Periodic epidemic outbursts explained by local saturation of clusters (preprint)

Adding the notion of spatial locality to the susceptible-infected-removed (or SIR) model, allows to capture local saturation of an epidemic. The resulting minimum model of an epidemic, consisting of five ordinary differential equations with constant model coefficients, reproduces slowly decaying periodic outbursts, as observed in the COVID-19 or Spanish flu epidemic. It is shown that if immunity decays, even slowly, the model yields a fully periodic dynamics.

Adapting French COVID-19 vaccination campaign duration to variant dissemination (preprint)

Background The outbreak of SARS-CoV-2 virus has caused a major international health crisis with serious consequences in terms of public health and economy. In France, two lockdown periods were decided in 2020 to avoid the saturation of intensive care units (ICU) and an increase in mortality. The rapid dissemination of variant SARS-CoV-2 VOC 202012/01 has strongly influenced the course of the epidemic. Vaccines have been rapidly developed. Their efficacy against the severe forms of the disease has been established, and their efficacy against disease transmission is under evaluation. The aim of this paper is to compare the efficacy of several vaccination strategies in the presence of variants in controlling the COVID-19 epidemic through population immunity. Methods An agent-based model was designed to simulate with different scenarios the evolution of COVID-19 pandemic in France over 2021 and 2022. The simulations were carried out ignoring the occurrence of variants then taking into account their diffusion over time. The expected effects of three Non-Pharmaceutical Interventions (Relaxed-NPI, Intensive-NPI, and Extended-NPI) to limit the epidemic extension were compared. The expected efficacy of vaccines were the values recently estimated in preventing severe forms of the disease (75% and 94%) for the current used vaccines in France (Pfizer-BioNTech and Moderna since January 11, 2021, and AstraZeneca since February 2, 2021). All vaccination campaigns reproduced an advanced age-based priority advised by the Haute Autorit[c] de Sant[c]. Putative reductions of virus transmission were fixed at 0, 50, 75 and 90%. The effects of four vaccination campaign durations (6-month, 12-month, 18-month and 24-month) were compared. Results In the absence of vaccination, the presence of variants led to reject the Relaxed-NPI because of a high expected number of deaths (170 to 210 thousands) and the significant overload of ICUs from which 35 thousand patients would be deprived. In comparison with the situation without vaccination, the number of deaths was divided by 7 without ICU saturation with a 6-month vaccination campaign. A 12-month campaign would divide the number of deaths by 3 with Intensive-NPI and by 6 with Extended-NPI (the latter being necessary to avoid ICU saturation). With 18-month and 24-month vaccination campaigns without Extended-NPI, the number of deaths and ICU admissions would explode. Conclusion Among the four compared strategies the 6-month vaccination campaign seems to be the best response to changes in the dynamics of the epidemic due to the variants. The race against the COVID-19 epidemic is a race of vaccination strategy. Any further vaccination delay would increase the need of strengthened measures such as Extended-NPI to limit the number of deaths and avoid ICU saturation.

Lessons learnt from the use of compartmental models over the COVID-19 induced lockdown in France (preprint)

BackgroundCompartmental models may help deciding on public health interventions. They were used during the first French COVID-19 lockdown to estimate the reproduction numbers and predict the number of hospital beds required. This study aimed to assess the ability of similar compartmental models to reflect equivalent epidemic dynamics. MethodsThe study considered three compartmental models independently designed to describe the COVID-19 outbreak in France. These models were scrutinized and their compartments and parameters expressed in a common framework. The parameters were set alike in the three models according to values taken from the literature. The models were calibrated using a common maximum likelihood function and the same hospitalization data taken from two official public databases. The calibration procedure was repeated over three different periods to compare model abilities to (1) fit over the whole lockdown; (2) predict the course of the epidemic during the lockdown; and, (3) provide a set of profiles to forecast the hospitalization prevalence after the lockdown. The study considered national and regional coverages. ResultsThe three models were all flexible enough to match hospitalization data during the lockdown, but the numbers of cases in the other compartments differed. The three models failed to predict reliably the number of hospitalizations after the fitting periods at national and regional levels. At the national scale, a refined calibration led to epidemic course profiles that reflected hospitalizations dynamics and corresponded to reproduction numbers coherent with official and literature estimates. This result could not be consistently obtained at the regional scale. ConclusionNot all predictions were consistent between models. Even over the period used for calibration by fitting to hospitalization cases, important differences remained regarding the prevalence in the other compartments. Prevalence data are needed to further constrain the calibration and perform selection between still divergent models. This underlines strongly the need for repeated prevalence studies on representative samples, stratified by age and regions, which would undergo virological or serological tests.

Clustering, diffusion and evolution of COVID19 infections during lock-down (preprint)

Epidemics such as the spreading of COVID19-virus are highly non linear, and therefore difficult to predict. In the present pandemy as time evolves, it appears more and more clearly that a clustered dynamics is a key element of description. This means that the disease rapidly evolves within spatially localized networks, that diffuse and eventually create new clusters. We improve upon the simplest possible compartmental model, the SIR model, by adding an additional compartment associated with the clustered individuals. The so-obtained SBIR model compares satisfactorily with results on the pandemic propagation in a number of European countries, during and immediately after lock-down. Especially, the decay exponent of the number of new cases after the first peak of the epidemic, is observed to be very similar for countries in which a strict lock-down is applied. We derive an analytical expression for the value of this exponent, relating it to the initial exponential growth phase of the epidemic and to the time-scale of cluster-diffusion.