scholarly journals Time-continuous and time-discrete SIR models revisited: theory and applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Benjamin Wacker ◽  
Jan Schlüter
Keyword(s):  
Computer Science ◽  
Unique Solvability ◽  
Interdisciplinary Research ◽  
Numerical Scheme ◽  
Sir Model ◽  
Implicit Time ◽  
Time Varying ◽  
Mathematical Epidemiology ◽  
Continuous Version ◽  
Discrete Sir Model

Abstract Since Kermack and McKendrick have introduced their famous epidemiological SIR model in 1927, mathematical epidemiology has grown as an interdisciplinary research discipline including knowledge from biology, computer science, or mathematics. Due to current threatening epidemics such as COVID-19, this interest is continuously rising. As our main goal, we establish an implicit time-discrete SIR (susceptible people–infectious people–recovered people) model. For this purpose, we first introduce its continuous variant with time-varying transmission and recovery rates and, as our first contribution, discuss thoroughly its properties. With respect to these results, we develop different possible time-discrete SIR models, we derive our implicit time-discrete SIR model in contrast to many other works which mainly investigate explicit time-discrete schemes and, as our main contribution, show unique solvability and further desirable properties compared to its continuous version. We thoroughly show that many of the desired properties of the time-continuous case are still valid in the time-discrete implicit case. Especially, we prove an upper error bound for our time-discrete implicit numerical scheme. Finally, we apply our proposed time-discrete SIR model to currently available data regarding the spread of COVID-19 in Germany and Iran.

scholarly journals Mathematical Analysis, Model and Prediction of COVID-19 Data

2020 ◽  
Author(s):  
Yit Chow Tong
Keyword(s):  
Mathematical Analysis ◽  
Interdisciplinary Research ◽  
Sir Model ◽  
Time Varying ◽  
Analysis Model ◽  
Growth Constant ◽  
Future Projections ◽  
Mathematical Procedure ◽  
Discrete Sir Model ◽  
Effective Growth

A simple and effective mathematical procedure for the description of observed COVID-19 data and calculation of future projections is presented. An exponential function E(t) with a time-varying Growth Constant k(t) is used. E(t) closely approximates observed COVID-19 Daily Confirmed Cases with NRMSDs of 1 to 2%. An example of prediction of future cases is presented. The Effective Growth Rates of a discrete SIR model were estimated on the basis of k(t) for COVID-19 data for Germany, and were found to be consistent with those reported in a previous study (1). The proposed procedure, which involves less than ten basic algebraic, logarithm and exponentiation operations for each data point, is suitable for use in promoting interdisciplinary research, exchange and sharing of information.

scholarly journals Digital—A New Open Access Journal to Report on Recent IT Advancements and Their Implementations for Interdisciplinary Research

Digital ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 64-65
Author(s):  
Yannis Manolopoulos
Keyword(s):  
Open Access ◽  
Computer Science ◽  
Interdisciplinary Research ◽  
Open Access Journal ◽  
Scientific Discipline

Many decades back, Computer Science emerged as a new scientific discipline at the crossroads of mathematics, physics and engineering [...]

A Modified Discrete SIR Model

2003 ◽  
Vol 34 (5) ◽  
pp. 399 ◽  
Author(s):  
Jennifer Switkes
Keyword(s):  
Sir Model ◽  
Discrete Sir Model

scholarly journals Estimating SARS-CoV-2 infections from deaths, confirmed cases, tests, and random surveys

2021 ◽  
Vol 118 (31) ◽  
pp. e2103272118
Author(s):  
Nicholas J. Irons ◽  
Adrian E. Raftery
Keyword(s):  
Herd Immunity ◽  
The United States ◽  
Sir Model ◽  
Mitigation Strategies ◽  
Time Varying ◽  
Fatality Rate ◽  
Multiple Sources ◽  
Population Prevalence ◽  
Sample Testing ◽  
True Infection

There are multiple sources of data giving information about the number of SARS-CoV-2 infections in the population, but all have major drawbacks, including biases and delayed reporting. For example, the number of confirmed cases largely underestimates the number of infections, and deaths lag infections substantially, while test positivity rates tend to greatly overestimate prevalence. Representative random prevalence surveys, the only putatively unbiased source, are sparse in time and space, and the results can come with big delays. Reliable estimates of population prevalence are necessary for understanding the spread of the virus and the effectiveness of mitigation strategies. We develop a simple Bayesian framework to estimate viral prevalence by combining several of the main available data sources. It is based on a discrete-time Susceptible–Infected–Removed (SIR) model with time-varying reproductive parameter. Our model includes likelihood components that incorporate data on deaths due to the virus, confirmed cases, and the number of tests administered on each day. We anchor our inference with data from random-sample testing surveys in Indiana and Ohio. We use the results from these two states to calibrate the model on positive test counts and proceed to estimate the infection fatality rate and the number of new infections on each day in each state in the United States. We estimate the extent to which reported COVID cases have underestimated true infection counts, which was large, especially in the first months of the pandemic. We explore the implications of our results for progress toward herd immunity.

scholarly journals Predicting the early depleting transmission dynamics of COVID-19: A time-varying SIR model

2020 ◽  
Author(s):  
Kian Boon Law ◽  
Kalaiarasu M Peariasamy ◽  
Balvinder Singh Gill ◽  
Sarbhan Singh Lakha Singh ◽  
Bala Murali Sundram ◽  
...  
Keyword(s):  
Temporal Trends ◽  
Model Fitting ◽  
Sir Model ◽  
Transmission Dynamics ◽  
Time Varying ◽  
Force Of Infection ◽  
Planning And Control ◽  
The Mean ◽  
And Control ◽  
Absolute Percent Error

Abstract The susceptible-infectious-removed (SIR) model offers the simplest framework to study transmission dynamics of COVID-19, however, it does not factor in its early depleting trend observed during a lockdown. We modified the SIR model to specifically simulate the early depleting transmission dynamics of COVID-19 to better predict its temporal trend in Malaysia. The classical SIR model was fitted to observed total (I total), active (I), and removed (R) cases of COVID-19 before lockdown to estimate the basic reproduction number. Next, the model was modified with a partial time-varying force of infection, given by a proportionally depleting transmission coefficient, βt, and a fractional term, z. The modified SIR model was then fitted to observed data over 6 weeks during the lockdown. Model fitting and projection were validated using the mean absolute percent error (MAPE). The transmission dynamics of COVID-19 was interrupted immediately by the lockdown. The modified SIR model projected the depleting temporal trends with lowest MAPE for I total, followed by I, I daily, and R. During lockdown, the dynamics of COVID-19 depleted at a rate of 4·7% each day with a decreased capacity of 40%. For 7–day and 14–day projections, the modified SIR model accurately predicted I total, I, and R. The depleting transmission dynamics for COVID-19 during lockdown can be accurately captured by time-varying SIR model. Projection generated based on observed data is useful for future planning and control of COVID-19.

scholarly journals Coworking, a Way to Achieve Sustainable Mobility? Designing an Interdisciplinary Research Project

2019 ◽  
Vol 11 (24) ◽  
pp. 7161 ◽  
Author(s):  
Patricia Lejoux ◽  
Aurore Flipo ◽  
Nathalie Ortar ◽  
Nicolas Ovtracht ◽  
Stéphanie Souche-Lecorvec ◽  
...  
Keyword(s):  
Computer Science ◽  
Interdisciplinary Research ◽  
Research Community ◽  
Community Research ◽  
Sustainable Mobility ◽  
Relevant Research ◽  
Research Project ◽  
Mobility Studies ◽  
Interdisciplinary Research Project ◽  
Transportation Studies

Sustainable mobility has been one of the central paradigms of research in the field of transport and mobility for several decades. However, the implications of adopting the concept of “sustainable mobility” for the conduct of interdisciplinary research has been little discussed within the relevant research community. Research in the field of transport and mobility has nevertheless been the setting for major debates in recent years on the question of interdisciplinarity, or even transdisciplinarity, with the emergence of mobility studies as opposed to transportation studies. The objective of this paper is to show, empirically, how researchers who are specialised in mobility and transport issues, but who belong to different disciplines (anthropology, computer science, economics, geomatics, sociology and urban planning) have sought to build an interdisciplinary research project—which is currently ongoing—around the links between the development of coworking, which is a new way of organising work, mobility and sustainability. This paper sets out to highlight cross-fertilisation between disciplines, the issues raised, and the difficulties encountered. As such, it provides an account that is as faithful as possible to our experience of conducting interdisciplinary research in the area of sustainable mobility.

scholarly journals An optimal control approach to manpower planning problem

2001 ◽  
Vol 7 (2) ◽  
pp. 155-175 ◽  
Author(s):  
H. W. J. Lee ◽  
X. Q. Cai ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Numerical Scheme ◽  
Manpower Planning ◽  
Planning Problem ◽  
Time Varying ◽  
Control Approach ◽  
Different Types ◽  
Minimum Number ◽  
Varying Demand ◽  
Optimal Control Approach

A manpower planning problem is studied in this paper. The model includes scheduling different types of workers over different tasks, employing and terminating different types of workers, and assigning different types of workers to various trainning programmes. The aim is to find an optimal way to do all these while keeping the time-varying demand for minimum number of workers working on each different tasks satisfied. The problem is posed as an optimal discrete-valued control problem in discrete time. A novel numerical scheme is proposed to solve the problem, and an illustrative example is provided.

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