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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. • Uncertainty is present in determining optimal control of pandemics • In a low infection model, infection dynamics do not impact optimal control • Infection dynamics have a second order impact on optimal control in moderate model [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In the paper, we propose a semiparametric framework for modeling the COVID-19 pandemic. The stochastic part of the framework is based on Bayesian inference. The model is informed by the actual COVID-19 data and the current epidemiological findings about the disease. The framework combines many available data sources (number of positive cases, number of patients in hospitals and in intensive care, etc.) to make outputs as accurate as possible and incorporates the times of non-pharmaceutical governmental interventions which were adopted worldwide to slow-down the pandemic. The model estimates the reproduction number of SARS-CoV-2, the number of infected individuals and the number of patients in different disease progression states in time. It can be used for estimating current infection fatality rate, proportion of individuals not detected and short term forecasting of important indicators for monitoring the state of the healthcare system. With the prediction of the number of patients in hospitals and intensive care units, policy makers could make data driven decisions to potentially avoid overloading the capacities of the healthcare system. The model is applied to Slovene COVID-19 data showing the effectiveness of the adopted interventions for controlling the epidemic by reducing the reproduction number of SARS-CoV-2. It is estimated that the proportion of infected people in Slovenia was among the lowest in Europe (0.350%, 90% CI [0.245–0.573]%), that infection fatality rate in Slovenia until the end of first wave was 1.56% (90% CI [0.94–2.21]%) and the proportion of unidentified cases was 88% (90% CI [83–93]%). The proposed framework can be extended to more countries/regions, thus allowing for comparison between them. One such modification is exhibited on data for Slovene hospitals. • Semiparametric framework combines epidemiological background with Bayesian inference. • Reproduction number, number of hospitalized/ICU patients according to interventions are estimated. • Given reliability and availability of the data, the model can be easily adapted. • Flexibility and reliability is showcased using Slovene COVID-19 data. • Software is publicly available, requiring basic R programming skills. [ABSTRACT FROM AUTHOR]