Transient diffraction grating measurements of molecular diffusion in the undergraduate laboratory

Spiegel, Daniel R.; Tuli, Santona

doi:10.1119/1.3581702

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…In connection with the pandemic, diffusion has been discussed, e.g., in [ 1 , 7 , 12 ]. The diffusion being a central process in many biological, social, chemical and physical systems is considered in [ 6 , 44 ]. A similar model but in another context has been discussed in [ 13 ].…”

Section: A Mathematical Diffusion Model To Respect Spatial Virus Propagationmentioning

confidence: 99%

Modeling of COVID-19 propagation with compartment models

Bärwolff

2021

Math Semesterber

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The current pandemic is a great challenge for several research areas. In addition to virology research, mathematical models and simulations can be a valuable contribution to the understanding of the dynamics of the pandemic and can give recommendations to both physicians and politicians. In this paper we give an overview about mathematical models to describe the pandemic by differential equations. As a matter of principle the historic origin of the epidemic growth models will be remembered. Moreover we discuss models for the actual pandemic of 2020/2021. This will be done based on actual data of people infected with COVID-19 from the European Centre for Disease Prevention and Control (ECDC), input parameters of mathematical models will be determined and applied. These parameters will be estimated for the UK, Italy, Spain, and Germany and used in a SIR-type model. As a basis for the model’s calibration, the initial exponential growth phase of the COVID-19 pandemic in the named countries is used. Strategies for the commencing and ending of social and economic shutdown measures are discussed. To respect heterogeneity of the people density in the different federal states of Germany diffusion effects are considered.

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Section: A Mathematical Diffusion Model To Respect Spatial Virus Propagationmentioning

confidence: 99%

Modeling of COVID-19 propagation with compartment models

Bärwolff

2021

Math Semesterber

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“…In connection with the pandemic, diffusion has been discussed, e.g., in [9][10][11]. The diffusion being a central process in many biological, social, chemical and physical systems is considered in [12,13]. A similar model but in another context has been discussed in [14].…”

Section: The Mathematical Diffusion Modelmentioning

confidence: 99%

A Local and Time Resolution of the COVID-19 Propagation—A Two-Dimensional Approach for Germany Including Diffusion Phenomena to Describe the Spatial Spread of the COVID-19 Pandemic

Bärwolff

2021

Physics

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The understanding of factors that affect the dissemination of a viral infection is fundamental to help combat it. For instance, during the COVID-19 pandemic that changed the lives of people all over the world, one observes regions with different incidences of cases. One can speculate that population density might be one of the variables that affect the incidence of cases. In populous areas, such as big cities or congested urban areas, higher COVID-19 incidences could be observed than in rural regions. It is natural to think that if population density is such an important factor, then a gradient or difference in population density might lead to a diffusion process that will proceed until equilibrium is reached. The aim of this paper consists of the inclusion of a diffusion concept into the COVID-19 modeling. With this concept, one covers a gradient-driven transfer of the infection next to epidemic growth models (SIR-type models). This is discussed for a certain period of the German situation based on the quite different incidence data for the different federal states of Germany. With this ansatz, some phenomena of the actual development of the pandemic are found to be confirmed. The model provides a possibility to investigate certain scenarios, such as border-crossings or local spreading events, and their influence on the COVID-19 propagation. The resulting information can be a basis for the decisions of politicians and medical persons in charge of managing a pandemic.

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“…The end of the year of 2019 and beginning of 2020 has been dominated by the spread of the coronavirus (COVID- 19). The disease started in the Hubei province in China in December 2019 and by early January 2020 started to spread.…”

Section: Introductionmentioning

confidence: 99%

Diffusion as a First Model of Spread of Viral Infection

Acioli

2020

Preprint

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The appearance of the coronavirus in late 2019 has dominated the news in the last few months as it developed into a pandemic. In every mathematics and physics classroom, instructors are using the time series of the number of cases to show exponential growth of the infection. In this manuscript we propose a simple diffusion process as the mode of spreading infections. This model is less sophisticated than other models in the literature, but it can capture the exponential growth and it can explain it in terms of mobility (diffusion constant), population density, and probability of transmission. Students can change the parameters and determine the growth rate and predict the total number of cases as a function of time. Students are also given the opportunity to add other factors that are not considered in the simple diffusion model.

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Transient diffraction grating measurements of molecular diffusion in the undergraduate laboratory

Cited by 5 publications

References 21 publications

Modeling of COVID-19 propagation with compartment models

Modeling of COVID-19 propagation with compartment models

A Local and Time Resolution of the COVID-19 Propagation—A Two-Dimensional Approach for Germany Including Diffusion Phenomena to Describe the Spatial Spread of the COVID-19 Pandemic

Diffusion as a First Model of Spread of Viral Infection

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