Mathematical models of the world

Synthese ◽  
1975 ◽  
Vol 31 (2) ◽  
pp. 211-227 ◽  
Author(s):  
David Berlinski
Keyword(s):  
Mathematical Models ◽  
The World

3. Do you believe in models? Simplicity and complexity

2018 ◽  
pp. 34-47
Author(s):  
Alain Goriely
Keyword(s):  
Mathematical Modelling ◽  
Mathematical Models ◽  
Applied Mathematics ◽  
Abstract Representation ◽  
The World ◽  
Insight Into

Models are central to the world of applied mathematics. In its simplest sense, a model is an abstract representation of a system developed in order to answer specific questions or gain insight into a phenomenon. In general, we expect a model to be based on sound principles, to be mathematically consistent, and to have some predictive or insight value. Models are the ultimate form of quantification since all variables and parameters that appear must be properly defined and quantified for the equations to make sense. ‘Do you believe in models? Simplicity and complexity’ discusses the complexity of models; the steps involved in developing mathematical models—the physics paradigm; and collaborative mathematical modelling.

scholarly journals Modelling ecological systems in a changing world

2012 ◽  
Vol 367 (1586) ◽  
pp. 181-190 ◽  
Author(s):  
Matthew R. Evans
Keyword(s):  
Environmental Change ◽  
Mathematical Models ◽  
Ecological Systems ◽  
Ecological Modelling ◽  
Causal Relationships ◽  
Future State ◽  
The World ◽  
The Future ◽  
The Impact ◽  
The Way

The world is changing at an unprecedented rate. In such a situation, we need to understand the nature of the change and to make predictions about the way in which it might affect systems of interest; often we may also wish to understand what might be done to mitigate the predicted effects. In ecology, we usually make such predictions (or forecasts) by making use of mathematical models that describe the system and projecting them into the future, under changed conditions. Approaches emphasizing the desirability of simple models with analytical tractability and those that use assumed causal relationships derived statistically from data currently dominate ecological modelling. Although such models are excellent at describing the way in which a system has behaved, they are poor at predicting its future state, especially in novel conditions. In order to address questions about the impact of environmental change, and to understand what, if any, action might be taken to ameliorate it, ecologists need to develop the ability to project models into novel, future conditions. This will require the development of models based on understanding the processes that result in a system behaving the way it does, rather than relying on a description of the system, as a whole, remaining valid indefinitely.

Modeling and Analyses of the N-Link Bent-Arm PenduBot

2010 ◽  
Vol 171-172 ◽  
pp. 644-647
Author(s):  
Shao Qiang Yuan ◽  
Xin Xin Li
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Nonlinear Model ◽  
Condition Number ◽  
Kinematics And Dynamics ◽  
Controllability Matrix ◽  
Human Arm ◽  
The World ◽  
The Mathematical Model ◽  
Natural Characteristics

Bent-arm PenduBot is more similar to human arm, which attaches more and more robot experts’ attention around the world. As the foundation of the multi-link PenduBot control, the mathematical model should be established first. Based on the method of kinematics and dynamics, the N-link bent-arm PenduBot mathematical models are established in this paper, including the nonlinear model and the linear model. The natural characteristics of different pendulum are analyzed. By using the condition number of the controllability matrix, the control difficulty for higher order systems is compared.

scholarly journals The Prediction of the Lifetime of the COVID-19 Virus using Parameter-dependent New Mathematical Models

2021 ◽  
Author(s):  
K.SELVAKUMAR . .
Keyword(s):  
Public Health ◽  
Mathematical Models ◽  
Large Mass ◽  
Medical Problem ◽  
Data Set ◽  
The People ◽  
The World ◽  
The Usa ◽  
Model C ◽  
Death Count

Abstract This article is about a complex real-world human medical problem that people all over the world face, a major international public Health problem due to the new coronavirus disease 2019(COVID-19), a highly communicable infectious disease between humans. Spreads rapidly among humans of both sexes of all ages, in large masses in the cyclical manner(seasonally) causing disease in susceptible human Hosts affecting most of the organs in humans mainly lungs resulting in Severe Acute Respiratory Syndrome resulting in mass acute deaths. Acute deaths are more common with Comorbidities like Diabetes mellitus, Ischaemic heart disease, Liver disease, Kidney disease, Gut, etc. Now it is the major emergency international pandemic public health medical disease. On the face of the earth, there are large masses of infection and mass acute deaths due to COVID-19 virus infection and so the life of every individual is uncertain at any time. Because of the mass acute deaths from the COVID-19 virus infection, everyone in the world is scared. From now on, it is the responsibility of the researchers of all nations to bring hope to people. In this article, by predicting the lifetime of disease-causing virus, hope to the people is given, to better protect all people and speed up the immediate general pandemic preparedness within the lifespan of the virus. To accelerate actions to save people's lives, mathematical models will help make public health decisions and reduce mortality using the resources available during this time of the COVID-19 pandemic. In this article, to better protect people from disease preparedness for the virus and a general pandemic by predicting the lifetime of the disease-causing coronavirus, three new mathematical models which are dependent on parameters are proposed. The parameters in the model function model uncertainty of death due to the present international real-life problem caused by different strains of the COVID-19 virus. The first model is a model with six parameters and the second and third models are models with seven parameters respectively. These three models are the generalization of the three models of Phem . The errors due to the models of this article are minimized from the errors due to the models of Phem. These three models can predict the acute death count outside the data period and can predict the lifetime. To illustrate the applicability of the models a big data set of size 54 days starting from February 29, 2020, to April 22, 2020, of acute death counts of USA( United States of America) is considered. The main focus is on the USA due to the significant large mass of infection and large mass of acute death from the COVID-19 virus. As a result, everyone's life is uncertain about death at any time. Since it is a major international public health-related medical problem in humans, with an accuracy of 95% of confidence the results using three models are erected. The large mass of acute deaths due to the number of COVID-19 virus infections in the USA are fitted by the model functions of three mathematical models and a solution is found to an international problem. Based on the acute death rate, the lifetime of the COVID-19 virus is estimated to be 1484.76198616309920 days from the first day of acute death, February 29, 2020. In other words, there will be no mass acute deaths from the COVID-19 virus in the USA after April 2024 if the nation follows the guidelines of the WHO(World Health Organization) and the recommendations of the pathogen. And when the people and the government are very well prepared for this crisis then the spread of infection can be prevented, the people and government can be saved from the economic crisis, and many lives can be saved from mass acute deaths. A comparative study of all models is presented for different measures of errors. The acute death count of the USA outside the date of the data set of 54 days is predicted using three models. The data set misses some counts during the collection of data and it is identified. From the ratio of standard deviation and average acute deaths, it is predicted that the total acute death counts during 54 days will be 62,969. Using the standard deviation around the line of regression it is shown that in the data set a large count is missing during the collection of data of USA. Using the coefficient of determination it is predicted that the Model-C, provides 100% of fitness with the given data set and only 0.0% variation. All three models are suitable to fit the data set of acute death counts of the USA, but Model-C is the best and optimal among the three models. Tt is predicted from Model-A, Model-B, and Model-C the total acute death counts during 54 days will be 66537, 67085, and 68523 respectively. Since Model-C is the best and optimal model, the predicted total acute death counts during 54 days will be 68523. Finally, this article suggests various steps to help control the spread and severity of the new disease. The prediction of the lifetime and data count missing in the data set presented in this research article is entirely new and differs totally from all other articles in the literature. To accelerate actions to save people's lives, mathematical models will help make public health decisions and reduce mortality using the resources available during this time of the COVID-19 pandemic.

scholarly journals Keep your droplets to yourself: Universal use of face masks along with social distancing

2021 ◽  
Vol 19 (2) ◽  
pp. 114-123
Author(s):  
Helena Carvalho ◽  
Daniel Contaifer Jr ◽  
Renata N. Aranha ◽  
Juliana A. De Matos
Keyword(s):  
Hand Hygiene ◽  
Mathematical Models ◽  
Control Mechanism ◽  
Respiratory Infections ◽  
Experimental Studies ◽  
World Health ◽  
Source Control ◽  
The World ◽  
Viral Respiratory Infections ◽  
Viral Respiratory

Introduction: As the COVID-19 pandemic progresses aroundthe world, the universal use of face masks imposes itself as ameasure to mitigate the transmission of SARS-CoV-2 and iscurrently recommended by the World Health Organization.However, its effectiveness as a method of preventing COVID-19 is still controversial. Objective: To review the literatureon the universal use of facial masks, including fabric ones, andtheir recommendations for use. Methods: Narrative reviewof published studies on the topic. Results: Face masks act predominantlyas a source control mechanism, as they capturethe droplets expelled by the user when speaking, coughingor sneezing, protecting other people and the environmentfrom contamination by potentially infecting droplets. Evidenceof the effectiveness of its universal use as a method ofmitigating epidemics of viral respiratory infections is derivedfrom experimental studies and mathematical models. Properuse of facial masks is essential to ensure their effectivenessand prevent damage, and includes covering the nose, mouthand chin, washing the fabric masks with soap and water afteruse and hand hygiene several times a day, especially whenhandling the mask. Conclusions: The universal use of facialmasks in the context of the COVID-19 pandemic is justified,especially considering the occurrence of virus transmissionin the pre-symptomatic period, and should be adopted inconjunction with other measures such as adequate socialdistance and hygiene from the hands, following the motto“I protect you and you protect me”.

scholarly journals The development of scientific outlook of students when teaching inverse problems for differential equations

2019 ◽  
Vol 16 (1) ◽  
pp. 46-55
Author(s):  
Viktor Semenovich Kornilov
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Research Work ◽  
Teaching Experience ◽  
Physical Processes ◽  
Mathematical Methods ◽  
Important Place ◽  
The World ◽  
Scientific Worldview

Problem and goal. Modern achievements of the world Science of nature and the world, physical laws and laws should be disclosed at an accessible level to University students. Among the scientific methods of research of physical processes and phenomena, an important place is the method of mathematical modeling, because mathematical models have scientific and cognitive potential and versatility (see, for example, [2-4]). The use of mathematical models of inverse problems for differential equations (IPDE) allows to effectively investigate many processes and phenomena occurring in the air, earth and water environment. It is not surprising that in some Russian universities in the physical and mathematical areas of training are taught IPDE in the form of a choice of courses. The goals and objectives of such teaching are set, as a result of which students would develop creative mathematical abilities, formed fundamental knowledge in the field of physical education, developed a scientific worldview. Methodology. The development of scientific outlook of students of physical and mathematical directions of preparation, as a result of teaching IPDE, ensured the successful will be implemented in practice, such conditions as: 1. the involvement of experts in the field IPDE with teaching experience at the university; 2. development of the content of lectures and practical classes on the basis of modern achievements of the theory of inverse and incorrect problems, taking into account the professional orientation of training students; 3. the implementation of the principles, methods and means of education IPDE; 4. involvement of students in research work in scientific seminars and participation in scientific conferences devoted to IPDE; 5. implementation of methodological approaches that allow students to develop the skills and abilities of independent analysis of applied and humanitarian nature of the results of research of IPDE. Results. In practical classes on the IPDE students acquire the ability and skills to apply effective approaches and mathematical methods of finding solutions to inverse problems, followed by a logical analysis of their solutions. As a result, students gain useful experience in the analysis of new information about the studied physical processes and phenomena, form new scientific knowledge about the world on the basis of which develop a scientific worldview. Conclusion. Developed, in the process of teaching IPDE, the scientific outlook helps students to understand that mathematical models IPDE are relevant to theory, experiment and philosophy - the basic methods of knowledge researchers; to understand the humanitarian value of mathematical models IPDE.

scholarly journals Mathematical Modeling to Perform an Analysis of Social Isolation Periods in the Dissemination of COVID-19

2021 ◽  
Vol 22 (4) ◽  
pp. 595-608
Author(s):  
A. Molter ◽  
R. S. Quadros ◽  
M. Rafikov ◽  
D. Buske ◽  
G. A. Gonçalves
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Social Isolation ◽  
Computer Simulations ◽  
The Other ◽  
Stable Level ◽  
The Social ◽  
The World ◽  
Second Peak

The outbreak of COVID-19 has made scientists from all over the world do not measureefforts to understand the dynamics of the disease caused by this coronavirus. Several mathematical models have been proposed to describe the dynamics and make predictions. This work proposes a mathematical model that includes social isolation of susceptible individuals as a strategy of suppression and mitigation of the disease. The Susceptible-Infectious-Isolated-Recovered-Dead (SIQRD) model is proposed to analyze three important issues about the dynamics of the disease taking into account social isolation: when the isolation should begin? How long to keep the isolation? How to get out of this isolation? To get answers, computer simulations are provided and their results discussed. The results obtained show that beginning social isolation on the 10th or 15th days, after confirmation of the 50th case, and with 70% of the population in isolation, seems to be promising, since the infected curve does not grow much until it enters the isolation and remains at a stable level during the isolation. On the other hand an abrupt release of the social isolation will imply a second peak of infected individuals above the first one, which is not desired. Therefore, the release from social isolation should be gradual.

scholarly journals Differential equation analysis on COVID-19

2020 ◽  
Vol 2 (1) ◽  
pp. 01-11
Author(s):  
Bin Zhao
Keyword(s):  
Infectious Diseases ◽  
Mathematical Models ◽  
Hubei Province ◽  
Chinese Government ◽  
Second Phase ◽  
The Novel ◽  
The World ◽  
Response Measures ◽  
The Government ◽  
Novel Coronavirus

Background: An infectious disease caused by a novel coronavirus called COVID-19 has raged across the world since December 2019. The novel coronavirus first appeared in Wuhan, China, and quickly spread to Asia and now many countries around the world are affected by the epidemic. The deaths of many patients, including medical staff, caused social panic, media attention, and high attention from governments and world organizations. Today, with the joint efforts of the government, the doctors and all walks of life, the epidemic in Hubei Province has been brought under control, preventing its spread from affecting the lives of the people. Because of its rapid spread and serious consequences, this sudden novel coronary pneumonia epidemic has become an important social hot spot event. Through the analysis of the novel coronary pneumonia epidemic situation, we can also have a better understanding of sudden infectious diseases in the future, so that we can take more effective response measures, establish a truly predictable and provide reliable and sufficient information for prevention and control model. Methods: We establish different models according to the different developments of the epidemic situation, different time points, and different response measures taken by the government. To be specific, during the period of 2020.1.23-2020.2.7, the traditional SIR model is adopted; during the period of 2020.2.8-2020.3.30, according to the scientific research results, it was considered that the novel coronary pneumonia has a latent period, so in the later phase of epidemic development, the government has effectively isolated patients, thus we adopt the SEIQR model accordingly. During the period of 2020.3.31-2020.5.16, because more asymptomatic infected people were found, we use the SEIQLR model to fit. Finally, through a SEIR simulator, considering the susceptible number, the latent number, the infected number, the cured number, death number and other factors, we simulate the change of various numbers of people from the beginning to the next 180 days of novel coronary pneumonia. Findings: The results based on the analysis of differential equations and kinetic models show that through the prediction of the model established in the first phase, the epidemic situation of novel coronary pneumonia in Hubei Province was controlled at the end of March, which is in line with the actual situation. The rest of Hubei province, except for Wuhan, lifted control of the departure channel from 0:00 am on March 25, and Wuhan was also unblocked on April 8. Through the establishment of the second-phase model, it is found that the epidemic situation will reach its peak in mid-February. For example, the quarantine admission of the hospital declined after mid-February, which is inseparable from the measures to build square cabin hospitals in early February so that more and more patients can be admitted. The model established in the third phase shows that the epidemic had been completely controlled by the end of May, which is also in line with the reality. Because in mid-May, the Wuhan government conducted a nucleic acid test on all the citizens to screen for asymptomatic infected persons to fundamentally control the spread of novel coronary pneumonia. Interpretation: Hubei Province, as the center of the initial outbreak of novel coronary pneumonia, people were forced to be isolated at home during the Spring Festival, the most important Chinese holiday, and the whole society was in a state of suspension of work and study. The Chinese government had taken many measures in response to the epidemic, such as shutting down the city, vigorously building square cabin hospitals, and prohibiting people from gathering. At the beginning of May this year, the epidemic in Hubei Province was finally effectively controlled. For ordinary citizens, we should not cause unnecessary panic about the unknown novel coronavirus. Instead, we should fully understand and be familiar with this virus. In addition to the relevant medical knowledge, we should also understand the spread of infectious diseases through appropriate mathematical models. By mathematical models, we can understand the degree of harm of infectious diseases, when to control it, how to stop it, and use scientific views to reveal the original face of the novel coronavirus to the public without causing social panic.

scholarly journals Forecasting the Stability of COVID-19 on Indian Dataset with Prophet Logistic Growth Model 

2020 ◽  
Author(s):  
Nishtha Phutela ◽  
Arushi G Bakshi ◽  
Sunil Gupta ◽  
Goldie Gabrani
Keyword(s):  
Infectious Disease ◽  
Mathematical Models ◽  
Growth Model ◽  
Logistic Growth ◽  
The World ◽  
Logistic Growth Model ◽  
The Stability

Abstract Recently COVID-2019, a highly infectious disease has been declared as Pandemic by WHO, and since then the researchers all over the world are making attempts to predict the likely progression of this pandemic using various mathematical models. In this paper, we are using logistic growth model to find out the stability of this pandemic and Prophet Model to forecast the total number of confirmed cases that would be caused by COVID-19 in India.

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