scholarly journals A mathematical model of common-cold epidemics on Tristan da Cunha

1971 ◽  
Vol 69 (3) ◽  
pp. 423-433 ◽  
Author(s):  
B. J. Hammond ◽  
D. A. J. Tyrrell
Keyword(s):  
Mathematical Model ◽  
Common Cold ◽  
Average Duration ◽  
Model Parameters ◽  
Epidemic Threshold ◽  
Tristan Da Cunha ◽  
Simulation Techniques ◽  
Time Courses ◽  
The Mathematical Model ◽  
Computer Simulation Techniques

SUMMARYRecords of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

scholarly journals The generation of a mathematical model of the biogas production process from organic municipal solid waste

2020 ◽  
Vol 180 ◽  
pp. 02019 ◽  
Author(s):  
Marzhan Temirbekova ◽  
Madina Aliyarova ◽  
Iliya Iliev ◽  
Aliya Yelemanova ◽  
Saule Sagintayeva
Keyword(s):  
Mathematical Model ◽  
Municipal Solid Waste ◽  
Solid Waste ◽  
Anaerobic Fermentation ◽  
Biogas Production ◽  
Biogas Plant ◽  
Model Parameters ◽  
Biochemical Processes ◽  
Biogas Plants ◽  
The Mathematical Model

This paper justifies the efficiency of the biogas collection and utilization at the MSW (municipal solid waste) landfill in Almaty with the installation of several modern biogas plants. The optimal mode of processes occurring in a biogas plant is determined by computer generated simulations. Mathematical model parameters were identified to describe biochemical processes occurring in a biogas plant. Two approaches are used to resolve the mathematical model: the finite-difference method for solving the system of differential equations and simulation modeling by using the Any Logic package. A program is written in the algorithmic language C ++. Numerous calculations were carried out, the results of which are presented in curves and their qualitative picture is consistent with the ongoing processes. The created computer program allows to make a preliminary forecast of anaerobic fermentation occurring in the bioreactor depending on volume of the substrate, methane microorganisms and temperature conditions.

Wind Energy Conversion: The Potential of a Novel Ducted Turbine for Residential and Commercial Applications

2013 ◽  
Author(s):  
N. Goudarzi ◽  
W. D. Zhu ◽  
H. Bahari
Keyword(s):  
Mathematical Model ◽  
Wind Power ◽  
Flow Behavior ◽  
Experimental Tests ◽  
Simulation Techniques ◽  
Ducted Turbine ◽  
Grid Applications ◽  
Commercial Applications ◽  
Four Quadrant ◽  
The Mathematical Model

A novel ducted turbine, referred to as a Wind Tower, for capturing wind power in either residential or commercial scale applications is studied theoretically and experimentally. A mathematical model is developed to predict the flow behavior inside the tower and a velocity coefficient is defined to correct the results at different test conditions. A wind tower prototype, including a four-quadrant-peak wind-catcher rooftop, a tower, a nozzle, and a turbine, is designed and fabricated. The captured wind power values from the mathematical model and the preliminary experimental tests are compared. While the mathematical model provides a good estimation of the output power in some cases, more precise experimental tests and simulation techniques are required to improve the mathematical model in some other cases. Significant changes in the output wind speed due to pressure differences created by the surrounding environment, the tower height, and the number of nozzles are observed. The advantages of being maintenance free, reliable, and sustainable, together with its special design that eliminates bird/bat mortality make the Wind Tower a promising solution for residential, commercial, and even off-grid applications.

Study on the Dynamic Models of Systems Biology from the View of Engineering

2012 ◽  
Vol 220-223 ◽  
pp. 952-957
Author(s):  
Chen Liu ◽  
Xiao Yan Liu
Keyword(s):  
Mathematical Model ◽  
Systems Biology ◽  
Dynamic Process ◽  
Biological System ◽  
Dynamic Models ◽  
Model Parameters ◽  
State Variables ◽  
Biochemical Pathway ◽  
The Right ◽  
The Mathematical Model

From the view of engineering, based on expatiating the features of systems biology, the paper discusses the workflows and the research emphasis of systems biology. It also explains how to model and analyze the dynamic process of signal transmitting network for a biological system by an example. Based on the complexity and uncertainty of the mathematical model, the right methods are chosen to realize the effective estimation of state variables and model parameters for the biochemical pathway.

Drying of solids; estimation of the mathematical model parameters

2010 ◽  
pp. n/a-n/a ◽  
Author(s):  
Aleksandra Sander ◽  
Jasna Prlić Kardum ◽  
Antun Glasnović
Keyword(s):  
Mathematical Model ◽  
Model Parameters ◽  
The Mathematical Model

Research on the Simulation of the Charge Mathematical Model of the Vehicle Starting Battery

2013 ◽  
Vol 680 ◽  
pp. 479-483
Author(s):  
Pei Ying Li ◽  
Yu Tian Pan
Keyword(s):  
Mathematical Model ◽  
Battery Life ◽  
Model Parameters ◽  
Analysis Method ◽  
Lead Acid Battery ◽  
Battery Charge ◽  
Charge Model ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Lead Acid

In order to meet the demands of practical, convenient and quick charge requirements, a mathematical model of a certain type of vehicle starting lead-acid battery is established. Using the method of circuit analysis, the model parameters are identified by the known test data. In addition, battery charge model is simulated in each charge stage using the intelligent three-stage charge method, simulation waveform and test waveform fit very well, absolute errors between them reach to 10-6. Simulation results show that the mathematical model and its analysis method is proper for the charge characteristics of vehicle starting lead-acid battery. This has a good guidance to design intelligent charger and extend the battery life.

scholarly journals Experimental studies of iron transformations kinetics and autocatalysis during its physicochemical removal from underground water

2021 ◽  
Author(s):  
S. Yu Martynov ◽  
V. L. Poliakov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Experimental Studies ◽  
Underground Water ◽  
Model Parameters ◽  
Kinetic Coefficients ◽  
Transfer Equations ◽  
The Mathematical Model ◽  
Autocatalytic Effect ◽  
Forms Of Iron

Abstract The mathematical model of physicochemical iron removal from groundwater was developed. It consists of three interrelated compartments. The results of the experimental research provide information in support of the first two compartments of the mathematical model. The dependencies for the concentrations of the adsorbed ferrous iron and deposited hydroxide concentrations are obtained as a result of the exact solution of the system of the mass transfer equations for two forms of iron in relation to the inlet surface of the bed. An analysis of the experimental data of the dynamics of the deposit accumulation in a small bed sample was made, using a special application that allowed to select the values of the kinetic coefficients and other model parameters based on these dependencies. We evaluated the autocatalytic effect on the dynamics of iron ferrous and ferric forms. The verification of the mathematical model was carried out involving the experimental data obtained under laboratory and industrial conditions.

scholarly journals Discovery of the spatial pattern of prickles on the stem of the rose and the mathematical model of the pattern

2019 ◽  
Author(s):  
Kazuaki Amikura ◽  
Hiroshi Ito
Keyword(s):  
Mathematical Model ◽  
Spatial Pattern ◽  
Plant Species ◽  
Statistical Data ◽  
Model Parameters ◽  
Developmental Patterns ◽  
The Mathematical Model ◽  
The Rose

Reproducible pattern is a key characteristic of organisms. Many developmental patterns are known that it is orchestrated by diffusion of the factors. Herein, we reported a novel patterning that seems to be controlled by diffusion factors. Although it looks like the prickles randomly emerge on the stem of rose, we deciphered patterns for the position of prickles with statistical data and proposed a mathematical model to explain the process via which the pattern emerged. By changing the model parameters, we reproduce another pattern on other plant species. This finding indicates that the patterns between many species are organized by similar systems. Moreover, although the pattern of organisms is often linked to its function, we consider the spatial pattern of prickles may have a function to play the role of prickles effectively. Further studies will clarify the role of prickles and reveal the entity of diffusive factors.

scholarly journals Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia

2019 ◽  
Vol 24 (1) ◽  
pp. 6 ◽  
Author(s):  
Gilberto C. González-Parra ◽  
Diego F. Aranda ◽  
Benito Chen-Charpentier ◽  
Miguel Díaz-Rodríguez ◽  
Jaime E. Castellanos
Keyword(s):  
Mathematical Model ◽  
Chikungunya Virus ◽  
Sufficient Conditions ◽  
Population Level ◽  
Specific Model ◽  
Model Parameters ◽  
Epidemic Threshold ◽  
Monte Carlo Techniques ◽  
Health Institutions

The Chikungunya virus is the cause of an emerging disease in Asia and Africa, and also in America, where the virus was first detected in 2006. In this paper, we present a mathematical model of the Chikungunya epidemic at the population level that incorporates the transmission vector. The epidemic threshold parameter R 0 for the extinction of disease is computed using the method of the next generation matrix, which allows for insights about what are the most relevant model parameters. Using Lyapunov function theory, some sufficient conditions for global stability of the the disease-free equilibrium are obtained. The proposed mathematical model of the Chikungunya epidemic is used to investigate and understand the importance of some specific model parameters and to give some explanation and understanding about the real infected cases with Chikungunya virus in Colombia for data belonging to the year 2015. In this study, we were able to estimate the value of the basic reproduction number R 0 . We use bootstrapping and Markov chain Monte Carlo techniques in order to study parameters’ identifiability. Finally, important policies and insights are provided that could help government health institutions in reducing the number of cases of Chikungunya in Colombia.

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