hubs for delivering healthcare services, with their Operating Rooms (ORs) as a pivotal and financially substantial component. Efficient surgery ward planning is crucial in healthcare institutions, aiming to improve medical service quality while reducing costs. This research delves into the intricacies of integrated OR planning and scheduling, focusing on elective and emergency patients in an uncertain environment. To address these challenges, a mixed integer programming (MIP) framework is developed to minimize inactivity and patient wait times while optimizing high-priority resource allocation. Both upstream and downstream units of the ward, the Pre-operative Holding Unit (PHU), Post Anesthesia Care Unit (PACU), and Intensive Care Unit (ICU) are included. The inherently uncertain aspects of surgery, including surgical duration, Length of Stay (LOS), and the influx of emergency patients, demand an intelligent optimization approach. Consequently, a robust optimization strategy is harnessed to effectively grapple with this pervasive uncertainty. A deterministic model is introduced and improved using an enhanced epsilon constraint method. The culmination of this analytical journey yields a collection of Pareto-optimal solutions. Empirical results, supported by managerial insights, highlight the superiority of the proposed method over the traditional weighting approach.

Flow past a random array of statistically homogeneously distributed stationary Platonic polyhedrons: Data analysis, Probability maps and Deep Learning models

We perform particle-resolved direct numerical simulations (PR-DNS) of the flow past a random array of stationary Platonic polyhedrons seeded in a tri-periodic box at Reynolds number Re=1, 10, and 100 and solid volume fraction 0.05, 0.1 and 0.2. Using Platonic polyhedrons enables us to examine the effects of particle angularity on the hydrodynamic force and torque exerted on the stationary particles in a controlled manner. We report the average drag, lift, and torque coefficients as well as their respective distribution. We explore the relationship between the particle angularity, particle angular position, flow disturbances created by the neighboring particles, and the hydrodynamic force and torque exerted on each individual particle. We attempt to extend our probability map based model (MPP), our Physics Informed neural network (PINN) model previously developed for spheres to Platonic polyhedrons, and propose an additional NN architecture. We show that ignoring the angular position and actual shape of the reference and neighboring particles constitutes a reasonable first order approximation that significantly simplifies the construction of deterministic models of hydrodynamic forces and torques at low Re=1 to moderate Re=10. At high Re=100, both the MPP model and the PINN model without any additional knowledge of the particle shape and angular position fail to properly predict the force and torque fluctuations. We then design a Convolutional Neural Network (CNN) architecture that is able to maintain a satisfactory performance at Re=100 but requires additional input data in the form of a coarse-grained velocity field around each particle. Overall, predicting the torque fluctuation remains a significant challenge.

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.

A deterministic compartment model for analyzing tuberculosis dynamics considering vaccination and reinfection

Tuberculosis is a pressing global health concern, particularly pervasive in many developing nations. This study investigates the influence of treatment failure on tuberculosis control strategies, incorporating vaccination interventions using a deterministic compartmental epidemiological model. Mathematical analysis unveils disease-free and endemic equilibrium points, with the control reproduction number determined using next-generation methods. Identifying endemic equilibrium points and determining the control reproduction number provide essential metrics for assessing the effectiveness of control strategies and guiding policy decisions. The model exhibits a backward bifurcation phenomenon, leading to multiple endemic equilibria despite a reproduction number below one due to reinfection. Sensitivity analysis using Latin Hypercube Sampling/Partial Rank Correlation Coefficient elucidates parameter impacts on the control reproduction number. Vaccination efficacy is crucial for quality and validity, with superior quality and longer validity yielding more significant effects. While reinfection may not directly affect the reproduction number, its influence is pivotal in determining tuberculosis persistence or extinction. This study underscores the intricate interplay of factors in tuberculosis control strategies, providing insights vital for effective interventions and policy formulation.

Fault-Tolerant Control of Stochastic High-Order Fully Actuated Systems.

In recent years, high-order fully actuated (HOFA) systems, founded by Prof. GR Duan, have recorded rapid progress for deterministic systems. However, the control issue of stochastic fully actuated systems is still an open problem. This study develops a novel stochastic HOFA system model that complements the existing HOFA methodology. Notably, stochastic signals can be considered in the proposed model, different from the case in the deterministic model. By adopting a high-order operator, equivalent control and stabilization control laws are realized to guarantee the global asymptotic stability in probability of the closed-loop system. For the system with sensor gain faults, an observer-based fault-tolerant control law is designed. Finally, the simulation results validate the effectiveness of the proposed control schemes.

The economic benefit of herd genotyping and using sexed semen for pure and beef-on-dairy breeding in dairy herds.

The cost benefits of herd genotyping and the benefits of using sexed semen have been affected by recent improvements in sexing technologies, the incorporation of direct health traits in the German total merit index for Holstein cattle, the deteriorating prices for purebred heifer calves and bull calves, and the introduction of herd genotyping programs. Inseminating the genetically superior dams with female-sexed Holstein semen increases the mean breeding value of the heifer calves and can produce more Holstein heifer calves than are needed for replacement. This provides an opportunity to increase the selection response in health and production traits at the farm level. A deterministic model is introduced that predicts the increase or decrease in net profit when a farmer takes part in a herd genotyping program and follows a certain insemination strategy. The types of semen that are allocated to cows and heifers are sexed semen or unsexed semen and Holstein semen or beef breed semen. The genetically superior heifers and cows are inseminated with female-sexed Holstein semen, intermediate dams with unsexed Holstein semen, and genetically inferior dams with unsexed or male-sexed beef breed semen. In general, participating in a herd genotyping program is beneficial for German Holstein breeders. The optimum proportions of cows and heifers that should be inseminated with a certain type of semen are sensitive to farm-specific peculiarities. A small price difference between crossbred bull calves and crossbred heifer calves often makes the use of male-sexed beef breed semen uneconomic. Under the conditions considered, it was found to be advantageous to inseminate approximately 50% of the heifers and 10% of the cows with the highest genetic merit with female-sexed Holstein semen. The optimum proportion of cows that should be inseminated with unsexed beef breed semen was found to be approximately 40%. In a herd with a low replacement rate, the selected heifers can exhibit their genetic superiority over a longer period of time, and a larger proportion of cows can be inseminated with beef breed semen. Participation in a herd genotyping program is, therefore, particularly beneficial for herds with low replacement rates.

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.

Dynamic analysis of HIV infection model with CTL immune response and cell-to-cell transmission

HIV infection is still a serious worldwide public health problem. During the early stage of HIV infection, the number of infected cells and viruses are extremely low and the process of infection is stochastic. In this paper, we use a stochastic model consisting of continuous-time Markov chain to investigate CTL immune response and two modes of infection (viral transmission and cellular transmission). A multitype branching process is used to approximate the probability of clearance and outbreak of HIV infection near the infection-free equilibrium. In addition, we compare the dynamics of the deterministic model with the results of the stochastic model, and the differences are as follows: (1) when R0>1, the deterministic model shows HIV infection outbreak, while the stochastic model indicates a positive probability of HIV infection elimination; (2) the initial number of infected cells and viruses have no effect on the dynamics of the deterministic model, whereas the dynamics of the stochastic model are highly dependent on the initial sizes and cannot be ignored.