جستجوی مقالات مرتبط با کلیدواژه "Mathematical model" در نشریات گروه "ریاضی"
تکرار جستجوی کلیدواژه «Mathematical model» در نشریات گروه «علوم پایه»-
Advanced mathematical modeling and prognosication of regulated spatio-temporal dynamics of MonkeypoxIranian Journal of Numerical Analysis and Optimization, Volume:14 Issue: 4, Autumn 2024, PP 1280 -1308This study explores a continuous spatio-temporal mathematical model to illustrate the dynamics of Monkeypox virus spread across various regions, considering both human and animal hosts. We propose a comprehensive strategy that includes awareness campaigns, security measures, and health interventions in areas where the virus is prevalent. The goal is to reduce transmission between humans and animals, thereby decreasing human infections and eradicating the virus in animal populations. Our model, which integrates spatial variables, accurately reflects the geographical spread of the virus and the impact of interventions, followed by the implementation and analysis of an applicable optimal control problem. Optimal control theory methods are applied in this work to demonstrate the existence of optimal control and the necessary conditions for optimality. We conduct numerical simulations using MATLAB with the forward-backward sweep method, revealing the efficiency of strategies focused on protecting vulnerable populations, preventing contact with infected individuals and animals, and promoting the use of quarantine facilities as the most effective means to control the spread of the Monkeypox virus. Additionally, the study examines the socio-economic impacts of the virus and the benefits of timely intervention. This approach provides valuable insights for policymakers and public health officials in managing and controlling the spread of Monkeypox.Keywords: Monkeypox, Optimal Control, Spatio-Temporal Model, Mathematical Model, Optimization
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Iranian Journal of Numerical Analysis and Optimization, Volume:14 Issue: 2, Spring 2024, PP 475 -499Atherosclerosis is one of the most common diseases in the world. Med-ication with metal stents plays an important role in treating this disease. There are many models for delivering drugs from stents to the arterial wall. This paper presents a model that describes drug delivery from the stent coating layers to the arterial wall tissue. This model complements the previous models by considering the mec hanical properties of the arte-rial wall tissue, which changes due to atherosclerosis and improves results for designing stents. The stability behavior of the model is analyzed, and a number of numerical results are provided with explanations. A compar-ison between numerical and experimental results, which examine a more accurate match between the in vivo and in vitro, is shown.Keywords: Stent coating, Viscoelastic, Mathematical model, Numerical simulation
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This paper aims to demonstrate the flexibility of mathematical models in analyzing carbon dioxide emissions and account for memory effects. The use of real data amplifies the importance of this study. This research focuses on developing a mathematical model utilizing fractional-order differential equations to represent carbon dioxide emissions stemming from the energy sector. By comparing simulation results with real-world data, it is determined that the fractional model exhibits superior accuracy when contrasted with the classical model. Additionally, an optimal control strategy is proposed to minimize the levels of carbon dioxide, CO2, and associated implementation costs. The fractional optimal control problem is addressed through the utilization of an iterative algorithm, and the effectiveness of the model is verified by presenting comparative results.Keywords: {Fractional, Mathematical Model, Optimal Control, Carbon Dioxide
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This article aims at proposing and developing a three-component mathematical model for susceptible, infected and recovered $(SIR)$ population, under the control of vaccination of the susceptible population and drug therapy (antivirus) of the infected population (patient) in case of an infectious disease. The infectious disease under study can be transmitted through direct contact with an infected person (horizontal transmission) and from parent to child (vertical transmission). We investigate the basic reproduction number of the mathematical model, the existence and local asymptotic stability of both the disease free and endemic equilibrium. Using Pontryagin's minimum principle, we investigate the conditions of reducing the susceptible and infected population and increasing the recovered population based on the use of these two controllers in society. A numerical simulation of the optimal control problem shows, using both controllers is much more effective and leads to a rapid increase in the recovered population and prevents the disease from spreading and becoming an epidemic inthe society.Keywords: optimal control, infectious diseases, basic reproduction number, Stability, Mathematical model
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Diabetes mellitus is a global health problem, escalating at a disturbing rate due to unbalanced lifestyles and some underlying health issues. In this work, a system of first-order linear ordinary differential equations as well as numerical simulations were employed to gain insight into the dynamics of the disease. The theoretical outcomeof the analysis was derived in terms of the model parameters while computer simulation was used to assess the behavior of the model in terms of the parameter values. Both the theoretical and numerical studies of the model revealed lifestyles and effective treatment as the parameters to be targeted for effective reduction in both diabetes prevalence and mortality. It is therefore concluded that diabetes prevalence and mortality reduction is a function of adjustment in unbalanced lifestyles as well as improvement in diabetes treatment.Keywords: Diabetes Mellitus, lifestyle, Simulation, Mathematical model, Treatments
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DES, or drug-eluting stents, have the advantage of reducing restenosis rates relative to bare-metal stents. Modeling and simulation can be used to improve device performance. In this study, a general mathematical model for releasing a hydrophobic drug from a drug-eluting stent, DES, with a biostable coating is modeled. Most mathematical models allow the drug in the polymer to be released freely. This is suitable when the initial concentration of the drug in the polymer is less than the solubility, in which case the dissolution of the drug can be considered instantaneously. On the other hand, matrix devices can be loaded above solubility to provide zero-order release. to this end, we have equipped a model with a function that determines how the dissolution processes change with the dispersed phase discharge. The general model is analyzed with some limitations, and it is reduced to a new model that is consistent with previous studies. We examine the effects of initial drug loading and dissolution rate constant in numerically solving one of the new models, which is novel in DESs.Keywords: Mathematical model, drug eluting stent, biostable polymer, Dissolution, Diffusion
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Data envelopment analysis models are able to rank decision-making units (DMUs) based on their efficiency scores. In spite of the fact that there exists a unique ranking of inefficient DMUs, ranking efficient DMUs is problematic. However, rather than ranking methods, another way to choose one of the efficient units is to determine the most efficient DMU. Up to the present, many models have been proposed to rank DMUs and determine the most efficient one. These models require solving nonlinear or integer programs, which are NP-hard and time-consuming. Considering efficient DMU's characteristics, this paper proposes a procedure to find the most efficient DMU through some simple operations. The validity of the proposed approach is verified and tested via some numerical examples.Keywords: Data envelopment analysis, Most efficient DMU, Input, output weights, Mathematical model
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International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 2, Summer-Autumn 2022, PP 899 -921
In this study, a mathematical model with optimal control measures was used to investigate the transmission dynamics of co-infection of hepatitis A virus and typhoid fever. A deterministic compartmental model was used and an analysis of the effect of various control measures was compared. The pathogen fitness that represents the epidemic indicator is obtained by using the next-generation matrix. We have shown the existence of two equilibrium states: the disease-free steady state in which there are no populations that are infected by the co-infection of hepatitis A virus and typhoid fever, the endemic state in which a co-infected population exists and is capable of transmitting the disease. The local and global stability conditions of the endemic equilibrium points were also proved. Further, it was proved that the co-infection of the model exhibited a backward bifurcation. Finally, a numerical simulation of the model was made and it reveals that prevention has a significant impact in reducing the transmission of the co-infection and applying all the control measures can successfully eliminate co-infection of hepatitis virus and typhoid fever from the community.
Keywords: Mathematical model, co-infections, Hepatitus A Virus, typhoid fever, Basic reproduction number, Simulations -
Electrocardiogram (ECG) signals is widely used as one of the common procedures for heart's disease diagnose. Since electrical signals generated by biological sources have low level, they are destroyed by interference. Therefore, it is difficult to achieve high resolution electrical signals. A new approach based on non-polynomial cubic spline has been developed to approximate the ECG signal. The Efficiency of proposed method is analyzed by simulation results and filter evaluation metrics.Keywords: ECG signal, Noise, Nonpolynomial cubic spline, Mathematical model, Filtering
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The novel coronavirus 2019 known as (COVID-19) pandemic caused by SARS-CoV-2 occurred in Wuhan town of China in 2019. The virus has rapidly spread all over the world and has continued to affect the public well-being. This paper focuses on a mathematical model with vaccination acceptability of COVID-19 with which to examine to what extent the vaccine would be accepted in Nigeria. Specifically, the paper introduces a compartmental model to measure the potential impact of the COVID-19 vaccine. The vaccination acceptability model results show that up to 80% of the Nigerian populace accepted the vaccination campaign, despite the gabs on the COVID-19 vaccine by some health workers and the communities in Nigeria. It also shows that 90% vaccinated susceptible plus 50% effectiveness of face-mask use has brought about a decrease of the pandemic while mortality rate has decreased drastically which shows that the vaccine is effective. The result also reveals that the recovered individuals from COVID-19 have increased in alignment and, the vaccine has a significant impact on the populace. Finally, possible extensions of the model as well as open challenges associated with the formulation and analysis of COVID-19 dynamics will be addressed.Keywords: Mathematical model, Vaccination acceptability, COVID-19, SARS-CoV-2
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International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 1, Winter-Spring 2022, PP 729 -735
The main goal of this paper is to obtain the estimated determination of the quantum dot potential for PbS and PbTe structures (in mV) which are compared to other values at different QD's diameters (in nm). In order to investigate this goal, the study relies on two methods of interpolation such as Neville and Spline methods, as well as it constructs mathematical models that help to find the estimate determination of quantum dot potential for PbS and PbTe structures compared to other values at different QD's diameters. The numerical results were very close to the real results. Finally, we estimated the determinations outside the fields and labs of the measured areas.
Keywords: Mathematical model, Neville’s method, Spline method, Quantum dot potential forPbS, PbTe, Diameter -
International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 1, Winter-Spring 2022, PP 1341 -1350
n this paper we present a dynamic model of the heart’s pumping blood. To predict blood flow and pressure applied to the area of blood vessels (arteries - veins - capillaries). The fluid dynamics model is derived from the continuum equation and the Navier-Stokes equations. For an incompressible Newton flow through a network of cylindrical vessels. This paper combined a model of pressure applied to the walls of blood vessels with a (regular - turbulent) flow model of blood, and the viscoelastic deformation of the walls (arteries - veins - capillaries) was studied with different blood density and prediction of the effect of the thickness of the rubber wall on the flow and the resulting pressure on the blood vessels. The results of this study show that the viscous elastic wall of the blood vessels allows more physiological prediction of pressure and vascular deformation, and that blood flow with varying intensity is more in the aorta than in the rest of the vessels, and this is subject to wide dilation.
Keywords: Mathematical model, elastic fiber, viscosity of blood -
در بررسی بیماری های ویروسی در گیاهان، واکنش سیستم ایمنی گیاه نقش اساسی ایفا می کند. در این مقاله، یک مدل ریاضی، بر اساس دستگاه معادلات دیفرانسیل با تاخیر زمانی برای واکنش سیستم ایمنی گیاه ارایه می شود. در ادامه، رفتار دینامیکی مدل حول نقاط تعادل بررسی شده و در پایان، یک گیاه در دو حالت متفاوت اورگانیک و غیراورگانیک در نظر گرفته می شود و رفتار منحنی های جواب با استفاده از نرم افزارمتلب بررسی می شود.
کلید واژگان: مدل ریاضی, نقطه تعادل, پایداری, انشعاب هاف.رده بندی ریاضی (2010): .37C75, 37H20, 00A71IntroductionOne of the major challenges in supporting a growing human population is supplies of food. Plants play a major rule in providing human food. Hence, it is important to study plant diseases and provide appropriate models for describing the relationship between plant infection and its growth and reproduction. One of effective models that describes this relationship is mathematical model. One of the important aspects that the mathematical model can presented is the dynamic of the plant’s immune system.In this paper, a mathematical model for diffusion of infection in the host plant is introduced. The model is based on a differential equation system with two time delays. In this model, the host population of cells is divided into the classes of susceptible cells consisting of mature cells and are susceptible to infection, infected cells that spread the infection, recovered cells that are no longer infectious and are proliferating cells that become susceptible after reaching maturity. We consider two time delays, and , in equations. The proliferating cells have the average maturity time , after which they are recruited to the susceptible class. is the average time of antiviral effects.In the next sections of this paper, stability conditions of equilibrium points are investigated. In the last section, we consider a plant in two different modes, organic and non- organic. Then the solution curves are plotted with different time delays and compare solutions together.
Material and methodsIn this scheme, first we explain the conditions of plant. Then, a mathematical model with two time delays is introduced. As follows, the dynamical behavior of the model is investigated. At the end of paper, we consider a plant with two different modes and plot the solution curves.
Results and discussionWe introduce a mathematical model which explain conditions of plant cells. In this model the independent variable is time, so the model is ODE with two time delays. As follows, using some theorems in dynamical systems, the dynamical behavior of the model is investigated. Using these results, we can provide good conditions for a plant that epidemic does not happen. At the end, we use of Matlab software to plot the solution curves in two different conditions. The curves explain the behavior of plant cells when they are infectious.
ConclusionThe following conclusions were drawn from this research.A mathematical model which is introduced in this paper is more realistic than the previous models because, the grow rate of a plant is considered to be logistic.Theorems show that how we can control the virus to prevent epidemic outbreak.We plot solution curves for two different plants (organic and non-organic). Solution curves show that how the conditions of plant cells change by changing the parameters.
Keywords: Mathematical model, Equilibrium point, Stability, Hopf bifurcation -
In this study, a deterministic mathematical model was used to investigate the dynamics of typhoid disease by using different optimal control strategies. The qualitative behavior of the control profile revealed that prevention has a higher impact in minimizing the incidence of the disease. Finally it was shown that applying all the three control strategies rapidly minimizes typhoid disease from the population.
Keywords: Mathematical model, Typhoid, Basic reproduction number, immunization, Deterministic model -
International Journal of Mathematical Modelling & Computations, Volume:7 Issue: 2, Spring 2017, PP 115 -128In this paper, effect of alternative resource for top predator in food chain model with holling type III functional response is seen . Proposed model is demonstrated in respect of analytical as well numerical results. Bifurcation study with the variation of alternative resource and half saturation constants are done numerically. Simulation results shows that suitable alternative resource has the capability to prevent top predator extinction.Keywords: Mathematical Model, stability analysis, Holling type III Functional Response, Alternative Resource
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در این مقاله، یک مدل ریاضی برای بررسی دینامیک بیماری اچ آی وی/ایدز ارائه می شود. در این مدل تاثیر استفاده از سرنگ های مشترک در جمعیت معتاد، در شیوع بیماری اچ آی وی/ایدز مورد بررسی قرار می گیرد. برای این منظور ابتدا عدد شیوع با استفاده از روش ماتریس نسل دوم بدست آورده شده و سپس عدد شیوع در دو حالت استفاده از سرنگ مشترک و عدم استفاده از سرنگ مشترک بررسی می شود. با اعمال کنترل های، استفاده از سرنگ استریل و غیر مشترک، استفاده از وسایل پیشگیری در روابط جنسی، شناسایی افراد بیمار ناآگاه و درمان افراد بیمار، بر مدل بیماری، مسئله کنترل بهینه فرمول بندی می شود. با استفاده از اصل حداقل یابی پونتریاگین شرایط لازم برای کنترل بهینه تعیین شده و در نهایت نتایج عددی با استفاده از روش رانگه-کوتا مرتبه چهار بدست می آید. نتایج نشان می دهد که تفاوت معناداری در کنترل شیوع بیماری، بین حالتی که کنترلی بر بیماری صورت نمی گیرد با حالتی که کنترل اعمال می شود، وجود دارد.کلید واژگان: بیماری اچ آی وی, ایدز, مدل ریاضی, عدد شیوع, کنترل بهینه, ماتریس نسل دومIn this paper, a mathematical model for studying HIV/AIDS dynamics is presented. Based on this model, the effects of contaminated needle sharing in addicted population on spread of HIV/AIDS is investigated. For this purpose, first, the effective reproduction number is obtained by using the next generation operator method. Then, the reproduction number is examined in two cases, one with sharing needles and the other one with not sharing needles. The optimal control problem is formulated by applying some controls on the disease model including use of non-shared and sterile needles, use of prevention methods, screening of unaware infectives and treating patients. Necessary conditions for optimal control is determined by using Pontryagins minimum principle. Finally, numerical results is obtained by the RungeKutta fourth-order method. The results show a significant difference in control of prevalence of disease between the cases applying and not applying control on the disease.Keywords: HIV, AIDS disease, Mathematical model, Reproduction number, Optimal control, Next generation matrix
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A novel mathematical model has been developed to aid the formulation of emulsion explosives. This mathematical model calculated heat of explosion, oxygen balance and raw material cost as a function of explosive ingredients, and the solution of the mathematical model was obtained by a MS Excel program. The effects of the different content of NH4NO3, NaNO3, H2O, and span-80 and composite fuel oil on the heat of explosion and the specific volume of emulsion explosive were discussed based on the proposed mathematical model. The results show that (1) with the increasing of the content of NH4NO3, the heat of explosion and the specific volume increase. (2) The better content of NaNO3, H2O and Span-80 in the formulation of emulsion explosive are 7%~9%, 9%~10%, 1.5%~2% respectively, and this formulation results in an oxygen balance of zero or close to zero.Keywords: Mathematical Model, Emulsion explosive, Explosion, oxygen balance
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