scholarly journals Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases

2021 ◽  
Vol 8 ◽  
Author(s):  
Heather Z. Brooks ◽  
Unchitta Kanjanasaratool ◽  
Yacoub H. Kureh ◽  
Mason A. Porter
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Mathematical Models ◽  
Human Behavior ◽  
Government Policies ◽  
Disease Spread

The COVID-19 pandemic has led to significant changes in how people are currently living their lives. To determine how to best reduce the effects of the pandemic and start reopening communities, governments have used mathematical models of the spread of infectious diseases. In this article, we introduce a popular type of mathematical model of disease spread. We discuss how the results of analyzing mathematical models can influence government policies and human behavior, such as encouraging mask wearing and physical distancing to help slow the spread of a disease.

scholarly journals Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases

2020 ◽  
Author(s):  
Heather Z. Brooks ◽  
Unchitta Kanjanasaratool ◽  
Yacoub H. Kureh ◽  
Mason A. Porter
Keyword(s):  
Infectious Diseases ◽  
Mathematical Models ◽  
Human Behavior ◽  
Compartmental Models ◽  
Government Policies

The COVID-19 pandemic has led to significant changes in how people are currently living their lives. To determine how to best reduce the effects of the pandemic and start reopening societies, governments have drawn insights from mathematical models of the spread of infectious diseases. In this article, we give an introduction to a family of mathematical models (called “compartmental models”) and discuss how the results of analyzing these models influence government policies and human behavior, such as encouraging mask wearing and physical distancing to help slow the spread of the disease.

scholarly journals Analysis of infectious disease transmission and prediction through SEIQR epidemic model

2021 ◽  
Vol 8 (1) ◽  
pp. 75-86
Author(s):  
Swati Tyagi ◽  
Shaifu Gupta ◽  
Syed Abbas ◽  
Krishna Pada Das ◽  
Baazaoui Riadh
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Disease Transmission ◽  
Disease Spread ◽  
Infectious Disease Transmission ◽  
Control Measurement ◽  
Dynamics And Control ◽  
The Stability ◽  
And Control ◽  
Special Case

Abstract In literature, various mathematical models have been developed to have a better insight into the transmission dynamics and control the spread of infectious diseases. Aiming to explore more about various aspects of infectious diseases, in this work, we propose conceptual mathematical model through a SEIQR (Susceptible-Exposed-Infected-Quarantined-Recovered) mathematical model and its control measurement. We establish the positivity and boundedness of the solutions. We also compute the basic reproduction number and investigate the stability of equilibria for its epidemiological relevance. To validate the model and estimate the parameters to predict the disease spread, we consider the special case for COVID-19 to study the real cases of infected cases from [2] for Russia and India. For better insight, in addition to mathematical model, a history based LSTM model is trained to learn temporal patterns in COVID-19 time series and predict future trends. In the end, the future predictions from mathematical model and the LSTM based model are compared to generate reliable results.

scholarly journals Design of Epidemic Prevention Medical Special Clothing Based on Mathematical Model Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hubin Liu ◽  
Qi Xu ◽  
Shan Wu ◽  
Yulong Liu
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Mathematical Models ◽  
Pathogenic Bacteria ◽  
Quality Evaluation ◽  
Model Analysis ◽  
Analytic Hierarchy ◽  
Protective Function ◽  
Clothing Design ◽  
Mathematical Model Analysis

Among the many diseases, the harm of infectious diseases is undoubtedly the first in terms of the scope of the disease and the threat to humans. In addition, most infectious diseases were regarded as terminal illnesses in the early stage of the outbreak. For example, smallpox and plague in history have even chosen to isolate patients and abandon them to prevent the spread of infectious diseases due to the lack of protection and treatment methods. Therefore, in the treatment of infectious diseases, epidemic prevention is very important. Based on this, this article discusses the research of special medical clothing design for epidemic prevention based on mathematical model analysis, hoping to provide strong help and support for epidemic prevention. First of all, this article understands the application status of mathematical models in the medical field and clothing design industry through literature research. Then, according to the functional requirements of antiepidemic medical special clothing in terms of protection from virus invasion and infection by other contact methods, this article established an antiepidemic clothing quality evaluation index system. Then, this article designs a simulation penetration test of pathogenic bacteria to test the protective function of the antiepidemic clothing and uses mathematical models to analyze the molecular structure and physical properties of the antiepidemic clothing materials. Finally, this article builds an analytic hierarchy model for the quality evaluation of epidemic prevention clothing based on the principle of analytic hierarchy process, analyzes the simulated experimental data and predicts the service life of the epidemic prevention clothing according to the performance degradation so that medical staff can replace it in time. The experimental results show that with the aid of mathematical model analysis, the quality of the epidemic prevention clothing is higher than the previous antiepidemic clothing design in terms of epidemic prevention performance, and in addition to the disposable epidemic prevention clothing, the multiple-use epidemic prevention clothing is not serious in the epidemic. Under these circumstances, it can maintain the antiepidemic performance for more than 2 months.

scholarly journals Modeling the onset of symptoms of COVID-19: Effects of SARS-CoV-2 variant

2021 ◽  
Vol 17 (12) ◽  
pp. e1009629
Author(s):  
Joseph R. Larsen ◽  
Margaret R. Martin ◽  
John D. Martin ◽  
James B. Hicks ◽  
Peter Kuhn
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Symptom Onset ◽  
Reference Strain ◽  
Viral Disease ◽  
Disease Spread ◽  
Infected People ◽  
The Usa ◽  
Using Data ◽  
Pharmaceutical Interventions

Identifying order of symptom onset of infectious diseases might aid in differentiating symptomatic infections earlier in a population thereby enabling non-pharmaceutical interventions and reducing disease spread. Previously, we developed a mathematical model predicting the order of symptoms based on data from the initial outbreak of SARS-CoV-2 in China using symptom occurrence at diagnosis and found that the order of COVID-19 symptoms differed from that of other infectious diseases including influenza. Whether this order of COVID-19 symptoms holds in the USA under changing conditions is unclear. Here, we use modeling to predict the order of symptoms using data from both the initial outbreaks in China and in the USA. Whereas patients in China were more likely to have fever before cough and then nausea/vomiting before diarrhea, patients in the USA were more likely to have cough before fever and then diarrhea before nausea/vomiting. Given that the D614G SARS-CoV-2 variant that rapidly spread from Europe to predominate in the USA during the first wave of the outbreak was not present in the initial China outbreak, we hypothesized that this mutation might affect symptom order. Supporting this notion, we found that as SARS-CoV-2 in Japan shifted from the original Wuhan reference strain to the D614G variant, symptom order shifted to the USA pattern. Google Trends analyses supported these findings, while weather, age, and comorbidities did not affect our model’s predictions of symptom order. These findings indicate that symptom order can change with mutation in viral disease and raise the possibility that D614G variant is more transmissible because infected people are more likely to cough in public before being incapacitated with fever.

A mathematical model and an algorithm for sampling sets of components on the Assembly enterprises of space technology

2018 ◽  
Vol 15 (1) ◽  
pp. 39-55
Author(s):  
V. B. Rudakov ◽  
V. M. Makarov ◽  
M. I. Makarov
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Space Technology ◽  
Economic Costs ◽  
Problem Statement ◽  
Optimal Plan ◽  
Product Mix ◽  
Technical Parameters ◽  
Complex Products ◽  
Assembly Plants

The article considers the problem of determining the rational plans of the input sampling reliability and technical parameters of components of space technology, the totality of which is supplied to the Assembly plants for the manufacture of complex products of space technology. Problem statement and mathematical model based on the minimization of the economic costs of control and losses related to the risks of taking wrong decisions, are given in the article. The properties of the mathematical models are investigated, the algorithm for its optimization is developed. The result is an optimal plan for the sampling of sets of components, which includes: an optimal product mix subject to mandatory control of the aggregate and optimum risks of first and second kind, when acceptance number of statistical plan is zero. The latter circumstance is due to the high requirements of reliability and technical parameters of products of space technology.

Rapid determination of glomerular filtration rate by single-bolus inulin: a comparison of estimation analyses

1998 ◽  
Vol 84 (6) ◽  
pp. 2154-2162 ◽  
Author(s):  
Cord Sturgeon ◽  
Albert D. Sam ◽  
William R. Law
Keyword(s):  
Mathematical Model ◽  
Glomerular Filtration Rate ◽  
Mathematical Models ◽  
Glomerular Filtration ◽  
Filtration Rate ◽  
Rapid Determination ◽  
Constant Infusion ◽  
Sprague Dawley ◽  
Single Bolus ◽  
Sprague Dawley Rats

Rapid measurement of glomerular filtration rate (GFR) by an inulin single-bolus technique would be useful, but its accuracy has been questioned. We hypothesized that reported inaccuracies reflect the use of inappropriate mathematical models. GFR was measured in 14 intact and 5 unilaterally nephrectomized conscious male Sprague-Dawley rats (mean weight 368 ± 12 g) by both single-bolus (25 mg/kg) and constant-infusion techniques (0.693 mg ⋅ kg−1 ⋅ min−1). The temporal decline in plasma inulin concentration was analyzed through biexponential curve fitting, which accounted for renal inulin loss before complete vascular and interstitial mixing. We compared our mathematical model based on empirical rationale with those of other investigators whose studies suggest inaccuracy of single-bolus methods. Our mathematical model yielded GFR values by single bolus that agreed with those obtained by constant infusion [slope = 0.94 ± 0.16 (SE); y intercept = 0.23 ± 0.64; r = 0.82]. In comparison to the data obtained by constant inulin infusion, this method yielded a very small bias of −0.0041 ± 0.19 ml/min. Two previously reported models yielded unsatisfactory values (slope = 1.46 ± 0.34, y intercept = 0.47 ± 1.5, r = 0.72; and slope = 0.17 ± 1.26, y intercept = 17.15 ± 5.14, r = 0.03). The biases obtained by using these methods were −2.21 ± 0.42 and −13.90 ± 1.44 ml/min, respectively. The data indicate that when appropriate mathematical models are used, inulin clearance after single-bolus delivery can be used to measure GFR equivalent to that obtained by constant infusion of inulin. Attempts to use methods of analysis for simplicity or expediency can result in unacceptable measurements relative to the clinical range of values seen.

scholarly journals A Framework of an Integrated Livestock Vehicle Trajectory Database Using Digital Tachograph Data

2021 ◽  
Vol 13 (5) ◽  
pp. 2694
Author(s):  
Heehyeon Jeong ◽  
Jungyeol Hong ◽  
Dongjoo Park
Keyword(s):  
Infectious Diseases ◽  
African Swine Fever Virus ◽  
African Swine Fever ◽  
Disease Spread ◽  
Transportation Engineering ◽  
The Public ◽  
Vehicle Trajectories ◽  
History Of ◽  
Vehicle Trajectory ◽  
Livestock Diseases

The outbreak of African swine fever virus has raised global concerns regarding epidemic livestock diseases. Therefore, various studies have attempted to prevent and monitor epidemic livestock diseases. Most of them have emphasized that integrated studies between the public health and transportation engineering are essential to prevent the livestock disease spread. However, it has been difficult to obtain big data related to the mobility of livestock-related vehicles. Thus, it is challenging to conduct research that comprehensively considers cargo vehicles’ movement carrying livestock and the spread of livestock infectious diseases. This study developed the framework for integrating the digital tachograph data (DTG) and trucks’ visit history of livestock facility data. The DTG data include commercial trucks’ coordinate information, but it excludes actual livestock-related vehicle trajectories such as freight types and facility visit history. Therefore, the integrated database we developed can be used as a significant resource for preventing the spread of livestock epidemics by pre-monitoring livestock transport vehicles’ movements. In future studies, epidemiological research on infectious diseases and livestock species will be able to conduct through the derived integrating database. Furthermore, the indicators of the spread of infectious diseases could be suggested based on both microscopic and macroscopic roadway networks to manage livestock epidemics.

Twin Models

1970 ◽  
Vol 19 (1-2) ◽  
pp. 141-141
Author(s):  
L. Gedda ◽  
G. Brenci ◽  
M. T. Lun
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Genetic Parameters ◽  
Simultaneous Recording ◽  
Theoretical Relationship ◽  
Twin Models

The theoretical relationship between the distribution of a given trait in a population of twin pairs and several genetic parameters has been examined. In particular, a series of mathematical models has been worked out, that, when applied to a twin population, nonselected for the occurrence of a given trait and nondiagnosed as to zygosity, leads to an estimate of:1) The MZ: DZ ratio in the population;2) The frequency of the genotype responsible for a given trait;3) The probability of manifestation of the trait;4) The value of epistatic factors.A further mathematical model affords the estimate of linkage in the hypothesis of simultaneous recording of more than one trait.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

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