Statistics Based Models for the Dynamics of Chernivtsi Children Disease

Abstract

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".

Statistics-Based Predictions of Coronavirus Epidemic Spreading in Mainland China

“…In [4] the equations (1)-(3) were solved by introducing the function ( ) ( ) ( ), V t I t R t  corresponding to the number of victims. The integration of corresponding equation…”

“…Since long-term data are available only for mainland China, we will try to predict the number of coronavirus victims V (number of persons who caught the infection and got sick) only in this area. The first estimations of V(t) exponential growth versus time t, typical for the initial stages of every epidemic (see e.g., [4]) have been done in [3]. For long-time predictions, more complicated mathematical models are necessary.…”

“…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]). These methods were applied for investigation of the children disease, which occurred in Chernivtsi (Ukraine) in 1988-1989.…”

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

“…Since the reliable long time data are available only for mainland China, we will try to predict the number of victims V of this virus only in this area. The first estimations of V exponential growth, typical for the initial stages of every epidemic (see e.g., [4]) have been done in [3]. For long time predictions, more complicated mathematical models are necessary.…”

“…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.…”