We develop a new data-driven immuno-epidemiological model with distributed infectivity, recovery and death rates determined from the epidemiological, clinical and experimental data. Immunity in the population is taken into account through the time-dependent number of vaccinated people with different numbers of doses and through the acquired immunity for recovered individuals. The model is validated with the available data. We show that for the first time from the beginning of pandemic COVID-19 some countries reached collective immunity. However, the epidemic continues because of the emergence of new variant BA.2 with a larger immunity escape or disease transmission rate than the previous BA.1 variant. Large epidemic outbreaks can be expected several months later due to immunity waning. These outbreaks can be restrained by an intensive booster vaccination.

A compartmental epidemiological model with distributed recovery and death rates is proposed. In some particular cases, the model can be reduced to the conventional SIR model. However, in general, the dynamics of epidemic progression in this model is different. Distributed recovery and death rates are evaluated from COVID-19 data. The model is validated by the epidemiological data for different countries, and it shows better agreement with the data than the SIR model. The time-dependent disease transmission rate is estimated.

Immuno-epidemiological models with distributed recovery and death rates can describe the epidemic progression more precisely than conventional compartmental models. However, the required immunological data to estimate the distributed recovery and death rates are not easily available. An epidemic model with time delay is derived from the previously developed model with distributed recovery and death rates, which does not require precise immunological data. The resulting generic model describes epidemic progression using two parameters, disease transmission rate and disease duration. The disease duration is incorporated as a delay parameter. Various epidemic characteristics of the delay model, namely the basic reproduction number, the maximal number of infected, and the final size of the epidemic are derived. The estimation of disease duration is studied with the help of real data for COVID-19. The delay model gives a good approximation of the COVID-19 data and of the more detailed model with distributed parameters.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

No abstract