scholarly journals Detections and SIR simulations of the COVID-19 pandemic waves in Ukraine

2021 ◽  
Vol 9 (1) ◽  
pp. 46-65
Author(s):  
Igor Nesteruk
Keyword(s):  
Mathematical Models ◽  
Sharp Increase ◽  
Statistical Approach ◽  
Sir Model ◽  
Economic Consequences ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Simple Method ◽  
Number Of Patients ◽  
June July

Abstract Background. Unfortunately, the COVID-19 pandemic is still far from stabilizing. Of particular concern is the sharp increase in the number of diseases in June-July, September-October 2020 and February-March 2021. The causes and consequences of this sharp increase in the number of cases are still waiting for their researchers, but there is already an urgent need to assess the possible duration of the pandemic, the expected number of patients and deaths. Correct simulation of the infectious disease dynamics needs complicated mathematical models and many efforts for unknown parameters identification. Constant changes in the pandemic conditions (in particular, the peculiarities of quarantine and its violation, situations with testing and isolation of patients) cause various epidemic waves, lead to changes in the parameter values of the mathematical models. Objective. In this article, pandemic waves in Ukraine will be detected, calculated and discussed. The estimations for durations and final sizes of the epidemic waves will be presented. Methods. We propose a simple method for the epidemic waves detection based on the differentiation of the smoothed number of cases. We use the generalized SIR (susceptible-infected-removed) model for the dynamics of the epidemic waves. The known exact solution of the SIR differential equations and statistical approach were used. We will use different data sets for accumulated number of cases in order to compare the results of simulations and predictions. Results. Nine pandemic waves were detected in Ukraine and corresponding optimal values of the SIR model parameters were identified. The number of cases and the number of patients spreading the infection versus time were calculated. In particular, the pandemic in Ukraine probably began in January 2020. If current trends continue, the end of the pandemic should be expected no earlier than in summer 2021. Conclusions. The differentiation of the smoothed number of cases, the SIR model and statistical approach to the parameter identification are helpful to select COVID-19 pandemic waves and make some reliable estimations and predictions. The obtained information will be useful to regulate the quarantine activities, to predict the medical and economic consequences of the pandemic.

scholarly journals Waves of COVID-19 pandemic. Detection and SIR simulations

2020 ◽  
Author(s):  
Igor Nesteruk
Keyword(s):  
Mathematical Models ◽  
Sharp Increase ◽  
Statistical Approach ◽  
Sir Model ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Simple Method ◽  
Reproduction Numbers ◽  
Number Of Patients ◽  
The World

Background. Unfortunately, the COVID-19 pandemic is still far from stabilizing. Of particular concern is the sharp increase in the number of diseases in June-July 2020. The causes and consequences of this sharp increase in the number of cases are still waiting for their researchers, but there is already an urgent need to assess the possible duration of the pandemic, the expected number of patients and deaths. The resumption of international passenger traffic needs the information for deciding which countries' citizens are welcome guests. Correct simulation of the infectious disease dynamics needs complicated mathematical models and many efforts for unknown parameters identification. Constant changes in the pandemic conditions (in particular, the peculiarities of quarantine and its violation, situations with testing and isolation of patients) cause various epidemic waves, lead to changes in the parameter values of the mathematical models. Objective. In this article, pandemic waves in Ukraine and in the world will be detected, calculated and discussed. The estimations for hidden periods, epidemic durations and final numbers of cases will be presented. The probabilities of meeting a person spreading the infection and reproduction numbers will be calculated for different countries and regions. Methods. We propose a simple method for the epidemic waves detection based on the differentiation of the smoothed number of cases. We use the known SIR (susceptible-infected-removed) model for the dynamics of the epidemic waves. The known exact solution of the SIR differential equations and statistical approach were modified and used. Results. The optimal values of the SIR model parameters were identified for four waves of pandemic dynamics in Ukraine and five waves in the world. The number of cases and the number of patients spreading the infection versus time were calculated. In particular, the pandemic probably began in August 2019. If current trends continue, the end of the pandemic should be expected no earlier than in March 2021 both in Ukraine and in the world, the global number of cases will exceed 20 million. The probabilities of meeting a person spreading the infection and reproduction numbers were calculated for different countries and regions. Conclusions. The SIR model and statistical approach to the parameter identification are helpful to make some reliable estimations of the epidemic waves. The number of persons spreading the infection versus time was calculated during all the epidemic waves. The obtained information will be useful to regulate the quarantine activities, to predict the medical and economic consequences of the pandemic and to decide which countries' citizens are welcome guests.

scholarly journals Statistics based predictions of coronavirus 2019-nCoV spreading in mainland China

2020 ◽  
Author(s):  
Igor Nesteruk
Keyword(s):  
Mathematical Models ◽  
Statistical Approach ◽  
Mainland China ◽  
Sir Model ◽  
High Rate ◽  
Model Parameters ◽  
Time Data ◽  
Unknown Parameters ◽  
Number Of Patients ◽  
Long Time

ABSTRACTBackgroundThe epidemic outbreak cased by coronavirus 2019-nCoV is of great interest to researches because of the high rate of spread of the infection and the significant number of fatalities. A detailed scientific analysis of the phenomenon is yet to come, but the public is already interested in the questions of the duration of the epidemic, the expected number of patients and deaths. For long time predictions, the complicated mathematical models are necessary which need many efforts for unknown parameters identification and calculations. In this article, some preliminary estimates will be presented.ObjectiveSince the reliable long time data are available only for mainland China, we will try to predict the epidemic characteristics only in this area. We will estimate some of the epidemic characteristics and present the most reliable dependences for victim numbers, infected and removed persons versus time.MethodsIn this study we use the known SIR model for the dynamics of an epidemic, the known exact solution of the linear equations and statistical approach developed before for investigation of the children disease, which occurred in Chernivtsi (Ukraine) in 1988-1989.ResultsThe optimal values of the SIR model parameters were identified with the use of statistical approach. The numbers of infected, susceptible and removed persons versus time were predicted.ConclusionsSimple mathematical model was used to predict the characteristics of the epidemic caused by coronavirus 2019-nCoV in mainland China. The further research should focus on updating the predictions with the use of fresh data and using more complicated mathematical models.

scholarly journals Estimates of the COVID-19 pandemic dynamics in Ukraine based on two data sets

2021 ◽  
Author(s):  
Igor Nesteruk
Keyword(s):  
Mathematical Models ◽  
Sir Model ◽  
Model Parameters ◽  
Data Sets ◽  
Unknown Parameters ◽  
Epidemic Dynamics ◽  
The Government ◽  
Linear Differential ◽  
June July ◽  
Epidemic Wave

ABSTRACTBackgroundTo simulate how the number of COVID-19 cases increases versus time, various data sets for the number of new cases and different mathematical models can be used. Since there are some differences in statistical data, the results of simulations can be different. Complex mathematical models contain many unknown parameters, the values of which must be determined using a limited number of observations of the disease over time. Even long-term monitoring of the epidemic may not provide reliable estimates of its parameters due to the constant change of testing conditions, isolation of infected and quarantine. Therefore, simpler approaches are necessary. In particular, previous simulations of the COVID-19 epidemic dynamics in Ukraine were based on smoothing of the dependence of the number of cases on time and the generalized SIR (susceptible-infected-removed) model. These approaches allowed to detect the waves of pandemic and to make adequate predictions of the their duration and final sizes. In particular, eight waves of the COVID-19 pandemic in Ukraine were investigated.ObjectiveWe will compare the results simulation of a new epidemic wave in Ukraine based on national statistics and data reported by Johns Hopkins University (JHU).MethodsIn this study we use the smoothing method for the dependences of the number of cases on time, the generalized SIR model for the dynamics of any epidemic wave, the exact solution of the linear differential equations, and statistical approach developed before.ResultsNinth epidemic wave in Ukraine was simulated. The optimal values of the SIR model parameters were calculated and compared with the use of two data sets. Both predictions are not very optimistic: new cases will not stop appearing until June-July 2021.ConclusionsNew waves of COVID-19 pandemic can be detected, calculated and predicted with the use of rather simple mathematical models. The results of calculations depend on the data sets for the number of confirmed cases. The expected long duration of the pandemic forces us to be careful and in solidarity. The government and all Ukrainians must strictly adhere to quarantine measures in order to avoid fatal consequences. Probably the presented results could be useful in order to estimate the efficiency of future vaccinations.

scholarly journals Predictions of COVID-19 Pandemic Dynamics in Ukraine and Qatar Based on Generalized SIR Model

2021 ◽  
Vol 5 (1) ◽  
pp. 37-46
Author(s):  
Igor Nesteruk ◽  
Noureddine Benlagha
Keyword(s):  
Mathematical Models ◽  
Sir Model ◽  
Model Parameters ◽  
Data Sets ◽  
Unknown Parameters ◽  
Epidemic Dynamics ◽  
Long Duration ◽  
Constant Change ◽  
Linear Differential ◽  
June July

Background. To simulate how the number of COVID-19 cases increases versus time, various data sets and different mathematical models can be used. Since there are some differences in statistical data, the results of simulations can be different. Complex mathematical models contain many unknown parameters, the values ​​of which must be determined using a limited number of observations of the disease over time. Even long-term monitoring of the epidemic may not provide reliable estimates of the model parameters due to the constant change of testing conditions, isolation of infected, quarantine conditions, pathogen mutations, vaccinations, etc. Therefore, simpler approaches are necessary. In particular, previous simulations of the COVID-19 epidemic dynamics in Ukraine were based on smoothing of the dependence of the number of cases on time and the generalized SIR (susceptible–infected–removed) model. These approaches allowed detecting the pandemic waves and calculating adequate predictions of their duration and final sizes. In particular, eight waves of the COVID-19 pandemic in Ukraine were investigated. Objective. We aimed to detect the changes in the pandemic dynamics and present the results of SIR simu­lations based on Ukrainian national statistics and data reported by Johns Hopkins University (JHU) for Ukraine and Qatar. Methods. In this study we use the smoothing method for the dependences of the number of cases on time, the generalized SIR model for the dynamics of any epidemic wave, the exact solution of the linear differential equations, and statistical approach for the model parameter identification developed before. Results. The optimal values of the SIR model parameters were calculated and some predictions about final sizes and durations of the epidemics are presented. Corresponding SIR curves are shown and compared with the real numbers of cases. Conclusions. Unfortunately, the forecasts are not very optimistic: in Ukraine, new cases will not stop appearing until June–July 2021; in Qatar, new cases are likely to appear throughout 2021. The expected long duration of the pandemic forces us to be careful and in solidarity. Probably the presented results could be useful in order to estimate the efficiency of vaccinations.

scholarly journals Visible and real sizes of the COVID-19 pandemic in Ukraine

2021 ◽  
Author(s):  
Igor Nesteruk
Keyword(s):  
Mathematical Models ◽  
Real Number ◽  
Sir Model ◽  
Data Sets ◽  
Unknown Parameters ◽  
The Real ◽  
Epidemic Dynamics ◽  
Optimal Values

Abstract To simulate how the number of COVID-19 cases increases versus time, various data sets and different mathematical models can be used. In particular, previous simulations of the COVID-19 epidemic dynamics in Ukraine were based on smoothing of the dependence of the number of cases on time and the generalized SIR (susceptible-infected-removed) model. Since real number of cases is much higher than the official numbers of laboratory confirmed ones, there is a need to assess the degree of data incompleteness and correct the relevant forecasts. We have improved the method of estimating the unknown parameters of the generalized SIR model and calculated the optimal values ​​of the parameters. It turned out that the real number of diseases exceeded the officially registered values ​​by about 4.1 times at the end of 2020 in Ukraine. This fact requires a reassessment of the COVID-19 pandemic dynamics in other countries and clarification of world forecasts.

scholarly journals Visible and real sizes of the COVID-19 pandemic in Ukraine

2021 ◽  
Author(s):  
Igor Nesteruk
Keyword(s):  
Mathematical Models ◽  
Real Number ◽  
Sir Model ◽  
Data Sets ◽  
Unknown Parameters ◽  
The Real ◽  
Epidemic Dynamics ◽  
Optimal Values

ABSTRACTTo simulate how the number of COVID-19 cases increases versus time, various data sets and different mathematical models can be used. In particular, previous simulations of the COVID-19 epidemic dynamics in Ukraine were based on smoothing of the dependence of the number of cases on time and the generalized SIR (susceptible-infected-removed) model. Since real number of cases is much higher than the official numbers of laboratory confirmed ones, there is a need to assess the degree of data incompleteness and correct the relevant forecasts. We have improved the method of estimating the unknown parameters of the generalized SIR model and calculated the optimal values of the parameters. It turned out that the real number of diseases exceeded the officially registered values by about 4.1 times at the end of 2020 in Ukraine. This fact requires a reassessment of the COVID-19 pandemic dynamics in other countries and clarification of world forecasts.

scholarly journals COVID-19 pandemic dynamics in Ukraine after September 1, 2020

2020 ◽  
Author(s):  
Igor Nesteruk
Keyword(s):  
Differential Equations ◽  
Sir Model ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Epidemic Dynamics ◽  
Direct Observations ◽  
Long Duration ◽  
Constant Change ◽  
Reproduction Numbers ◽  
Linear Differential

ABSTRACTBackgroundThe threats of the COVID-19 pandemic require the mobilization of scientists, including mathematicians. To understand how the number of cases increases versus time, various models based on direct observations of a random number of new cases and differential equations can be used. Complex mathematical models contain many unknown parameters, the values of which must be determined using a limited number of observations of the disease over time. Even long-term monitoring of the epidemic may not provide reliable estimates of its parameters due to the constant change of testing conditions, isolation of infected and quarantine. Therefore, simpler approaches should also be used, for example, some smoothing of the dependence of the number of cases on time and the known SIR (susceptible-infected-removed) model. These approaches allowed to detect the waves of pandemic in different countries and regions and to make adequate predictions of the duration, hidden periods, reproduction numbers, and final sizes of its waves. In particular, seven waves of the COVID-19 pandemic in Ukraine were investigated.ObjectiveWe will detect new epidemic waves in Ukraine that occurred after September 1, 2020 and estimate the epidemic characteristics with the use of generalized SIR model. Some predictions of the epidemic dynamics will be presented.MethodsIn this study we use the smoothing method for the dependence of the number of cases on time; the generalized SIR model for the dynamics of any epidemic wave, the exact solution of the linear differential equations and statistical approach developed before.ResultsSeventh and eights epidemic waves in Ukraine were detected and the reasons of their appearance were discussed. The optimal values of the SIR model parameters were calculated. The prediction for the COVID-19 epidemic dynamics in Ukraine is not very optimistic: new cases will not stop appearing until June 2021. Only mass vaccination and social distancing can change this trend.ConclusionsNew waves of COVID-19 pandemic can be detected, calculated and predicted with the use of rather simple mathematical simulations. The expected long duration of the pandemic forces us to be careful and in solidarity.The government and all Ukrainians must strictly adhere to quarantine measures in order to avoid fatal consequences.

scholarly journals Statistical Approach to Incorporating Experimental Variability into a Mathematical Model of the Voltage-Gated Na+ Channel and Human Atrial Action Potential

Cells ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 1516
Author(s):  
Daniel Gratz ◽  
Alexander J Winkle ◽  
Seth H Weinberg ◽  
Thomas J Hund
Keyword(s):  
Action Potential ◽  
Mathematical Models ◽  
Cardiac Myocyte ◽  
Population Level ◽  
Na Channel ◽  
Model Parameters ◽  
Healthy Population ◽  
Experimental Measurements ◽  
Voltage Gated ◽  
Experimental Variability

The voltage-gated Na+ channel Nav1.5 is critical for normal cardiac myocyte excitability. Mathematical models have been widely used to study Nav1.5 function and link to a range of cardiac arrhythmias. There is growing appreciation for the importance of incorporating physiological heterogeneity observed even in a healthy population into mathematical models of the cardiac action potential. Here, we apply methods from Bayesian statistics to capture the variability in experimental measurements on human atrial Nav1.5 across experimental protocols and labs. This variability was used to define a physiological distribution for model parameters in a novel model formulation of Nav1.5, which was then incorporated into an existing human atrial action potential model. Model validation was performed by comparing the simulated distribution of action potential upstroke velocity measurements to experimental measurements from several different sources. Going forward, we hope to apply this approach to other major atrial ion channels to create a comprehensive model of the human atrial AP. We anticipate that such a model will be useful for understanding excitability at the population level, including variable drug response and penetrance of variants linked to inherited cardiac arrhythmia syndromes.

scholarly journals Modelling the spread of American foulbrood in honeybees

2013 ◽  
Vol 10 (88) ◽  
pp. 20130650 ◽  
Author(s):  
Samik Datta ◽  
James C. Bull ◽  
Giles E. Budge ◽  
Matt J. Keeling
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Control Strategies ◽  
Sir Model ◽  
Model Parameters ◽  
American Foulbrood ◽  
Inspection Period ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
The Impact

We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae , that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of honeybee apiaries across the island. We use a spatial SIR model with an underlying owner network to simulate the epidemic and characterize the epidemic using a Markov chain Monte Carlo (MCMC) scheme to determine model parameters and infection times (including undetected ‘occult’ infections). Likely methods of infection spread can be inferred from the analysis, with both distance- and owner-based transmissions being found to contribute to the spread of AFB. The results of the MCMC are corroborated by simulating the epidemic using a stochastic SIR model, resulting in aggregate levels of infection that are comparable to the data. We use this stochastic SIR model to simulate the impact of different control strategies on controlling the epidemic. It is found that earlier inspections result in smaller epidemics and a higher likelihood of AFB extinction.

Identification of Viscously Damped Distributed Structural Dynamic Systems

1991 ◽  
Author(s):  
R. Chander ◽  
M. Meyyappa ◽  
S. Hanagud
Keyword(s):  
Dynamic Systems ◽  
Beam Theory ◽  
Continuous Functions ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Structural Dynamic ◽  
Domain Identification ◽  
Forcing Function ◽  
Cardinal Splines ◽  
Stiffness And Damping

Abstract A frequency domain identification technique applicable to damped distributed structural dynamic systems is presented. The technique is developed for beams whose behavior can be modeled using the Euler-Bernoulli beam theory. External damping of the system is included by means of a linear viscous damping model. Parameters to be identified, mass, stiffness and damping distributions are assumed to be continuous functions over the beam. The response at a discrete number of points along the length of the beam for a given forcing function is used as the data for identification. The identification scheme involves approximating the infinite dimensional response and parameter spaces by using quintic B-splines and cubic cardinal splines, respectively. A Galerkin type weighted residual procedure, in conjunction with the least squares technique, is employed to determine the unknown parameters. Numerically simulated response data for an applied impulse load are utilized to validate the developed technique. Estimated values for the mass, stiffness and damping distributions are discussed.

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