Research Article Z-Control on COVID-19-Exposed Patients in Quarantine Nita H. Shah , Nisha Sheoran, and Ekta Jayswal Department of Mathematics, Gujarat University, Ahmedabad, Gujarat, India Correspondence should be addressed to Nita H. Shah; nitahshah@gmail.com Received 3 April 2020; Accepted 23 May 2020; Published 19 June 2020 Academic Editor: Sining Zheng Copyright © 2020 Nita H. Shah et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, a mathematical model for diabetic or hypertensive patients exposed to COVID-19 is formulated along with a set of first-order nonlinear differential equations. e system is said to exhibit two equilibria, namely, exposure-free and endemic points. e reproduction number is obtained for each equilibrium point. Local stability conditions are derived for both equilibria, and global stability is studied for the endemic equilibrium point. is model is investigated along with Z-control in order to eliminate chaos and oscillation epidemiologically showing the importance of quarantine in the COVID-19 environment. 1. Introduction COVID-19, an infectious disease with the first case reported in Wuhan city of China, has spread throughout the world. On 30 January 2020, the WHO declared its outbreak as a “public health emergency of international concern.” As on 2 April 2020, 08:02 GMT, it has caused 47,249 deaths worldwide and a total of 936,237 cases have been confirmed [1]. COVID-19 spreads through the contact of individuals with infected persons when they cough or sneeze. It is a respiratory disease with mild to moderate symptoms like dry cough, fever, and tiredness, and in more severe cases difficulty breathing [2]. Also, few individuals showing mild symptoms of the disease may recover themselves if they avoid contacting infected cases and maintain good hygiene. COVID-19 is a major health threat to those with a past medical history and also to those who are older than 60 years (elderly population). is was reported by Li et al. [3], who calculated the median age of 425 patients infected with COVID-19 in Wuhan, China, as 59 years and almost half of the patients were 60 years old. Governments throughout the world are taking several preventive measures to control the spread of the epidemic. Preventing the spread is the only way since no vaccine has been developed till date to fight the virus. Preventive measures include maintaining at least 1 meter distance from a person sneezing or coughing, washing hands regularly, and maintaining social distance. Various mathematical models have been developed so far to address various challenges in predicting the spread of COVID-19 disease. Batista [4] has used the basic SIR-model to find the actual size of the epidemic. Peng et al. [5] analysed the scenario of COVID-19 in China by formulating the SEIR dynamical system and have predicted that the situation will be under control at the beginning of April. Sun et al. [6] discussed various aspects of COVID-19 situation in China which helps understand the fatality rate and transmission rate of COVID-19 and control the epi- demic spread. In the case of COVID-19 epidemic, exposure to disease plays a vital role in the spread of the disease. Rabajante [7] studied various models and concluded that with the basic reproduction number being 2 and considering the 14-day infectious period, if an infected person stays for more than 9 hours with others, he could infect others. If the exposure time is 18 hours, the model recommends full protection with more than 70% effectiveness to the attendees of the social gathering. In order to control the disease, the importance of travel quarantine or travel restriction, which delayed the progression of disease, in Wuhan was studied by Chinazzi et al. [8]. A similar result was also shown by Kucharski et al. [9]. ey showed that with the air travel restriction in Wuhan, the daily reproduction number de- clined from 2.35 to 1.05. ere is also a model evaluated by Tang et al. [10] and Tang et al. [11] in which they divided the subpopulation into quarantined and unquarantined classes to understand the transmission risk of the epidemic. Hindawi International Journal of Differential Equations Volume 2020, Article ID 7876146, 11 pages https://doi.org/10.1155/2020/7876146