Control of a multigroup COVID-19 model with immunity: treatment and test elimination
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ORIGINAL PAPER
Control of a multigroup COVID-19 model with immunity: treatment and test elimination Shidong Zhai Junli Tao
· Hui Gao · Guoqiang Luo ·
Received: 27 April 2020 / Accepted: 14 September 2020 © Springer Nature B.V. 2020
Abstract This paper introduces a multigroup COVID-19 model with immunity, in which the total population of each group is partitioned into five compartments, that is, susceptible, exposed, infective, infective in treatment and recovered compartment. If the basic reproduction number is less than or equal to one, and the infection graph is strongly connected, then the disease-free equilibrium is globally asymptotically stable and the disease dies out. However, the COVID-19 is already in a pandemic state, and the basic reproduction number is large than one. Hence, in order to make the COVID-19 die out in some groups in an area, we design some appropriate control strategies which reduce the number of exposed people and increase the number of people treated. These two methods have been proved to be the most effective methods at present. An effective algorithm is proposed to identify the groups that need to be controlled. Finally, we use the actual limited data of Hubei, Guangdong and Zhejiang provinces in China to illustrate the effectiveness of the obtained results.
S. Zhai (B)· H. Gao · G. Luo The School of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China e-mail: [email protected] J. Tao (B) Chongqing University Cancer Hospital, Chongqing 400030, China e-mail: [email protected]
Keywords Multigroup model · Basic reproduction number · Stability
1 Introduction In December 31, 2019, the Health Commission of Hubei province, China announced that a new coronavirus disease was found in Wuhan, the capital of Hubei province [1]. This coronavirus disease quickly spread around the world, and was tentatively named by World Health Organization (WHO) as the 2019 novel coronavirus (COVID-19) [2,3]. As of July 10, 2020, over 12.27 million people have infected worldwide. Hence, the COVID-19 is now in a state of pandemic worldwide. However, in some local areas, this virus has been completely controlled, such as Hubei, Guangdong and Zhejiang provinces in China. This shows that through strict nucleic acid detection and treatment measures, this virus can be completely controlled in local areas. The aim of this paper is to introduce a new multigroup COVID-19 model to simulate the outbreak in different groups (country, city or community), and design some appropriate control strategies such that the COVID-19 dies out. To this end, we will first recall the references about multigroup epidemic model. Multigroup epidemic model has been attracting much interest from researchers in various fields because the transmission of many infectious diseases can be modeled in this form, such as mumps, gonorrhea, measles, HIV/AIDS. In reality, the group can describe country,
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city or community. The study of multigroup epidemic model can be traced back to the
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