ABSTRACT
Adding the notion of spatial locality to the susceptible-infected-recovered (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.
ABSTRACT
The major economic and health consequences of COVID-19 called for various protective measures and mass vaccination campaigns. A previsional model was used to predict the future impacts of various measure combinations on COVID-19 mortality over a 400-day period in France. Calibrated on previous national hospitalization and mortality data, an agent-based epidemiological model was used to predict individual and combined effects of booster doses, vaccination of refractory adults, and vaccination of children, according to infection severity, immunity waning, and graded non-pharmaceutical interventions (NPIs). Assuming a 1.5 hospitalization hazard ratio and rapid immunity waning, booster doses would reduce COVID-19-related deaths by 50-70% with intensive NPIs and 93% with moderate NPIs. Vaccination of initially-refractory adults or children ≥5 years would half the number of deaths whatever the infection severity or degree of immunity waning. Assuming a 1.5 hospitalization hazard ratio, rapid immunity waning, moderate NPIs and booster doses, vaccinating children ≥12 years, ≥5 years, and ≥6 months would result in 6212, 3084, and 3018 deaths, respectively (vs. 87,552, 64,002, and 48,954 deaths without booster, respectively). In the same conditions, deaths would be 2696 if all adults and children ≥12 years were vaccinated and 2606 if all adults and children ≥6 months were vaccinated (vs. 11,404 and 3624 without booster, respectively). The model dealt successfully with single measures or complex combinations. It can help choosing them according to future epidemic features, vaccination extensions, and population immune status.
ABSTRACT
The outbreak of the SARS-CoV-2 virus, enhanced by rapid spreads of variants, has caused a major international health crisis, with serious public health and economic consequences. An agent-based model was designed to simulate the evolution of the epidemic in France over 2021 and the first six months of 2022. The study compares the efficiencies of four theoretical vaccination campaigns (over 6, 9, 12, and 18 months), combined with various non-pharmaceutical interventions. In France, with the emergence of the Alpha variant, without vaccination and despite strict barrier measures, more than 600,000 deaths would be observed. An efficient vaccination campaign (i.e., total coverage of the French population) over six months would divide the death toll by 10. A vaccination campaign of 12, instead of 6, months would slightly increase the disease-related mortality (+6%) but require a 77% increase in ICU bed-days. A campaign over 18 months would increase the disease-related mortality by 17% and require a 244% increase in ICU bed-days. Thus, it seems mandatory to vaccinate the highest possible percentage of the population within 12, or better yet, 9 months. The race against the epidemic and virus variants is really a matter of vaccination strategy.
ABSTRACT
The dynamics of the spread of epidemics, such as the recent outbreak of the SARS-CoV-2 virus, is highly nonlinear and therefore difficult to predict. As time evolves in the present pandemic, it appears more and more clearly that a clustered dynamics is a key element of the 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. This sophistication is compatible with more advanced compartmental models and allows, at the lowest level of complexity, to leverage the well-mixedness assumption. The so-obtained SBIR model takes into account the effect of inhomogeneity on epidemic spreading, and 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 captured without the need to vary the coefficients of the model with time. We show that this decay exponent is directly determined by the diffusion of the ensemble of clustered individuals and can be related to a global reproduction number, that overrides the classical, local reproduction number.