# Combinatorics Seminar 2018

Date: Wed, Mar 28, 2018

Time: 15:20 - 16:20

Venue: 3323A

Title: Optimal directed graphs for epidemics control

Abstract:

A virus is multiplying and spreading in a network by two means: (1) slow spread, where it moves from one individual to an individual in a neighboring location, (2) fast spread, through the air, where it moves to a random individual in the whole network. To be more precise:

• The network is represented by a (directed) graph $G$.

• Initially, one individual is infected.

• In every round, an infected individual $u$ infects $\alpha$ individuals randomly chosen from those in $u$'s neighborhood (slow spread).

• Additionally, it infects $\beta$ individuals randomly chosen from position in the whole network (fast spread).

We can vaccinate individuals to make them immune to the disease. What is the minimum fraction of individuals one has to vaccinate in order to contain the disease, i.e., to make sure the expected number of infected individuals goes to 0 over time?

In this line of research, we also have the liberty of designing the network itself; we ask: given the "spread numbers" $\alpha$ and $\beta$, what are the best networks, i.e., those where we can contain the disease by vaccinating a minimum fraction of the population?

This is joint work with Wu Yaokun.

Slides: View slides

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