One major bottleneck in the ongoing COVID-19 pandemic is the limited number of critical care beds. Due to the dynamic development of infections and the time lag between when patients are infected and when a proportion of them enters an intensive care unit (ICU), the need for future intensive care can easily be underestimated. To infer future ICU load from reported infections, we suggest a simple statistical model that (1) accounts for time lags and (2) allows for making predictions depending on different future growth of infections. We have evaluated our model for three regions, namely Berlin (Germany), Lombardy (Italy), and Madrid (Spain). Before extensive containment measures made an impact, we first estimate the region-specific model parameters. Whereas for Berlin, an ICU rate of 6%, a time lag of 6 days, and an average stay of 12 days in ICU provide the best fit of the data, for Lombardy and Madrid the ICU rate was higher (18% and 15%) and the time lag (0 and 3 days) and the average stay (4 and 8 days) in ICU shorter. The region-specific models are then used to predict future ICU load assuming either a continued exponential phase with varying growth rates (0-15%) or linear growth. Thus, the model can help to predict a potential exceedance of ICU capacity. Although our predictions are based on small data sets and disregard non-stationary dynamics, our model is simple, robust, and can be used in early phases of the disease when data are scarce.
We consider here an extended SIR model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care unit (ICU) capacity. Our model enables a tractable quantitative analysis of the optimal policy for the control of the epidemic dynamics using both lockdown and detection intervention levers. With parametric specification based on literature on COVID-19, we investigate the sensitivities of various quantities on the optimal strategies, taking into account the su…
We estimate the growth in demand for ICU beds in Chicago during the emerging COVID-19 epidemic, using state-of-the-art computer simulations calibrated for the SARS-CoV-2 virus. The questions we address are these: (1) Will the ICU capacity in Chicago be exceeded, and if so by how much? (2) Can strong mitigation strategies, such as lockdown or shelter in place order, prevent the overflow of capacity? (3) When should such strategies be implemented? Our answers are as follows: (1) The ICU capacity may be exceeded by a large amount, probably by a factor of ten. (2) Strong mitigation can avert this …
Forecasting models have been influential in shaping decision-making in the COVID-19 pandemic. However, there is concern that their predictions may have been misleading. Here, we dissect the predictions made by four models for the daily COVID-19 death counts between March 25 and June 5 in New York state, as well as the predictions of ICU bed utilisation made by the influential IHME model. We evaluated the accuracy of the point estimates and the accuracy of the uncertainty estimates of the model predictions. First, we compared the "ground truth" data sources on daily deaths against which these m…
We analyze an approach to managing the COVID-19 pandemic without shutting down the economy while staying within the capacity of the healthcare system. We base our analysis on a detailed heterogeneous epidemiological model, which takes into account different population groups and phases of the disease, including incubation, infection period, hospitalization, and treatment in the intensive care unit (ICU). We model the healthcare capacity as the total number of hospital and ICU beds for the whole country. We calibrate the model parameters to data reported in several recent research papers. For h…
Objective: To conduct an early estimation of the Basic Reproduction Number (BRN) induced by government interference, and to project resulting day to day number of in-patients, ICU-patients and cumulative number of deaths in a Danish setting. Method: We used the Kermack and McKendrick model with varying basic reproduction number to estimate number infected and age stratified percentages to estimate number of in-patients, ICU-patients and cumulative number of deaths. Changes in basic reproduction number was estimated based on current in-patient numbers. Results: The basic reproductive number in …
We use a simple SIR-like epidemic model which integrates known age-contact patterns for the United States to model the effect of age-targeted mitigation strategies for a COVID-19-like epidemic. We find that, among strategies which end with population immunity, strict age-targeted mitigation strategies have the potential to greatly reduce mortalities and ICU utilization for natural parameter choices.
For countries starting to receive steady supplies of vaccines against SARS-CoV-2, the course of Covid-19 for the following months will be determined by the emergence of new variants and successful roll-out of vaccination campaigns. To anticipate this scenario, we used a multilayer network model developed to forecast the transmission dynamics of Covid-19 in Costa Rica, and to estimate the impact of the introduction of the Delta variant in the country, under two plausible vaccination scenarios, one sustaining Costa Rica's July 2021 vaccination pace of 30,000 doses per day and with high acceptanc…
Mass vaccination offers a promising exit strategy for the COVID-19 pandemic. However, as vaccination progresses, demands to lift restrictions increase, despite most of the population remaining susceptible. Using our age-stratified SEIRD-ICU compartmental model and curated epidemiological and vaccination data, we quantified the rate (relative to vaccination progress) at which countries can lift non-pharmaceutical interventions without overwhelming their healthcare systems. We analyzed scenarios ranging from immediately lifting restrictions (accepting high mortality and morbidity) to reducing ca…
Large scale virological testing of SARS-Cov2 is implemented since May 2020 in France. We assume that the positivity of asymptomatic people not being contact cases (ANBC) is representative of the positivity of the whole French population, which allows estimating the real incidence. We estimate, using Santé Public France reports, that the incidence at the beginning of August was about 0.8% and rose to about 2.4% of the total population at the beginning of September. This corresponds to about 1.6 million people simultaneously infected and 230.000 new infections each day. These evaluations allow t…
Since the onset of the COVID-19 outbreak in Wuhan, China, numerous forecasting models have been proposed to project the trajectory of coronavirus infection cases. We propose a new discrete-time Markov chain transition matrix model that directly incorporates stochastic behavior and for which parameter estimation is straightforward from available data. Using such data from China's Hubei province (for which Wuhan is the provincial capital city), the model is shown to be flexible, robust, and accurate. As a result, it has been adopted by the first Shanghai assistance medical team in Wuhan's Jinyin…
This study presents a new risk-averse multi-stage stochastic epidemics-ventilator-logistics compartmental model to address the resource allocation challenges of mitigating COVID-19. This epidemiological logistics model involves the uncertainty of untested asymptomatic infections and incorporates short-term human migration. Disease transmission is also forecasted through a new formulation of transmission rates that evolve over space and time with respect to various non-pharmaceutical interventions, such as wearing masks, social distancing, and lockdown. The proposed multi-stage stochastic model…
Solid estimates describing the clinical course of SARS-CoV-2 infections are still lacking due to under-ascertainment of asymptomatic and mild-disease cases. In this work, we quantify age-specific probabilities of transitions between stages defining the natural history of SARS-CoV-2 infection from 1,965 SARS-CoV-2 positive individuals identified in Italy between March and April 2020 among contacts of confirmed cases. Infected contacts of cases were confirmed via RT-PCR tests as part of contact tracing activities or retrospectively via IgG serological tests and followed-up for symptoms and clini…
The prevalence of COVID-19 has been the most serious health challenge of the 21th century to date, concerning national health systems on a daily basis, since December 2019 when it appeared in Wuhan City. Nevertheless, most of the proposed mathematical methodologies aiming to describe the dynamics of an epidemic, rely on deterministic models that are not able to reflect the true nature of its spread. In this paper, we propose a SEIHCRDV model - an extension/improvement of the classic SIR compartmental model - which also takes into consideration the populations of exposed, hospitalized, admitted…
The COVID-19 pandemic has created unprecedented challenges worldwide. Strained healthcare providers make difficult decisions on patient triage, treatment and care management on a daily basis. Policy makers have imposed social distancing measures to slow the disease, at a steep economic price. We design analytical tools to support these decisions and combat the pandemic. Specifically, we propose a comprehensive data-driven approach to understand the clinical characteristics of COVID-19, predict its mortality, forecast its evolution, and ultimately alleviate its impact. By leveraging cohort-leve…
The Covid-19 pandemic has made clear the need to improve modern multivariate time-series forecasting models. Current state of the art predictions of future daily deaths and, especially, hospital resource usage have confidence intervals that are unacceptably wide. Policy makers and hospitals require accurate forecasts to make informed decisions on passing legislation and allocating resources. We used US county-level data on daily deaths and population statistics to forecast future deaths. We extended the SIR epidemiological model to a novel model we call the PECAIQR model. It adds several new v…
In the night of February 20, 2020, the first case of novel coronavirus disease (COVID-19) was confirmed in the Lombardy Region, Italy. In the week that followed, Lombardy experienced a very rapid increase in the number of cases. We analyzed the first 5,830 laboratory-confirmed cases to provide the first epidemiological characterization of a COVID-19 outbreak in a Western Country. Epidemiological data were collected through standardized interviews of confirmed cases and their close contacts. We collected demographic backgrounds, dates of symptom onset, clinical features, respiratory tract speci…
We argue that frequent sampling of the fraction of infected people (either by random testing or by analysis of sewage water), is central to managing the COVID-19 pandemic because it both measures in real time the key variable controlled by restrictive measures, and anticipates the load on the healthcare system due to progression of the disease. Knowledge of random testing outcomes will (i) significantly improve the predictability of the pandemic, (ii) allow informed and optimized decisions on how to modify restrictive measures, with much shorter delay times than the present ones, and (iii) ena…
In December 2019, a newly discovered SARS-CoV-2 virus was emerged from China and propagated worldwide as a pandemic. In the absence of preventive medicine or a ready to use vaccine, mathematical models can provide useful scientific insights about transmission patterns and targets for drug development. In this study, we propose a within-host mathematical model of SARS-CoV-2 infection considering innate and adaptive immune responses. We analyze the equilibrium points of the proposed model and obtain an expression of the basic reproduction number. We then numerically show the existence of a trans…
A Nine-Compartment Nonlinear Epidemic Model with Spline-Based Identification of Time-Varying Transmission and Vaccination Dynamics: Application to the COVID-19 Third Wave in Italy
University of Palermo（巴勒莫大学）；University of Bayreuth（拜罗伊特大学）；Regional Health Care and Social Agency of Lodi, Azienda Socio-Sanitaria Territoriale (ASST) Lodi（洛迪地区卫生与社会服务机构，地方社会卫生企业（ASST）洛迪）；InEmbryo S.r.l.s.（InEmbryo有限公司）；Department of Internal Medicine “PROMISE”, University of Palermo（巴勒莫大学“PROMISE”内科学系）
Predicting an accurate expected number of future COVID-19 cases is essential to properly evaluate the effectiveness of any treatment or preventive measure. This study aimed to identify the most appropriate mathematical model to prospectively predict the expected number of cases without any intervention. The total number of cases for the COVID-19 epidemic in 28 countries was analyzed and fitted to several simple rate models including the logistic, Gompertz, quadratic, simple square, and simple exponential growth models. The resulting model parameters were used to extrapolate predictions for mor…
