Abstract
We derive a novel model escorted by large scale compartments, based on a set of coupled delay differential equations with extensive delays, in order to estimate the incubation, recovery and decease periods of COVID-19, and more generally any infectious disease. This is possible thanks to some optimization algorithms applied to publicly available database of confirmed corona cases, recovered cases and death toll. In this purpose, we separate (1) the total cases into 14 groups corresponding to 14 incubation periods, (2) the recovered cases into 406 groups corresponding to a combination of incubation and recovery periods, and (3) the death toll into 406 groups corresponding to a combination of incubation and decease periods. In this paper, we focus on recovery and decease periods and their correlation with the incubation period. The estimated mean recovery period we obtain is 22.14 days (95% Confidence Interval (CI) 22.00–22.27), and the 90th percentile is 28.91 days (95% CI 28.71–29.13), which is in agreement with statistical supported studies. The bimodal gamma distribution reveals that there are two groups of recovered individuals with a short recovery period, mean 21.02 days (95% CI 20.92–21.12), and a long recovery period, mean 38.88 days (95% CI 38.61–39.15). Our study shows that the characteristic of the decease period and the recovery period are alike. From the bivariate analysis, we observe a high probability domain for recovered individuals with respect to incubation and recovery periods. A similar domain is obtained for deaths analyzing bivariate distribution of incubation and decease periods.
Highlights
We derive a novel model escorted by large scale compartments, based on a set of coupled delay differential equations with extensive delays, in order to estimate the incubation, recovery and decease periods of COVID-19, and more generally any infectious disease
There are several statistical studies[4,5,6,7,8,9,10,11,12], based on various samples of patients such as severe, non-severe, ICU, non-ICU, large size, small size, meta-analysis, estimated the recovery time of the current pandemic. In addition to those statistical approaches, there are numerous analytical and computational studies based on mathematical models, involving Ordinary Differential Equations (ODE)[13,14,15,16,17,18,19,20,21,22,23] as well as Delay Differential Equations (DDE)[24,25,26,27,28,29], to calculate the basic reproduction number R0 and understand the underlying dynamics of the epidemic
To the best of our knowledge, we demonstrate for the first time a substantial compartment based model, with a total 830 partitions, in order to estimate the key periods of COVID19 as well as the bivariate distribution of incubation and recovery periods, and the bivariate distribution of incubation and decease periods
Summary
We derive a novel model escorted by large scale compartments, based on a set of coupled delay differential equations with extensive delays, in order to estimate the incubation, recovery and decease periods of COVID-19, and more generally any infectious disease This is possible thanks to some optimization algorithms applied to publicly available database of confirmed corona cases, recovered cases and death toll. To the best of our knowledge, we demonstrate for the first time a substantial compartment based model, with a total 830 partitions, in order to estimate the key (incubation, recovery, decease periods) periods of COVID19 as well as the bivariate distribution of incubation and recovery periods, and the bivariate distribution of incubation and decease periods This will be achieved using publicly available d atabase[30] of the total number of corona-positive cases, recovery and death toll. We do not consider the patient’s gender or age due to lack of the required data
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