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

Swarnali Sharma; Vitaly Volpert; Malay Banerjee; Swarnali Sharma; Vitaly Volpert; Malay Banerjee

doi:10.3934/mbe.2020386

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7562-7604. doi: 10.3934/mbe.2020386

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

1.
Department of Mathematics, Vijaygarh Jyotish Ray College, Kolkata - 700032, India
2.
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
3.
INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
4.
Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
5.
Department of Mathematics & Statistics, IIT Kanpur, Kanpur - 208016, India

Received: 09 August 2020 Accepted: 19 October 2020 Published: 02 November 2020

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.
- COVID-19,
- reproduction number,
- two group model,
- relapse
Citation: Swarnali Sharma, Vitaly Volpert, Malay Banerjee. Extended SEIQR type model for COVID-19 epidemic and data analysis[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7562-7604. doi: 10.3934/mbe.2020386

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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.

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