Comparison of mathematical models for the dynamics of the Chernivtsi children disease

Research Bulletin of the National Technical University of Ukraine "Kyiv Politechnic Institute"

2017

Background. Simple mathematical models of contamination and SIR-model of spreading an infection were used to simulate the time dynamics of the unknown before children disease, which occurred in Chernivtsi (Ukraine). The cause of many cases of alopecia, which began in this city in August 1988 is still not fully clarified. According to the official report of the governmental commission, the last new cases occurred in the middle of November 1988, and the reason of the illness was reported as chemical exogenous intoxication. Later this illness became the name "Chernivtsi chemical disease". Nevertheless, the significantly increased number of new cases of the local alopecia was registered almost three years and is still not clarified. Objective. The comparison of two different versions of the disease: chemical exogenous intoxication and infection. Identification of the parameters of mathematical models and prediction of the disease development. Methods. Analytical solutions of the contamination models and SIR-model for an epidemic are obtained. The optimal values of parameters with the use of linear regression were found. Results. The optimal values of the models parameters with the use of statistical approach were identified. The calculations showed that the infectious version of the disease is more reliable in comparison with the popular contamination one. The possible date of the epidemic beginning was estimated. Conclusions. The optimal parameters of SIR-model allow calculating the realistic number of victims and other characteristics of possible epidemic. They also show that increased number of cases of local alopecia could be a part of the same epidemic as "Chernivtsi chemical disease".

“…For example, when many people have eaten an infected food or a bacterial weapon has been used, the initial value I 0 and S 0  N  I 0 must be used in (11).…”

Section: Infection Version Exact and Approximate Solutions Of Sir-eqmentioning

confidence: 99%

“…We solve (8)- (10) by introducing the function V (t )  I (t )  R (t ), corresponding to the number of victims, see [11]. It follows from (9), (10) and (13) that:…”

Section: Infection Version Exact and Approximate Solutions Of Sir-eqmentioning

confidence: 99%

Statistics Based Models for the Dynamics of Chernivtsi Children Disease

Research Bulletin of the National Technical University of Ukraine "Kyiv Politechnic Institute"

2017

“…In this study, we use the known SIR model for the dynamics of an epidemic [4][5][6][7][8]. For the parameter identification, we will use the exact solution of the SIR set of linear equations and statistical approach developed in [4] (tested also in [9]).…”

Section: Introductionmentioning

confidence: 99%

Statistics-Based Predictions of Coronavirus Epidemic Spreading in Mainland China

2020

Innov Biosyst Bioeng

Self Cite

101

138

Background. The epidemic outbreak caused by coronavirus COVID-19 is of great interest to researches because of the high rate of the infection spread 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 epidemic duration, the expected number of patients and deaths. Long-time predictions require complicated mathematical models that need a lot of effort to identify and calculate unknown parameters. This article will present some preliminary estimates. Objective. Since the 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 dependencies for victim numbers, infected and removed persons versus time.Methods. In this study we use the known SIR model for the dynamics of an epidemic, the known exact solution of the linear differential equations and statistical approach developed before for investigation of the children disease, which occurred in Chernivtsi (Ukraine) in 1988-1989. Results. The 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 and compared with the new data obtained after February 10, 2020, when the calculations were completed. Conclusions. The simple mathematical model was used to predict the characteristics of the epidemic caused by coronavirus in mainland China. Unfortunately, the number of coronavirus victims is expected to be much higher than that predicted on February 10, 2020, since 12289 new cases (not previously included in official counts) have been added two days later. Further research should focus on updating the predictions with the use of up-to-date data and using more complicated mathematical models.

“…In this study, we use the known SIR model for the dynamics of an epidemic [4][5][6][7][8] To the parameter identification, we will use the exact solution of the SIR set of linear equations and statistical approach developed in [4]. These methods were applied for investigation of the children disease, which occurred in Chernivtsi (Ukraine) in 1988-1989.…”

Section: Introductionmentioning

confidence: 99%

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

2020

Preprint

Self Cite

Background. The 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.Objective. Since 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.Methods. In 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. Results.The 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.Conclusions. Simple 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 All rights reserved. No reuse allowed without permission. perpetuity. : medRxiv preprint updating the predictions with the use of fresh data and using more complicated mathematical models.