Mathematical model of Boltzmann's sigmoidal equation applicable to the spreading of the coronavirus (Covid-19) waves.
Mathematical model of Boltzmann's sigmoidal equation applicable to the spreading of the coronavirus (Covid-19) waves.
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DOI：
10.1007/s11356-020-11188-y
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发表时间：
2021-08
期刊：
影响因子：
--
通讯作者：
Tajouri T
中科院分区：
文献类型：
--
作者：
El Aferni A;Guettari M;Tajouri T
目前，对新型冠状病毒（Covid-19）新冠疫情的建模、预测和动态传播研究正在深入进行。在目前的工作中，sigmoidal-Boltzmann数学模型被应用于研究15个不同国家的Covid-19传播。累计感染人数I已被sigmoidal-Boltzmann方程（SBE）精确拟合，从而产生不同的流行病学参数，如大流行高峰tp、最大感染人数Imax和流行稳定时间t∞。相对于S形Δt的时间常数（也称为斜率因子）被揭示为影响所有流行病学参数的决定性参数。不同参数之间的经验规律使我们能够提出一个修改后的sigmoidal-Boltzmann方程来描述大流行病的传播。扩展速度Vp的表达式被进一步确定为S形参数的函数。这使得有可能评估病毒的最大传播速度Vpmax，并追踪每个国家的速度分布。此外，对于经历第二波大流行的国家，已成功地通过双S形玻尔兹曼方程（DSBE）调整了累计感染人数I，从而可以比较两波大流行。最后，两波Vp max 1和Vp max 2的最大病毒传播之间的比较表明，对于所有研究的国家来说，新冠肺炎第二波的强度低于第一波。
Currently, investigations are intensively conducted on modeling, forecasting, and studying the dynamic spread of coronavirus (Covid-19) new pandemic. In the present work, the sigmoidal-Boltzmann mathematical model was applied to study the Covid-19 spread in 15 different countries. The cumulative number of infected persons I has been accurately fitted by the sigmoidal-Boltzmann equation (SBE), giving rise to different epidemiological parameters such as the pandemic peak tp, the maximum number of infected persons Imax, and the time of the epidemic stabilization t∞. The time constant relative to the sigmoid Δt (called also the slope factor) was revealed to be the determining parameter which influences all the epidemiological parameters. Empirical laws between the different parameters allowed us to propose a modified sigmoidal-Boltzmann equation describing the spread of the pandemic. The expression of the spread speed Vp was further determined as a function of the sigmoid parameters. This made it possible to assess the maximum speed of spread of the virus Vpmax and to trace the speed profile in each country. In addition, for countries undergoing a second pandemic wave, the cumulative number of infected people I has been successfully adjusted by a double sigmoidal-Boltzmann equation (DSBE) allowing the comparison between the two waves. Finally, the comparison between the maximum virus spread of two waves Vp max 1 and Vp max 2 showed that the intensity of the second wave of Covid-19 is low compared to the first for all the countries studied.
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影响因子：
2.4
作者：
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DOI：
10.1590/0103-8478cr20160646
发表时间：
2017-01-01
期刊：
Ciência Rural
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