학술논문
Additive multiple contacts and saturation phenomena in epidemiological models are not detected by $R_0$.
Document Type
Journal
Author
Villavicencio-Pulido, José Geiser (MEX-UAM7) AMS Author Profile; Barradas, Ignacio (MEX-CIM) AMS Author Profile; Nila-Luévano, Claudia AMS Author Profile
Source
Subject
34 Ordinary differential equations -- 34C Qualitative theory
34C60Qualitative investigation and simulation of models
92Biology and other natural sciences -- 92B Mathematical biology in general
92B05General biology and biomathematics
34C60
92
92B05
Language
English
Abstract
Summary: ``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 $R_0$ 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 $R_0$, 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 $R_0$. This shows that trying to control the epidemics by controlling $R_0$ could be unsufficient or, in some cases, waste resources.''