The 2019-2020 coronavirus disease pandemic is a pandemic started by an outbreak that emerged in late 2019 , caused by the coronavirus-2 virus of the severe acute respiratory syndrome (SARS-CoV-2). It To prevent the spread of the virus, governments have imposed travel restrictions, confinements, event cancellations, and the closure of establishments and quarantines as described in (Zhu et al, 2020) . These restrictive measures have focused mainly on trying to flatten the epidemic curve (Tobias, 2020) In this article, a Systems Dynamics model has been developed, this methodology is widely known to model and simulate epidemics, such as Ebola, MERS, and other infectious diseases (SDS, 2020) With this model, different quarantine periods were simulated and evaluated, and it was possible to see the effectiveness in reducing contacts and deaths.
The Stock and Flows diagram for the COVID-19 epidemic is presente in Fig. 1 . The model was elaborated with the Systems Dynamics methodology, following to Sterman (2000) and is composed of four stock variables: the susceptible, infected, recovered, and deaths. Similarly, piecewise functions were included to represent the different quarantine scenarios. The model also presents auxiliary variables and parameters that were constructed from bibliographic references or some estimated, as shown in the Table. 1. For the simulation of the model, a time limit of 150 days was taken into account, and the integration method was the RK-4 established in the Vensim Ple software. From the Stock and Flows diagram, it is possible to obtain the mathematical model (Complete model and notation in appendix 1) that represents the studied problem, as shown below:
The simulation without any type of intervention (Scenario 0) is presented in Fig. 2 , where the typical behavior of an epidemic is presented. Here we start with a daily contact rate of 70 contacts/person and an infectivity rate of 0.025 for an R0 = 2.5. Table 1 shows the initial conditions of the model. The Greenline is scenario A, and The Grayline is without lockdown. Scenario A is when only an extended lockdown or quarantine is considered, and it is want to try to decrease the contagion curve, this could be useful when the local economy is durable and can withstand a long period of confinement.
Scenario B considers two short lockdowns and a smart lockdown between them, that is, after the end of the first lockdown, another period of equal duration is left, where activities are resumed, but guaranteeing a reduction in daily contacts of at least 50 % Scenario C represents a first "medium" lockdown of 40 days is implemented. Then a 40-day smart lockdown is opened, guaranteeing in this a limit of contacts of up to 40% of the contacts in ordinary life.
For all initial quarantines, isolation effectiveness of 90% was considered, that is, they reduce contacts by this percentage.
Once the lockdown scenarios were over, a contact restriction of 50% was maintained, to prevent future infection so that it can gradually return to normal activities implemented. Suddenly, it could be said that the three types of quarantine proposed are effective in reducing infected concerning the scenario in which there is no quarantine. However, scenario B and scenario C may be the best strategies in which the infected do not collapse hospital capacity. Fig.6 shows the comparison of the number of deaths that could have in the four proposed scenarios.
A lockdown to prevent the increase of COVID infection must be evaluated for well-defined contexts. It is different from doing a lockdown in Wuhan than Buenos Aires or Bogotá or Madrid, each city has different characteristics, such as the population, economy, transport, and health systems, this changes the levels of contact that a person can have daily. However, it is also necessary to evaluate the lockdown for intermediate and small cities since their economic models could have damages that are almost impossible to repair.
Lockdowns are essential to save time and strengthen health systems that can become overloaded. The actual contagion data is limited and short, so it is necessary to prospectively evaluate each measure that public health authorities and governments wish to implement.
The recommendation, according to the simulations, is to carry out an extended initial lockdown and then gradually return to activities, controlling social contacts so that at the end of this period should only be a maximum of 40% of the contacts they had before the quarantine.
Quarantine duration times should be very cautious as they could shift the contagion curve over time and generate a spike with a delay time.
The authors declare that they have no competing interests.
J o u r n a l P r e -p r o o f 