Additive multiple contacts and saturation phenomena in epidemiological models are not detected by R₀

¹ Universidad Autónoma Metropolitana, Av. Hidalgo Poniente No. 46, Col. La Estación, 52006, Lerma de Villada, Estado de México, Mexico
² Centro de Investigación en Matemáticas, 36023 Guanajuato, Guanajuato, Mexico
³ Independent researcher

^* Corresponding author: j.villavicencio@correo.ler.uam.mx

Received: 23 March 2023
Accepted: 23 March 2024

Abstract

Many infections are transmitted by direct contacts. Usually, one single direct contact is needed to transmit the required minimum infectious load. Most models describe contagions by single contacts using a term of the type mass action law. However, modelling infections that are transmitted after the susceptible individual had contact with several sources of infection requires more than mass action law terms. We call additive multiple contacts those that do not produce infection by themselves, but can produce infection if they happen simultaneously. We are interested in understanding the role played by R₀ missing the mark in infections in which the minimum infectious load is reached not only by single contacts but also by additive multiple contacts. We propose different mathematical models describing not only infections by one single contact but also by additive multiple contacts. We show that all models have the same value of R₀, but correspond to different epidemiological mechanisms. Two models show contagions by additive multiple contacts and a third one shows reduction of infections by some saturation process which is not captured by R₀. This shows that trying to control the epidemics by controlling R₀ could be unsufficient or, in some cases, waste resources.