Multiple peaks in network SIR epidemic models

• Published in: 2022 IEEE 61st Conference on Decision and Control (CDC) pp. 5614 - 5619
• Main Authors: Alutto, Martina, Cianfanelli, Leonardo, Como, Giacomo, Fagnani, Fabio
• Format: Conference Proceeding
• Language: English
• Published: IEEE 06-12-2022
• Subjects: Analytical models; Behavioral sciences; Epidemic models; Epidemics; reproduction number; Sociology; Statistics; Sufficient conditions; Susceptible-Infected-Recovered model
• ISSN: 2576-2370
• DOI: 10.1109/CDC51059.2022.9992408

We study network SIR (Susceptible-Infected-Recovered) epidemic models in the case of two interacting populations. We analyze the dynamics behavior of the fractions of infected individuals in the two populations. In contrast to the classical scalar SIR epidemic model, where the fraction of infected individuals is known to have an unimodal behavior (either decreasing throughout time or initially increasing, until reaching a peak and decreasing everafter), we show the possible occurrence of a novel multimodal behaviors in the network SIR model. Specifically, we show that the curve of the fraction of infected individuals in a population may incur in a change of monotonicity even when it starts with a decreasing trend. Our analysis focuses on a homogeneous mixing model, whereby all contacts have unitary frequency. We study the initial conditions and network characteristics sufficient for the aforementioned multimodal behavior to emerge and those that instead guarantee the classical unimodal behavior.