부산대학교 도서관

Summary: ``Many infections are transmitted by direct contacts. Usually,one single direct contact is needed to transmit the required minimuminfectious load. Most models describe contagions by single contactsusing a term of the type mass action law. However, modelling infectionsthat are transmitted after the susceptible individual had contact withseveral sources of infection requires more than mass action law terms.We call additive multiple contacts those that do not produce infectionby themselves, but can produce infection if they happen simultaneously.We are interested in understanding the role played by $R_0$ missing themark in infections in which the minimum infectious load is reached notonly by single contacts but also by additive multiple contacts. Wepropose different mathematical models describing not only infections byone single contact but also by additive multiple contacts. We show thatall models have the same value of $R_0$, but correspond to differentepidemiological mechanisms. Two models show contagions by additivemultiple contacts and a third one shows reduction of infections by somesaturation process which is not captured by $R_0$. This shows thattrying to control the epidemics by controlling $R_0$ could beunsufficient or, in some cases, waste resources.''