Ricevo e inoltro.
---------- Forwarded message ---------- From: "fosp@math.tugraz.at" fosp@math.tugraz.at Subject: [fosp-announce] Strukturtheorie-Seminar: Donnerstag, 20.1.2022, 11:00 s.t. Resent-From: woess@tugraz.at
Vortragende(r): Prof. Daniela Bertacchi
Herkunft: Univ. Milano-Bicocca
Titel: An epidemic model in inhomogeneous environment
Zeit: Donnerstag, 20.1.2022, 11:00 s.t.
Ort: Webex meeting
We consider a SIR model on the complete graph with n nodes. Each vertex represents an individual which may be susceptible, infected or removed. At the beginning only one node is infected and each node $x$ has a random spread capacity $L_x$. Once infected, the node $x$ becomes an emitter and has $L_x$ attempts to infect other nodes, which are randomly chosen. If the attempt is towards a susceptible node $y$, then $y$ becomes infected, if it is towards an infected or removed node, then $x$ loses an infection attempt. When $x$ has used all its spread capacity, it becomes removed and no longer interacts with the rest of the population. This model was studied by Comets et al. in the case where the spread capacities are i.i.d. and the nodes which one attempt to infect are chosen uniformly. We study the case where the population is divided into J types and each type has a possibly different susceptibility, that is, some individuals have a larger probability of being chosen as targets. Also the law of the spread capacity may depend on the type. We obtain a law of large numbers and a central limit theorem for the duration of the process and the proportion of infected nodes. We prove that when the spread capacity is homogeneous, then a population with inhomogeneous susceptibility is overall less affected by the epidemics than a population with homogeneous susceptibility.
This is joint work with J.Kampf, E.Sava-Huss and F.Zucca.
Webex meeting, meeting link:
{https://tugraz.webex.com/tugraz-de/j.php?MTID=mfb7a477bc53fac8b0a6db53cf1f26...
Meeting number: 2734 226 6767
Password: Je3q3w37mJG
The meeting opens at 10:40, the 50min talk starts at 11:00
Organisator/in: W. Woess
Institut für Diskrete Mathematik