Extended SEIQR type model for COVID-19 epidemic and data analysis

Abstract

An extended SEIQR type model is considered in order to model the COVID-19 epidemic. It contains the classes of susceptible individuals, exposed, infected symptomatic and asymptomatic, quarantined, hospitalized and recovered. The basic reproduction number and the final size of epidemic are determined. The model is used to fit available data for some European countries. A more detailed model with two different subclasses of susceptible individuals is introduced in order to study the influence of social interaction on the disease progression. The coefficient of social interaction $K$ characterizes the level of social contacts in comparison with complete lockdown (K=0) and the absence of lockdown (K=1). The fitting of data shows that the actual level of this coefficient in some European countries is about 0.1, characterizing a slow disease progression. A slight increase of this value in the autumn can lead to a strong epidemic burst.

Epidemic Progression and Vaccination in a Heterogeneous Population. Application to the Covid-19 epidemic

“…Hospitalized individuals can recover or die with the rates ν and ρ 2 : This model was introduced in [9] where the basic reproduction number and the final size of epidemic were found. It was also used to fit the data on the Covid-19 epidemic in some countries before and during the lockdown and to determine the parameters by fitting the numerical simulation with the epidemiological data.…”

“…Increase of the coefficient of social interaction k during the fourth stage is related to the beginning of the academic year and the intensification of professional activity after summer vacation. [9]. The values around β 11 = 4 and β 22 = 1 are quite specific, and we used them in the previous sections of this work.…”

“…In all cases the vaccine is administrated on day 5. Best fitted values for the parameters of the full model for Germany [9].…”

“…Symptomatic individuals move to the quarantine class, and the rate of their transfer to hospital and recovered class are ξ 1 and ξ 2 , respectively. The equation for the quarantined class writes: Hospitalized individuals can recover or die with the rates ν and ρ 2 : This model was introduced in [9] where the basic reproduction number and the final size of epidemic were found. It was also used to fit the data on the Covid-19 epidemic in some countries before and during the lockdown and to determine the parameters by fitting the numerical simulation with the epidemiological data.…”

“…The influence of heterogeneity of the population with respect to its role in the epidemic progression is largely discussed in the existing literature [9, 10, 11, 12, 13]. Different age and social groups can have different frequency of interactions and implementation of the measures of social distancing.…”