Nowcasting and forecasting COVID-19 waves: the recursive and stochastic nature of transmission

Month-to-month all-cause mortality forecasting: a method allowing for changes in seasonal patterns

Forecasting of seasonal mortality patterns can provide useful information for planning health-care demand and capacity. Timely mortality forecasts are needed during severe winter spikes and/or pandemic waves to guide policy-making and public health decisions. In this article, we propose a flexible method for forecasting all-cause mortality in real time considering short-term changes in seasonal patterns within an epidemiologic year. All-cause mortality data have the advantage of being available with less delay than cause-specific mortality data. In this study, we use all-cause monthly death counts obtained from the national statistical offices of Denmark, France, Spain, and Sweden from epidemic seasons 2012-2013 through 2021-2022 to demonstrate the performance of the proposed approach. The method forecasts deaths 1 month ahead, based on their expected ratio to the next month. Prediction intervals are obtained via bootstrapping. The forecasts accurately predict the winter mortality peaks before the COVID-19 pandemic. Although the method predicts mortality less accurately during the first wave of the COVID-19 pandemic, it captures the aspects of later waves better than other traditional methods. The method is attractive for health researchers and governmental offices for aiding public health responses because it uses minimal input data, makes simple and intuitive assumptions, and provides accurate forecasts both during seasonal influenza epidemics and during novel virus pandemics.

Stochastic transmission in epidemiological models

Recent empirical evidence suggests that the transmission coefficient in susceptible-exposed-infected-removed-like (SEIR-like) models evolves with time, presenting random patterns, and some stylized facts, such as mean-reversion and jumps. To address such observations we propose the use of jump-diffusion stochastic processes to parameterize the transmission coefficient in an SEIR-like model that accounts for death and time-dependent parameters. We provide a detailed theoretical analysis of the proposed model proving the existence and uniqueness of solutions as well as studying its asymptotic behavior. We also compare the proposed model with some variations possibly including jumps. The forecast performance of the considered models, using reported COVID-19 infections from New York City, is then tested in different scenarios. Despite the simplicity of the epidemiological model, by considering stochastic transmission, the forecasted scenarios were fairly accurate.

The role of delay in vaccination rate on Covid-19

The role of vaccination in tackling Covid-19 and the potential consequences of a time delay in vaccination rate are discussed. This study presents a mathematical model that incorporates the rate of vaccination and parameters related to the presence and absence of time delay in the context of Covid-19. We conducted a study on the global dynamics of a Covid-19 outbreak model, which incorporates a vaccinated population and a time delay parameter. Our findings demonstrate the global stability of these models. Our observation indicates that lower vaccination rates are associated with an increase in the overall number of infected individuals. The stability of the corresponding time delay model is determined by the value of the time delay parameter. If the time delay parameter is less than the critical value at which the Hopf bifurcation occurs, the model is stable. The results are supported by numerical illustrations that have epidemiological relevance.

A hospital demand and capacity intervention approach for COVID-19

The mathematical interpretation of interventions for the mitigation of epidemics in the literature often involves finding the optimal time to initiate an intervention and/or the use of the number of infections to manage impact. Whilst these methods may work in theory, in order to implement effectively they may require information which is not likely to be available in the midst of an epidemic, or they may require impeccable data about infection levels in the community. In reality, testing and cases data can only be as good as the policy of implementation and the compliance of the individuals, which implies that accurately estimating the levels of infections becomes difficult or complicated from the data that is provided. In this paper, we demonstrate a different approach to the mathematical modelling of interventions, not based on optimality or cases, but based on demand and capacity of hospitals who have to deal with the epidemic on a day to day basis. In particular, we use data-driven modelling to calibrate a susceptible-exposed-infectious-recovered-died type model to infer parameters that depict the dynamics of the epidemic in several regions of the UK. We use the calibrated parameters for forecasting scenarios and understand, given a maximum capacity of hospital healthcare services, how the timing of interventions, severity of interventions, and conditions for the releasing of interventions affect the overall epidemic-picture. We provide an optimisation method to capture when, in terms of healthcare demand, an intervention should be put into place given a maximum capacity on the service. By using an equivalent agent-based approach, we demonstrate uncertainty quantification on the likelihood that capacity is not breached, by how much if it does, and the limit on demand that almost guarantees capacity is not breached.