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Lockdown and social distancing restrictions have been widely used as part of policy efforts aimed at controlling the ongoing COVID-19 pandemic. Since these restrictions have a negative impact on the economy, there exists a strong incentive to relax these policies while protecting public health. Using a modified SEIR epidemiological model, this paper explores the costs and benefits associated with the sequential release of specific groups based on age and risk from lockdown and social distancing measures. The results in this paper suggest that properly designed staggered-release policies can do better than simultaneous-release policies in terms of protecting the most vulnerable members of a population, reducing health risks overall, and increasing economic activity., Highlights • Uses SEIR-type epidemic models for COVID-19 with multiple age-groups. • Analyzes effects of staggering the release of different groups from restrictions. • Staggered-release policies can reduce health risks and increase economic activity.

The COVID-19 pandemic has challenged authorities at different levels of government administration aroundthe globe. When faced with diseases of this severity, it is useful for the authorities to have prediction tools to estimate in advance the impact on the health system as well as the human, material, and economic resources that will be necessary. In this paper, we construct an extended Susceptible?Exposed?Infected?Recovered modelthat incorporates the social structure of Mar del Plata, the 4◦ most inhabited city in Argentina and head ofthe Municipality of General Pueyrredón. Moreover, we consider detailed partitions of infected individualsaccording to the illness severity, as well as data of local health resources, to bring predictions closer to thelocal reality. Tuning the corresponding epidemic parameters for COVID-19, we study an alternating quarantinestrategy: a part of the population can circulate without restrictions at any time, while the rest is equally dividedinto two groups and goes on successive periods of normal activity and lockdown, each one with a durationof days. We also implement a random testing strategy with a threshold over the population. We found that = 7 is a good choice for the quarantine strategy since it reduces the infected population and, conveniently,it suits a weekly schedule. Focusing on the health system, projecting from the situation as of September 30,we foresee a difficulty to avoid saturation of the available ICU, given the extremely low levels of mobility thatwould be required. In the worst case, our model estimates that four thousand deaths would occur, of which30% could be avoided with proper medical attention. Nonetheless, we found that aggressive testing wouldallow an increase in the percentage of people that can circulate without restrictions, and the medical facilitiesto deal with the additional critical patients would be relatively low. Fil: Vassallo, Lautaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina Fil: Pérez, Ignacio Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina Fil: Alvarez Zuzek, Lucila G.. University Of Georgetown; Estados Unidos Fil: Amaya, Julián. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina Fil: Torres, Marcos F.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina Fil: Valdez, Lucas Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina Fil: la Rocca, Cristian Ernesto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina Fil: Braunstein, Lidia Adriana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina

Coronavirus disease 2019 (COVID-19), an infectious disease caused by the infection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is spreading and causing the global coronavirus pandemic. The viral dynamics of SARS-CoV-2 infection have not been quantitatively investigated. In this paper, we use mathematical models to study the pathogenic features of SARS-CoV-2 infection by examining the interaction between the virus, cells and immune responses. Models are fit to the data of SARS-CoV-2 infection in patients and non-human primates. Data fitting and numerical simulation show that viral dynamics of SARS-CoV-2 infection have a few distinct stages. In the initial stage, viral load increases rapidly and reaches the peak, followed by a plateau phase possibly generated by lymphocytes as a secondary target of infection. In the last stage, viral load declines due to the emergence of adaptive immune responses. When the initiation of seroconversion is late or slow, the model predicts viral rebound and prolonged viral persistence, consistent with the observation in non-human primates. Using the model we also evaluate the effect of several potential therapeutic interventions for SARS-CoV-2 infection. Model simulation shows that anti-inflammatory treatments or antiviral drugs combined with interferon are effective in reducing the duration of the viral plateau phase and diminishing the time to recovery. These results provide insights for understanding the infection dynamics and might help develop treatment strategies against COVID-19., Highlights • Mathematical models are developed to study SARS-CoV-2 infection. • Models are fit to viral load data of patients and non-human primates. • Viral dynamics of SARS-CoV-2 infection has a few distinct stages. • Model explains viral rebound and prolonged viral persistence. • Implication for treatment strategies is discussed.

The COVID-19 pandemic illustrates the importance of treatment-related decision making in populations. This article considers the case where the transmission rate of the disease as well as the efficiency of treatments is subject to uncertainty. We consider two different regimes, or submodels, of the stochastic SIR model, where the population consists of three groups: susceptible, infected and recovered and dead. In the first regime the proportion of infected is very low, and the proportion of susceptible is very close to 100the proportion of infected is moderate, but not negligible. We show that the first regime corresponds almost exactly to a well-known problem in finance, the problem of portfolio and consumption decisions under mean-reverting returns (Wachter, JFQA 2002), for which the optimal control has an analytical solution. We develop a perturbative solution for the second problem. To our knowledge, this paper represents one of the first attempts to develop analytical/perturbative solutions, as opposed to numerical solutions to stochastic SIR models.

This paper investigates the lockdowns to contain the spread of the SARS-CoV-2 coronavirus in France, Germany, Italy, Spain, the UK and the US and also recent developments since these lockdowns have been relaxed. The analysis employs a two-stage SEIR model with different reproductive numbers pre- and post-lockdown. These parameters are estimated from data on the daily number of confirmed cases in a process that automatically detects the time at which the lockdown became effective. The model is evaluated by considering its predictive accuracy on current data and is then extended to a three-stage version to explore relaxations. The results show the extent to which each country was successful in reducing the reproductive number and demonstrate how the approach is able to model recent increases in the number of cases in all six countries, including the second peak in the US. The results also indicate that the current levels of relaxation in all five European countries could lead to significant second waves that last longer than the corresponding first waves. While there is uncertainty about the implications of these findings at this stage, they do suggest that a lot of vigilance is needed.