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Currently submitted to: Journal of Medical Internet Research

Date Submitted: May 26, 2020
(closed for review but you can still tweet)

Warning: This is an author submission that is not peer-reviewed or edited. Preprints - unless they show as "accepted" - should not be relied on to guide clinical practice or health-related behavior and should not be reported in news media as established information.

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

  • Andrey Gerasimov; 
  • Georgy Lebedev; 
  • Mikhail Lebedev; 
  • Irina Semenycheva; 



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.


The objective of this paper was to develop a heterogeneous model of COVID-19 dynamics.


The heterogeneous model of COVID-19 dynamics 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.


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.


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. Clinical Trial: This is a modeling study; no trial was conducted.


Please cite as:

Gerasimov A, Lebedev G, Lebedev M, Semenycheva I

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

JMIR Preprints. 26/05/2020:20681


Per the author's request the PDF is not available.