Dynamic Mathematical Model Research Articles

A Compartmental Mathematical Model of Novel Coronavirus-19 Transmission Dynamics

A Compartmental Mathematical Model of Novel Coronavirus-19 Transmission Dynamics

Mathematical modelling of the transmission dynamics of Marburg virus disease with optimal control and cost-effectiveness analysis based on lessons from Ebola virus disease

Marburg virus, like Ebola, causes haemorrhagic disease with high fatality rates. We developed a deterministic SEIRDVT model incorporating vaccination and treatment to study the disease dynamics. Qualitative analysis revealed a backward bifurcation when R0=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$R_{0}=1$\\end{document}, meaning R0<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$R_{0} <1$\\end{document} is insufficient to eradicate the virus. Sensitivity analysis using Latin Hypercube Sampling showed that applying four control measures—screening, prevention, continuous vaccination, and treatment—significantly reduced transmission. The most cost-effective strategy combines prevention, vaccination, and treatment. These findings provide a framework for designing efficient interventions to combat Marburg virus.

Study on the Process of Soil Clod Removal and Potato Damage in the Front Harvesting Device of Potato Combine Harvester

To improve soil clod removal and reduce potato damage in potato combine harvesters, this study investigates the processes involved in soil clod removal and potato collisions within the bar-lift chain separation device of the harvester. It outlines the structure and working principles of the machine, theoretically analyzes the key dimensions of the digging device and potato–soil separation components, and derives specific structural parameters. A dynamic mathematical model of the bar-lift chain is established, from which the dynamic equations are formulated. The analysis identifies factors that influence the dynamic characteristics of the bar-lift chain. This study examines the working principles and separation performance of the potato–soil separation device, with a focus on the collision characteristics between potatoes and both the screen surface and the bars. Key factors such as the separation screen’s line speed, the harvester’s forward speed, and the tilt angle of the separation screen are considered. Simulations are performed using a coupling method based on the Discrete Element Method (DEM) and Multi-Body Dynamics (MBD). Through simulation experiments, the optimal parameter combinations for the potato–soil separation device are determined. The optimal working parameters are identified as a separation screen line speed of 1.25 m/s, a forward speed of 0.83 m/s, and a tilt angle of 25°. Field harvesting experiments indicate a potato loss rate of 1.8%, a damage rate of 1.2%, an impurity rate of 1.9%, a skin breakage rate of 2.1%, and a yield of 0.15–0.21 ha/h. All results meet national and industry standards. The findings of this research provide valuable theoretical references for simulating potato–soil separation in combine harvesters and optimizing the parameters of these devices. Future potential research will consider the automatic regulation of the excavation volume of the potato–soil mixture, aiming to achieve intelligent control of the potato–soil separation operation.

Analysis of mathematical methods for describing financial flows: dynamic modeling of an innovative company

Purpose. Development of a dynamic mathematical model of an innovative company operating in accordance with Ukrainian legislation, allowing for the analysis and adjustment of its financial activities. Methodology. When developing a model and description of financial flows, a factor analysis of the necessary indicators of the financial condition of the enterprise in question was carried out, which were used in the calculations of the presented mathematical modeling. A mathematical apparatus has been developed for calculating financial indicators depending on time. Using inductive, deductive and logical methods, an analysis of the financial situation for the year was carried out. Findings. The main methods and tools for describing financial flows have been analyzed. Mathematical modeling of the innovative company is carried out, which allows analyzing the costs of the enterprise and determining the size of its free funds. The calculation of financial indicators of the enterprise, which are demonstrated in the form of tables, is performed and the dynamics is shown in charts and graphs. All calculations were made on the basis of existing Ukrainian legislation using modern information technologies. Originality. A mathematical dynamic model of changes in financial flows at the enterprise has been developed and implemented. The proposed model takes into account various items of expenses and profits in accordance with the state legislation. Calculations allow for dynamic analysis and determination of the impact of various indicators on the financial condition of the enterprise, which allows for faster adoption and implementation of decisions in managing financial flows. This dynamic model is a convenient tool for any enterprise in Ukraine. Practical value. The results that were obtained during the study can become the basis for creating the necessary digital tools for researching, analyzing and adjusting the financial flows of a particular enterprise. Now methods are available that allow analyzing and describing financial flows more accurately and forecasting their changes in the future. The methodology presented allows the creation of dynamic models that can account for complex dependencies between different indicators and forecast the behavior of financial flows in real time. The financial model allows the simulation of cash flows of planned activities and the evaluation of financial planning in advance, taking into account the conducted research. It is straightforward to use and allows the analysis of different scenarios of business development, significantly reducing the time required.

Collateral sensitivity counteracts the evolution of antifungal drug resistance in Candida auris.

Antifungal drug resistance represents a serious global health threat, necessitating new treatment strategies. Here we investigated collateral sensitivity (CS), in which resistance to one drug increases sensitivity to another, and cross-resistance (XR), in which one drug resistance mechanism reduces susceptibility to multiple drugs, since CS and XR dynamics can guide treatment design to impede resistance development, but have not been systematically explored in pathogenic fungi. We used experimental evolution and mathematical modelling of Candida auris population dynamics during cyclic and combined drug exposures and found that especially CS-based drug cycling can effectively prevent the emergence of drug resistance. In addition, we found that a CS-based treatment switch can actively select against or eradicate resistant sub-populations, highlighting the potential to consider CS in therapeutic decision-making upon resistance detection. Furthermore, we show that some CS trends are robust among different strains and resistance mechanisms. Overall, these findings provide a promising direction for improved antifungal treatment approaches.

Adaptive multimodal control of trans-media vehicle based on deep reinforcement learning

To solve the problem that the control system is prone to instability due to the sudden change of physical characteristics, strong interference, and nonlinear in the process of multimodal movement of trans-media vehicle, an adaptive control method combining the Deep Deterministic Policy Gradient (DDPG) and traditional Proportional-Integral-Derivative (PID) controller is proposed in this paper. In this approach, the upper-level DDPG controller continuously monitors the vehicle's state and environmental conditions, dynamically adjusting the PID parameters in real-time. The lower-level PID controller then utilizes these updated parameters to modulate the output thrust of the vehicle's motors, thereby achieving excellent control over the vehicle's entire movement. Firstly, according to the hydrodynamic analysis, the kinematics and dynamics mathematical model of the self-designed trans-media vehicle is constructed. This model includes the multi-stage motion modal process of aerial flight, underwater navigation, and cross-media motion, which is suitable for the simulation and verification of the control method. Then, an adaptive controller called RL-PID combining DDPG and PID is built, so that PID can adjust parameters in real-time according to the changes in the external environment. Finally, after theoretical stability proof, a comparison study is performed across three approaches, namely the novel RL-PID, Fuzzy PID, and PID. The experimental results illustrate the superiority of the proposed approach over the competing ones and the generalization of the proposed approach under different interference.

Mathematical Model for Antimicrobial Resistance Transmission Dynamics in Hospitals

In this study, we formulate and analyze a mathematical model to describe the possible transmission routes of Antimicrobial Resistance (A.M.R) in a hospital setting. We have examined the significant means of transmission of resistance in hospitals and found that the significant means of transmission is the use of antibiotics and through the contamination by health care workers. It has been shown that the resistance free equilibrium point is locally asymptotically stable. We have also shown that the model has a unique positive endemic equilibrium point which is locally asymptotically stable.

Enhancing Production in Robot-Enabled Manufacturing Systems: A Dynamic Model and Moving Horizon Control Strategy for Mobile Robot Assignment

Abstract This paper presents a dynamic mathematical model for a robot-enabled manufacturing system, where mobile robots independently manage workstation tasks. Each robot possesses one or multiple skills, enabling collaborative work at workstations. A real-time robot assignment problem is formulated to maximize production of the system, and a novel control strategy is developed to address this problem. Leveraging system properties derived from the model and moving window downtime prediction, the problem of maximizing system production is transformed into a more tractable control problem focused on identifying and achieving a defined ideal clean configurations. The proposed solution significantly outperforms various benchmarks, including a pure reinforcement learning-based strategy, underscoring the importance of system understanding and its crucial role in enhancing flexibility and productivity in manufacturing systems.

Analysis of Influential Parameters in the Dynamic Loading and Stability of the Swing Drive in Hydraulic Excavators

The proper design and configuration of the swing drive mechanism of a hydraulic excavator are crucial to improve energy consumption and efficiency and ensure operational stability. This paper analyzes the influence of the relationship between the parameters of a hydraulic motor and a reducer, which form the integrated transmission of a swing drive, the dynamic characteristics of a hydraulic excavator on loading, and the dynamic stability of the drive. The analysis deals with an excavator model that has the same parameters of the kinematic chain members, the same parameters of the upper structure drive mechanisms, and two variants of the swing drive that, with different integrated transmission parameters, provide the upper structure with the identical number of revolutions and equal rotating moment. One swing drive variant possesses an integrated transmission with a hydraulic motor with a low specific flow and a reducer with a high transmission ratio, while the other drive variant has the opposite parameters. Understanding this relationship is essential for optimizing the design of excavators to achieve better performance and dynamic stability under varying operational conditions. As an example, this paper provides the analysis results regarding the influence of the relationship between the parameters of the integrated transmission hydraulic motor and reducer on the loading and dynamic stability of the swing drive in a tracked hydraulic excavator of 100,000 kg in mass and 4.4 m3 in loading bucket volume, as obtained from the developed dynamic mathematical models of the excavator using the MSC ADAMS program. The results indicate that the dynamic loads on the swing drive’s axial bearing are higher in the variant with a low-specific-flow motor and high transmission ratio reducer during the acceleration and deceleration phases. However, this configuration demonstrated better dynamic stability, with lower oscillation amplitudes and shorter damping times compared to the variant with a high-flow motor and low transmission ratio. Those findings provide valuable criteria for the optimal synthesis of swing drive mechanisms in large hydraulic excavators using multi-criteria optimization methods.

MATHEMATICAL MODEL OF LASSA FEVER TRANSMISSION DYNAMICS IN PREVALENT COMMUNITIES IN NIGERIA: THE CASE STUDY OF ONDO STATE

With the current waive of global health problems and resurgence of many disease around the world. Cholera, Yellow fever,SARS-CoV-2, Monkey pox and Lassa fever resurgence in some West African countries, with Ondo State recording highest number of Lassa fever case in Nigeria. Prompting Nigeria Centre for Disease Control (NCDC), Ondo State Primary Health (OSPH) expert and researchers begin ways to reduce transmission dynamics of Lassa Fever Disease (LFD). In this research, we developed and investigated using System of Ordinary Differential Equation (ODE) mathematical model of Lassa fever disease transmission dynamics, verifying positivity of system of equation as well as feasible region of the model. However, the Disease Free Equilibrium (DFE) of the model is computed and analysed with basic reproduction number $R_0$ of the model, showing the global stability of the DFE. Furthermore, we determined using model-fitting parameters the condition to attain stability. Finally, numerical simulations shows reduction in transmission with effective pest control measure.

Mathematical modelling of Lassa-fever transmission dynamics with optimal control of selected control measures

Mathematical modelling of Lassa-fever transmission dynamics with optimal control of selected control measures

Smoking and alcoholism dual addiction dissemination model analysis with optimal control theory and cost-effectiveness.

A mathematical model of the dual addiction dissemination dynamics of alcoholism and smoking was created and examined in this work, along with cost-effectiveness and optimal control techniques. The primary goal of the research is to determine which cost-efficient management techniques are most helpful in lowering the problem of dual addiction dispersion in the community. The smoking addiction sub-model, the alcohol addiction sub-model, and the dual addiction model between alcohol and smoking were all calculated, and their stability was examined in this study. The effective reproduction numbers of the models are computed using the next-generation operator technique. When the model's effective reproduction number is smaller than one, the backward bifurcation phenomenon is seen. Six time-dependent control measures are taken into consideration when formulating and analyzing the optimum control issue. Utilizing and applying the parameter values and using MATLAB ode45 solver we performed numerical simulations for both the dual addiction model and its optimal control problem. Furthermore, using the incremental cost-effectiveness ratio (ICER), we carried out the cost-effectiveness analyses. The cost-effectiveness analysis shows that implementing all the protection (education) control measures simultaneously (i.e., implementing Strategy A) is the most cost-effective strategy. Finally, we recommend that the public health stakeholders must put great effort into the implementation of Strategy A to reduce the smoking and alcoholism dual addiction dissemination problem in the community.

Mathematical Modeling and Analysis of Ebola Virus Disease Dynamics: Implications for Intervention Strategies and Healthcare Resource Optimization

Mathematical Modeling and Analysis of Ebola Virus Disease Dynamics: Implications for Intervention Strategies and Healthcare Resource Optimization

Fractional-order analysis of temperature- and rainfall-dependent mathematical model for malaria transmission dynamics

Malaria remains a substantial public health challenge and economic burden globally. Currently, malaria has been declared as endemic in 85 countries. In this study, we developed and analyzed a fractional-order mathematical model for malaria transmission dynamics that incorporates variability of temperature and rainfall using Caputo-type AB operators. The existence and uniqueness of the model's solutions were established using the Banach fixed-point theorem. The model system's equilibria (both disease-free and endemic) were identified, and lemmas and theorems were developed to prove their stability. Furthermore, we used different temperature ranges and rainfall data, validating them against existing literature. Numerical simulations using the Toufik-Atangana schemes with various fractional-order alpha values revealed that as the value of alpha approaches 1, the behavior of the fractional-order model converges to that of the classical model. The numerical results are promising and are expected to be valuable for future research related to fractional-order models.

The development of drug resistance in metastatic tumours under chemotherapy: An evolutionary perspective

We present a mathematical model of the evolutionary dynamics of a metastatic tumour under chemotherapy, comprising non-local partial differential equations for the phenotype-structured cell populations in the primary tumour and its metastasis. These equations are coupled with a physiologically-based pharmacokinetic model of drug administration and distribution, implementing a realistic delivery schedule. The model is carefully calibrated from the literature, focusing on BRAF-mutated melanoma treated with Dabrafenib as a case study. By means of long-time asymptotic and global sensitivity analyses, as well as numerical simulations, we explore the impact of cell migration from the primary to the metastatic site, physiological aspects of the tumour tissues and drug dose on the development of chemoresistance and treatment efficacy. Our findings provide a possible explanation for empirical evidence indicating that chemotherapy may foster metastatic spread and that metastases may be less impacted by the chemotherapeutic agent.

Analysis of multi-frequency ultrasound effect on acoustic microcavitations in [formula omitted]-dimensional fluid

Acoustic microcavitation and associated mechanical effects, such as stress and strain, are significant in decreasing cavitation thresholds and improving cavitation effects at multiple (i.e., single, dual, and triple) frequencies. Ultrasonic excitation and the introduction of microbubbles as cavitation nuclei are both extremely successful techniques. Besides, the enhancing effects brought on by a dual and triple frequency approach, the cavitation dynamics of microbubbles in viscoelastic tissues under the influence of dual and triple frequency excitation are poorly known. This work deals with the modelling and numerical investigation of acoustic cavitation in N-dimensional fluid based on the multifrequency of ultrasound fields. The mathematical model of ultrasonic microcavitation bubble dynamics is formulated by continuity and Navier-Stokes equations in N-dimensions and the equation of pressure due to acoustic multifield. The proposed model is solved and investigated numerically based on the hybrid-B-Spline method. The numerical results illustrate that the behaviour of the microcavitation bubble dynamics increases with a decrease of the value of the N-dimensional fluid. Moreover, the results of the numerical simulation show the importance of the effect of different multifrequency on the behaviour of the microbubble dynamics, as the results obtained showed that in the case of a single frequency, the radius of the microbubbles is higher than in the cases of dual and triple frequency. Additionally, at different initial radii values for cavitation microbubbles, the growth and departure rates for microcavitation dynamics were examined. Finally, in the proposed model, numerical solutions are studied, their stability is verified, and they are compared with previous theoretical works.

We are all different: Modeling key individual differences in physiological systems.

Mathematical models of whole-body dynamics have advanced our understanding of human integrative systems that regulate physiological processes such as metabolism, temperature, and blood pressure. For most of these whole-body models, baseline parameters describe a 35-year-old young adult man who weighs 70 kg. As such, even among adults those models may not accurately represent half of the population (women), the older population, and those who weigh significantly more than 70 kg. Indeed, sex, age, and weight are known modulators of physiological function. To more accurately simulate a person who doesn't look like that "baseline person," or to explain the mechanisms that yield the observed sex or age differences, these factors should be incorporated into mathematical models of physiological systems. Another key modulator is the time of day, because most physiological processes are regulated by the circadian clocks. Thus, ideally, mathematical models of integrative physiological systems should be specific to either a man or woman, of a certain age and weight, and a given time of day. We illustrate the importance of capturing these individual differences, using the blood pressure regulatory system as an example, and explain how that such models can be built.

Design of an Optimal Multivariable PID Controller for a Two-Link Robot Arm

Incorporating manipulator robots into various industries has revolutionized automation and manufacturing processes. Manipulator robots are versatile machines equipped with robotic arms and end-effectors, enabling them to handle complex tasks with precision and efficiency. This research aims to design an optimal Mutivariable PID (MPID) controller that ensures precise and accurate movements of two-link robot arm. Theoretical foundations of the MPID controller are discussed together with its relevance to robotic arm systems, and the challenges associated with its implementation. The research methodology involves mathematical modelling of the two-link robot arm dynamics, and the use of an optimization algorithm to determine the optimal MPID controller coefficients. Simulation results demonstrate performance enhancement and productivity of the two-link robot arm through the improved MPID controller.

Modeling and forecasting biogas production from anaerobic digestion process for sustainable resource energy recovery

Anaerobic digestion (AD) is one of the most extensively accepted processes for organic waste cleanup, and production of both bioenergy and organic fertilizer. Numerous mathematical models have been conceived for modeling the anaerobic process.In this study, a new modified dynamic mathematical model for the simulation of the biochemical and physicochemical processes involved in the AD process for biogas production was proposed. The model was validated, and a sensitivity analysis based on the OAT approach (one-at-a-time) was carried out as a screening technique to identify the most sensitive parameters. The model was developed by updating the bio-chemical framework and including more details concerning the physico-chemical process. The fraction XP was incorporated into the model as a particulate inert product arising from biomass decay (inoculum). New components were included to distinguish between the substrate and inoculum, and a surface-based kinetics was used to model the substrate disintegration. Additionally, the sulfate reduction process and hydrogen sulfide production have been included. The model was validated using data extracted from the literature. The model's ability to generate accurate predictions was testified using statistical metrics. The model exhibited excellent performance in forecasting the parameters related to the biogas process, with measurements falling within a reasonable error margin. The relative absolute error (rAE) and root mean square error (RMSE) were both less than 5 %, indicating a high ability of the current model in comparison with the literature. Additionally, the scatter index (SI) was below 10 %, and the Nash-Sutcliffe efficiency (NES) approached one, which affirms the model's accuracy and reliability. Finally, the model was applied to investigate the performances of the AD of food waste (FW). The findings of this study support the robustness of the developed model and its applicability as a virtual platform to evaluate the efficiency of the AD treatment and to forecast biogas production and its quality, CO2 emission, and energy potential across various organic solid waste types.

Динамическая модель харвестера, оснащенного канатной анкерной системой, при проведении лесозаготовительных работ на крутом склоне

The efficiency of using logging machines for work in mountainous or hilly areas characterized by the presence of steep slopes depends on many factors, among which the quantitative parameters of the dynamic state of both the harvester itself and the anchor system play a priority role to ensure the safe operation of these technological machines. This article considers a complex spatial dynamic model that combines into a common interconnected system all the main components of the simulated phenomenon, including directly a harvester with a hydraulic manipulator mounted on it, a movable assortment in space, an anchor system consist-ing of an anchor rope and a winch, an anchor tree for attaching an anchor rope and the soil of the support surface. The dynamic mathematical model of such a six-component system includes 35 generalized coordinates that determine the linear and angular displacements of the mass centers of the listed system components. A system of 35 differential equations constructed using the Lagrange’s equation was solved by the 4-th-order Runge-Kutta method. For this purpose, a computer program has been developed, the description of which is contained in the article. In relation to the basic version of the simulated system with quantitative initial characteristics focused on the characteristics of a three-axle wheeled harvester with a 6K6 wheel formula, calculations of oscillatory processes for dynamic parameters determining the loading of the anchor system and the safety of harvester operation in the process of assortment manipulation were carried out.