Final Size for Epidemic Models with Asymptomatic Transmission

• Published in: Bulletin of mathematical biology Vol. 85; no. 6; p. 52
• Main Authors: Barril, Carles, Bliman, Pierre-Alexandre, Cuadrado, Sílvia
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2023; Springer Nature B.V; Springer Verlag
• Subjects: Basic Reproduction Number; Cell Biology; Dynamical Systems; Epidemic models; Epidemics; Humans; Life Sciences; Mathematical and Computational Biology; Mathematical Concepts; Mathematics; Mathematics and Statistics; Models, Biological; Original; Original Article; Santé publique et épidémiologie; Reproduction number; Final infection size; Symptomatic population; reproduction number; final infection size symptomatic population reproduction number; symptomatic population; final infection size
• ISSN: 0092-8240; 1522-9602
• DOI: 10.1007/s11538-023-01159-y

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.