COVID-19 effective reproduction number determination: an application, and a review of issues and influential factors

Objectives An essential indicator of COVID-19 transmission is the effective reproduction number (R t ), the number of cases which an infected individual is expected to infect at a particular point in time; curves of the evolution of R t over time (transmission curves) reflect the impact of preventive measures and whether an epidemic is controlled. Methods We have created a Shiny/R web application (https://alfredob.shinyapps.io/estR0/) with user-selectable features: open data sources with daily COVID-19 incidences from all countries and many regions, customizable preprocessing options (smoothing, proportional increment, etc.), different MonteCarlo-Markov-Chain estimates of the generation time or serial interval distributions and state-of-the-art R t estimation frameworks (EpiEstim, R 0). This application could be used as a tool both to obtain transmission estimates and to perform interactive sensitivity analysis. We have analyzed the impact of these factors on transmission curves. We also have obtained curves at the national and sub-national level and analyzed the impact of epidemic control strategies, superspreading events, socioeconomic factors and outbreaks. Results Reproduction numbers showed earlier anticipation compared to active prevalence indicators (14-day cumulative incidence, overall infectivity). In the sensitivity analysis, the impact of different R t estimation methods was moderate/small, and the impact of different serial interval distributions was very small. We couldn’t find conclusive evidence regarding the impact of alleged superspreading events. As a limitation, dataset quality can limit the reliability of the estimates. Conclusions The thorough review of many examples of COVID-19 transmission curves support the usage of R t estimates as a robust transmission indicator.

The impact of quarantine on Covid-19 infections

Objectives: Coronavirushas had profound effects on people’s lives and the economy of many countries, generating controversy between the need to establish quarantines and other social distancing measures to protect people’s health and the need to reactivate the economy. This study proposes and applies a modification of the SIR infection model to describe the evolution of coronavirus infections and to measure the effect of quarantine on the number of people infected. Methods: Two hypotheses, not necessarily mutually exclusive, are proposed for the impact of quarantines. According to the first hypothesis, quarantine reduces the infection rate, delaying new infections over time without modifying the total number of people infected at the end of the wave. The second hypothesis establishes that quarantine reduces the population infected in the wave. The two hypotheses are tested with data for a sample of 10 districts in Santiago, Chile. Results: The results of applying the methodology show that the proposed model describes well the evolution of infections at the district level. The data shows evidence in favor of the first hypothesis, quarantine reduces the infection rate; and not in favor of the second hypothesis, that quarantine reduces the population infected. Districts of higher socio-economic levels have a lower infection rate, and quarantine is more effective. Conclusions: Quarantine, in most districts, does not reduce the total number of people infected in the wave; it only reduces the rate at which they are infected. The reduction in the infection rate avoids peaks that may collapse the health system.

An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting

Recently, various mathematical models have been proposed to model COVID-19 outbreak. These models are an effective tool to study the mechanisms of coronavirus spreading and to predict the future course of COVID-19 disease. They are also used to evaluate strategies to control this pandemic. Generally, SIR compartmental models are appropriate for understanding and predicting the dynamics of infectious diseases like COVID-19. The classical SIR model is initially introduced by Kermack and McKendrick (cf. (Anderson, R. M. 1991. “Discussion: the Kermack–McKendrick Epidemic Threshold Theorem.” Bulletin of Mathematical Biology 53 (1): 3–32; Kermack, W. O., and A. G. McKendrick. 1927. “A Contribution to the Mathematical Theory of Epidemics.” Proceedings of the Royal Society 115 (772): 700–21)) to describe the evolution of the susceptible, infected and recovered compartment. Focused on the impact of public policies designed to contain this pandemic, we develop a new nonlinear SIR epidemic problem modeling the spreading of coronavirus under the effect of a social distancing induced by the government measures to stop coronavirus spreading. To find the parameters adopted for each country (for e.g. Germany, Spain, Italy, France, Algeria and Morocco) we fit the proposed model with respect to the actual real data. We also evaluate the government measures in each country with respect to the evolution of the pandemic. Our numerical simulations can be used to provide an effective tool for predicting the spread of the disease.

Modifying the network-based stochastic SEIR model to account for quarantine: an application to COVID-19

Objectives: Diseases such as SARS-CoV-2 have novel features that require modifications to the standard network-based stochastic SEIR model. In particular, we introduce modifications to this model to account for the potential changes in behavior patterns of individuals upon becoming symptomatic, as well as the tendency of a substantial proportion of those infected to remain asymptomatic. Methods: Using a generic network model where every potential contact exists with the same common probability, we conduct a simulation study in which we vary four key model parameters (transmission rate, probability of remaining asymptomatic, and the mean lengths of time spent in the exposed and infectious disease states) and examine the resulting impacts on various metrics of epidemic severity, including the effective reproduction number. We then consider the effects of a more complex network model. Results: We find that the mean length of time spent in the infectious state and the transmission rate are the most important model parameters, while the mean length of time spent in the exposed state and the probability of remaining asymptomatic are less important. We also find that the network structure has a significant impact on the dynamics of the disease spread. Conclusions: In this article, we present a modification to the network-based stochastic SEIR epidemic model which allows for modifications to the underlying contact network to account for the effects of quarantine. We also discuss the changes needed to the model to incorporate situations where some proportion of the individuals who are infected remain asymptomatic throughout the course of the disease.

Covid-19: were curfews in France associated with hospitalisations?

Objectives A curfew was introduced in France in October 2020 to reduce the spread of Covid-19. This was done for two weeks in 16 departments, or for one week in 38 others, 42 departments not being subjected to the curfew. This article compares the number of new daily hospital admissions in these departments. Methods The ratio of the number of new hospitalisations during these two weeks and in the previous two weeks was computed in the three categories of departments. Results The increase in new hospitalisations was lower in departments under curfew for two weeks than in all other departments, and this result does not seem to be linked to characteristics of the departments before curfew. Conclusions This result shows that the two-week curfew is linked to a lower increase of hospitalisations, but not that the curfew by itself is the cause of this result, as other factors may have played a role.

Mathematical formation and analysis of COVID-19 pool tests strategies

Objectives The excessive spread of the pandemic COVID-19 around the globe has put mankind at risk. The medical infrastructure and resources are frazzled, even for the world's top economies, due to the large COVID-19 infection. To cope up with this situation, countries are exploring the pool test strategies. In this paper, a detailed analysis has been done to explore the efficient pooling strategies. Given a population and the known fact that the percentage of people infected by the virus, the minimum number of tests to identify COVID-19 positive cases from the entire population are found. In this paper, the problem is formulated with an objective to find a minimum number of tests in the worst case where exactly one positive sample is there in a pool which can happen considering the fact that the groups are formed by choosing samples randomly. Therefore, the thrust stress is on minimizing the total number of tests by finding varying pool sizes at different levels (not necessarily same size at all levels), although levels can also be controlled. Methods Initially the problem is formulated as an optimization problem and there is no constraint on the number of levels upto which pooling can be done. Finding an analytical solution of the problem was challenging and thus the approximate solution was obtained and analyzed. Further, it is observed that many times it is pertinent to put a constraint on the number of levels upto which pooling can be done and thus optimizing with such a constraint is also done using genetic algorithm. Results An empirical evaluation on both realistic and synthetic examples is done to show the efficiency of the procedures and for lower values of percentage infection, the total number of tests are very much less than the population size. Further, the findings of this study show that the general COVID-19 pool test gives the better solution for a small infection while as the value of infection becomes significant the single COVID-19 pool test gives better results. Conclusions This paper illustrates the formation and analysis of polling strategies, which can be opted for the better utilization of the resources. Two different pooling strategies are proposed and these strategies yield accurate insight considering the worst case scenario. The analysis finds that the proposed bounds can be efficiently exploited to ascertain the pool testing in view of the COVID-19 infection rate.

Dynamic data-driven algorithm to predict cumulative COVID-19 infected cases using susceptible-infected-susceptible model

Objectives In recent times, researchers have used Susceptible-Infected-Susceptible (SIS) model to understand the spread of the COVID-19 pandemic. The SIS model has two compartments, susceptible and infected. In this model, the interest is to determine the number of infected cases at a given time point. However, it is also essential to know the cumulative number of infected cases at a given time point, which is not directly available from the SIS model's present structure. The objective is to provide a modified SIS model to address that gap. Methods In this work, we propose a modified structure of the SIS model to determine the cumulative number of infected cases at a given time point. We develop a dynamic data-driven algorithm to estimate the model parameters based on an optimally chosen training phase to predict the number of cumulative infected cases. Results We demonstrate the proposed algorithm's prediction performance using COVID-19 data from Delhi, India's capital city. Considering different time periods, we observed the proposed algorithm’s performance using the modified SIS model is well to predict the cumulative infected cases with two different prediction periods 30 and 40. Our study supports the idea of estimating the modified SIS model's parameters based on the optimal training phase instead of the entire history as the training phase. Conclusions Here, we have provided a modified SIS model that accounts for deaths due to disease and predicts cumulative infected cases based on an optimally chosen training phase. The proposed estimation process is beneficial when the disease under study changes its spreading pattern over time. We have developed the modified SIS model considering COVID-19 as the disease under focus. However, the model and algorithms can be applied to predict the cumulative cases of other infectious diseases.

Delaying the peak of the COVID-19 epidemic with travel restrictions

Objectives: Travel restrictions is an often-used tool for governments to prevent the spread of COVID-19. Methods: We here used a simple simulation model to investigate the potential effects of travel restrictions within a country. Results: We found that travel restrictions can delay the peak of the epidemic considerably, but do not affect the spread within the country. We also investigated the effect of implementing travel restrictions early or later in the epidemic, and found that fast implementation is crucial for delaying the epidemic. Conclusions: Fast implementation of travel restrictions is crucial for delaying the peak of a subsequent outbreak of COVID-19 within a country.

Applying SEIR model without vaccination for COVID-19 in case of the United States, Russia, the United Kingdom, Brazil, France, and India

Objectives: Compartmental models are helpful tools to simulate and predict the spread of infectious diseases. In this work we use the SEIR model to discuss the spreading of COVID-19 pandemic for countries with the most confirmed cases up to the end of 2020, i.e. the United States, Russia, the United Kingdom, France, Brazil, and India. The simulation considers the susceptible, exposed, infective, and the recovered cases of the disease. Method: We employ the order Runge–Kutta method to solve the SIER model equations-for modelling and forecasting the spread of the new coronavirus disease. The parameters used in this work are based on the confirmed cases from the real data available for the countries reporting most cases up to December 29, 2020. Results: We extracted the coefficients of the exposed, infected, recovered and mortality rate of the SEIR model by fitting the collected real data of the new coronavirus disease up to December 29, 2020 in the countries with the most cases. We predict the dates of the peak of the infection and the basic reproduction number for the countries studied here. We foresee COVID-19 peaks in January-February 2021 in Brazil and the United Kingdom, and in February-March 2021 in France, Russia, and India, and in March-April 2021 in the United States. Also, we find that the average value of the SARS-CoV-2 basic reproduction number is 2.1460. Conclusion: We find that the predicted peak infection of COVID-19 will happen in the first half of 2021 in the six considered countries. The basic SARS-CoV-19 reproduction number values range within 1.0158–3.6642 without vaccination.

Stepwise Markov model: a good method for forecasting mechanical ventilator crisis in COVID-19 pandemic

Objectives One important variable influencing day-to-day decisions in COVID-19 pandemic has been an impending shortage of mechanical ventilators due to the large number of people that become infected with the virus due to its high contagiousness. We developed a stepwise Markov model (a) to make a short-term prediction of the number of patients on ventilator, and (b) to determine a possible date for a ventilator crisis. Methods Starting with the exponential curve of new cases in the previous 14 days, we calculated a Markov model every 5 days thereafter, resulting in a daily estimate of patients on ventilator for the following 25 days, which we compared with the daily number of devices in use to predict a date for ventilator crisis. Results During the modeled period, the observed and predicted Markov curves of patients on ventilator were very similar, a finding confirmed by both linear regression (r=0.984; p<0.0001) and the near coincidence with the identity line. Our model estimated ventilator shortage in Chile for June 1st, if the number of devices had remained stable. However, the crisis did not occur due to acquisition of new ventilators by the Ministry of Health. Conclusions In Chile as in many other countries experiencing several asynchronous local peaks of COVID-19, the stepwise Markov model could become a useful tool for predicting the date of mechanical ventilator crisis. We propose that our model could help health authorities to: (a) establish a better ventilator distribution strategy and (b) be ready to reinstate restrictions only when necessary so as not to paralyze the economy as much.