Reaching collective immunity for COVID-19: an estimate with a heterogeneous model based on the data for Italy

Abstract

Background. At the current stage of COVID-19 pandemic, forecasts become particularly important regarding the possibility that the total incidence could reach the level where the disease stops spreading because a considerable portion of the population has become immune and collective immunity could be reached. Such forecasts are valuable because the currently undertaken restrictive measures prevent mass morbidity but do not result in the development of a robust collective immunity. Thus, in the absence of efficient vaccines and medical treatments, lifting restrictive measures carries the risk that a second wave of the epidemic could occur. Methods. We developed a heterogeneous model of COVID-19 dynamics. The model accounted for the differences in the infection risk across subpopulations, particularly the age-depended susceptibility to the disease. Based on this model, an equation for the minimal number of infections was calculated as a condition for the epidemic to start declining. The basic reproductive number of 2.5 was used for the disease spread without restrictions. The model was applied to COVID-19 data from Italy. Findings. We found that the heterogeneous model of epidemic dynamics yielded a lower proportion, compared to a homogeneous model, for the minimal incidence needed for the epidemic to stop. When applied to the data for Italy, the model yielded a more optimistic assessment of the minimum total incidence needed to reach collective immunity: 43% versus 60% estimated with a homogeneous model. Interpretation. Because of the high heterogeneity of COVID-19 infection risk across the different age groups, with a higher susceptibility for the elderly, homogeneous models overestimate the level of collective immunity needed for the disease to stop spreading. This inaccuracy can be corrected by the homogeneous model introduced here. To improve the estimate even further additional factors should be considered that contribute to heterogeneity, including social and professional activity, gender and individual resistance to the pathogen.

Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model

“…This is consistent with the factor q = 7 found in [40]. Of course important factors like risk status or age (see for instance [16,18]) have been put in evidence, but they are not easy to study from the point of view of transmission rates. In our approach, it is clear that we take oversimplifying assumptions, but this is probably the price to pay to prove results and put them numerically in evidence.…”

“…Recent papers have emphasized that the heterogeneity of the transmissions rates is important in the current pandemic and that it lowers herd immunity thresholds in various modeling frameworks. During the revision of this paper, we became aware of [14,16,17]. Superspreaders and superspreading events are known to play an essential role in the propagation of Covid-19 according to [1,3,19,20,27,38,39].…”

Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model

“…This is consistent with the factor q = 7 found in [40]. Of course important factors like risk status or age (see for instance [16,18]) have been put in evidence, but they are not easy to study from the point of view of transmission rates. In our aproach, it is clear that we take oversimplifying assumptions, but this is probably the price to pay to prove results and put them numerically in evidence.…”

“…Recent papers have emphasized that the heterogeneity of the transmissions rates is important in the current pandemic and that it lowers herd immunity thresholds in various modeling frameworks. During the revision of this paper, we became aware of [14,16,17]. Superspreaders and superspreading events are known to play an essential role in the propagation of Covid-19 according to [1,3,19,20,27,38,39].…”