Estimation of the basic reproduction number of COVID-19 from the incubation period distribution

Abstract

The estimates of the future course of spreading of the SARS-CoV-2 virus are frequently based on Markovian models in which the duration of residence in any compartment is exponentially distributed. Accordingly, the basic reproduction number R0 is also determined from formulae where it is related to the parameters of such models. The observations show that the start of infectivity of an individual appears nearly at the same time as the onset of symptoms, while the distribution of the incubation period is not an exponential. Therefore, we propose a method for estimation of R0 for COVID-19 based on the empirical incubation period distribution and assumed very short infectivity period that lasts only few days around the onset of symptoms. We illustrate this venerable approach to estimate R0 for six major European countries in the first wave of the epidemic. The calculations show that even if the infectivity starts 2 days before the onset of symptoms and stops instantly when they appear (immediate isolation), the value of R0 is larger than that from the classical, SIR model. For more realistic cases, when only individuals with mild symptoms spread the virus for few days after onset of symptoms, the respective values are even larger. This implies that calculations of R0 and other characteristics of spreading of COVID-19 based on the classical, Markovian approaches should be taken very cautiously.

Dynamics of the COVID-19 pandemic: nonlinear approaches on the modelling, prediction and control

“…The study is performed employing four different approaches, and the results are found to behave in an "up-down-up" pattern and also help in predicting the workload of the healthcare systems and assist in the allocation of sufficient resources to the states in need. Markovian-type models for estimating the spread of the COVID-19 virus in the future considering the exponentially distributed time duration of the population in each compartment of the model are proposed by Basnarkov et al [29]. The study reveals that the starting time of the infection among individuals coincides with the same time as that of symptoms, while the incubation period is not exponentially distributed.…”

“…This special issue is a compilation of original research articles that address the dynamics and applications of COVID-19 through nonlinear dynamics. The articles are organized in five sections, comprising mathematical modeling and epidemics [1][2][3][4][5][6][7], the dynamics of several waves and transmission [8][9][10][11][12][13][14][15][16][17], neural network and deep learning related to COVID-19 [18][19][20][21][22][23][24], predictions and estimations related to COVID-19 [25][26][27][28][29][30], and detailed analysis on the pandemic and its applications [31][32][33][34][35].…”

Flexible Bayesian estimation of incubation times

“…1 Knowledge of incubation times helps in assessing the transmission potential of an infectious disease (Cheng et al, 2021;Basnarkov et al, 2022) as the incubation period can be used to estimate the reproduction number (i.e., the average number of secondary cases generated by an infector in a fully susceptible population). The incubation period is also of direct interest for case definition (Virlogeux et al, 2016) and to measure the effectiveness of contact tracing.…”