Final Size for Epidemic Models with Asymptomatic Transmission

Carles Barril, Pierre-Alexandre Bliman, Sílvia Cuadrado Gavilán

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


The final infection size is defined as the total number of individuals that become infected throughout an epidemic. Despite its importance for predicting the fraction of the population that will end infected, it does not capture which part of the infected population will present symptoms. Knowing this information is relevant because it is related to the severity of the epidemics. The objective of this work is to give a formula for the total number of symptomatic cases throughout an epidemic. Specifically, we focus on different types of structured SIR epidemic models (in which infected individuals can possibly become symptomatic before recovering), and we compute the accumulated number of symptomatic cases when time goes to infinity using a probabilistic approach. The methodology behind the strategy we follow is relatively independent of the details of the model.
Original languageEnglish
Article number52
Number of pages28
JournalBulletin of Mathematical Biology
Issue number6
Publication statusPublished - 8 May 2023


  • Final infection size
  • Symptomatic population
  • Reproduction number


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