key: cord-0693041-pswq6s8x authors: Góis, Aédson Nascimento; Laureano, Estevão Esmi; Santos, David da Silva; Sánchez, Daniel Eduardo; Souza, Luiz Fernando; Vieira, Rita de Cássia Almeida; Oliveira, Jussiely Cunha; Santana-Santos, Eduesley title: Lockdown as an Intervention Measure to Mitigate the Spread of COVID-19: a modeling study date: 2020-10-21 journal: Revista da Sociedade Brasileira de Medicina Tropical DOI: 10.1590/0037-8682-0417-2020 sha: 7776585e6ca58238c95074388ddc26fdb61c2e3a doc_id: 693041 cord_uid: pswq6s8x INTRODUCTION: This work aims to develop a biomathematical transmission model of COVID-19, in the State of Sergipe, Brazil, to estimate the distribution of cases over time and project the impact on the spread of the epidemic outbreak due to interventions and control measures over the local population. METHODS: This is an epidemiological mathematical modeling study conducted to analyze the dynamics of the accumulated cases of COVID-19, which used a logistic growth model that adds a term of withdrawal of individuals as a control measure. Three possible COVID-19 propagation scenarios were simulated based on three different rates of withdrawal of individuals. They were adjusted with real data of the infected and measures of control over the population. RESULTS: The lockdown would be the best scenario, with a lower incidence of infected people, when compared to the other measures. The number of infected people would grow slowly over the months, and the number of symptomatic individuals in this scenario would be 40,265 cases. We noticed that the State of Sergipe is still in the initial stage of the disease in the scenarios. It was possible to observe that the peak of cases and the equilibrium, in the current situation of social isolation, will occur when reaching the new support capacity, at the end of August in approximately 1,171,353 infected individuals. CONCLUSIONS: We established that lockdown is the intervention with the highest ability to mitigate the spread of the virus among the population. The infection caused by the new coronavirus, responsible for causing respiratory infections of zoonotic viral origin, has been the subject of constant research on its dissemination and potential for contagion among the population. The first reported case occurred in late December 2019, still of unknown etiology in the city of Wuhan, China. On February 11, 2020, the World Health Organization (WHO) recognized the virus as SARS-CoV-2, responsible for causing the disease COVID-19, which quickly spread around the world and became a pandemic with high dissemination and contagion level. In Brazil, the first case was dated February 26, 2020, in the southeastern part of the country, in the State of São Paulo, and quickly spread to several states. On March 6, the first case ever was recorded in the northeast of the country, in the State of Bahia. On March 15, the first case was confirmed in Aracaju, the capital of the State of Sergipe, warning of the high speed of the spread of the disease [1] [2] [3] . Until this moment, it is known that the primary means of transmission are droplets and aerosols (droplet nuclei) from the air and respiratory tracts and can also be transmitted by indirect contact through the surfaces or objects on which the infected come into contact 4 . When a person is infected, some characteristic signs and symptoms similar to a flu-like syndrome are presented, such as fever, tiredness, cough, nasal congestion, runny nose, and/or sore throat 5 . Cases considered severe evolve to respiratory distress syndrome 6 . In cases where individuals are infected and symptomatic, a study reveals that approximately 20% will need hospitalizations, aiming at improving their clinical condition. For 5% of these, due to hemodynamic instability, there is a need for treatment in an intensive care unit (ICU) 7 . For such patients, the worst prognosis is directly related to the presence of comorbidities, such as advanced age, immunosuppression, diabetes mellitus, respiratory and cardiac diseases 8 . While a vaccine to combat COVID-19 is yet to be developed, the authorities have established the use of a mask, social distancing, social isolation, and quarantine as forms of containment of COVID-19 9 due to the number of ICU beds (0,7% of the total in the country) needed to support the most severely ill patients. Additionally, studies are required to contribute to the analysis of estimates regarding the distribution of cases in the States as well as possible impacts of the epidemic given the control measures adopted. In the current scenario in which strategies to contain or minimize the spread of the virus are essential, the objective of this study was to develop a biomathematical transmission model of COVID-19 in the State of Sergipe, Brazil. Wherein, using numerical simulation computational tools to estimate the distribution of cases over time and to assess the impact of interventions (control measures on isolation and/or social distance) on the size and speed of growth of the epidemic outbreak. This is an epidemiological mathematical modeling study. The epidemiological data used were from people infected in the State of Sergipe, in northeastern Brazil, made available by the Ministry of Health 10 . For that, a logistic growth model was used that adds a withdrawal term for individuals as a control measure 11 . The logistic growth model was chosen in relation to the usual compartmental models due to the analytical advantages that will be presented below. Although it is possible to obtain a numerical solution for the number of accumulated cases via computer simulations and parameter adjustments, the associated uncertainty is high since many parameters are used. The following Initial Value Problem (IVP) satisfactorily models our problem: In this equation I(t) represents the number of individuals infected by the coronavirus at time t, given in days, r refers to the rate of contagion with free mobility between people, K is the carrying capacity of the environment and p; the percentage of individuals (infected or not) removed from social life via isolation. We can still rewrite the differential equation as: This way, 0 ≤ p ≤ r will be considered because the withdrawal rate p = 0 establishes no control measure applied, and p = r means maximum control measure capacity achieved. In a classic logistical model, the carrying capacity may be conceptualized as the maximum number of individuals that an ecosystem can sustainably support 11 . Thus, for our model, K refers to the maximum number of infected individuals to reach in a specific region. Given the possibility of contagion most individuals, except for interventions, we used the population of the State of Sergipe, K = 2,298,696, as an initial support capacity 12 . It is possible to notice that p is established as the factor responsible for the control of I. Therefore if p = 0 we will have the case of the classic logistic model in which growth is free and equilibrium over time will occur in I = K, that is, without any control measures. In the past, if p ≠ 0, with p