The impact of asymptomatic individuals on the strength of public health interventions to prevent the second outbreak of

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ORIGINAL PAPER

The impact of asymptomatic individuals on the strength of public health interventions to prevent the second outbreak of COVID-19 Xiaochen Wang . Shengfeng Wang . Yueheng Lan . Xiaofeng Tao . Jinghua Xiao

Received: 24 April 2020 / Accepted: 30 May 2020 Ó Springer Nature B.V. 2020

Abstract The pandemic of coronavirus disease 2019 (COVID-19) has threatened the social and economic structure all around the world. Generally, COVID-19 has three possible transmission routes, including presymptomatic, symptomatic and asymptomatic transmission, among which the last one has brought a severe challenge for the containment of the disease. One core scientific question is to understand the influence of asymptomatic individuals and of the strength of control measures on the evolution of the disease, particularly on a second outbreak of the disease. To explore these issues, we proposed a novel compartmental model that takes the infection of asymptomatic individuals into account. We get the relationship between asymptomatic individuals and critical strength of control measures theoretically. Furthermore, we verify the reliability of our model and the accuracy of the theoretical analysis by using the X. Wang  X. Tao National Engineering Laboratory for Mobile Network Technologies, Beijing University of Posts and Telecommunications, Beijing 100876, China S. Wang  Y. Lan  J. Xiao (&) School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China e-mail: [email protected] Y. Lan  J. Xiao State Key Lab of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China

real confirmed cases of COVID-19 contamination. Our results, showing the importance of the asymptomatic population on the control measures, would provide useful theoretical reference to the policymakers and fuel future studies of COVID-19. Keywords COVID-19  Asymptomatic individuals  SIR-typed model  Control measures  Second outbreak

1 Introduction By May 23, 2020, there are 5,103,006 confirmed cases of coronavirus disease 2019 (COVID-19) in the world, and 3,33,401 people have died of the disease [1]. To contain the outbreak of COVID-19, policies, including quarantining cities, limiting public activities, extending holidays, are implemented. These control measures have to be implemented strictly in order to reduce the spreading of COVID-19 [2, 3], which already caused significant disruption to the social and economic structure [4–6]. Therefore, in the study of epidemiological models [7, 8], on the one hand, it is needed to predict the evolution of COVID-19; on the other hand, it should be helpful to access how long these control measures should last and to what extent these control measures should keep. Different models

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Fig. 1 The sketch of the SALIR model. Individuals are divided into five states in the SALIR model at each time step: S, A, L, I and R. S represents the susceptible state, A