Mathematical Research Seminar - Archive

Link Zoom: https://zoom.us/j/297328207

Network-based adaptations of traditional compartmental infection models such as SIR or SEIR can be used to model the spreading of diseases between cities, countries or other geographical regions. One of the common challenges arising in these applications is the lack of available transmission probabilities between these geographical units. The task of inverse infection is the systematic estimation of these values. Several methods have been proposed recently for solving this task. One of them is the Generalized Inverse Infection Model (GIIM) [1]. GIIM offers a large amount of modeling flexibility and allows transmission probabilities to be defined as a function of known attributes, or risk factors in an epidemic context. In this presentation we will see how GIIM works in two specific real-life outbreaks.

Both examples are embedded in a geographical and temporal setting. The first one considers the 2015-2016 Zika virus outbreak in the Americas, where the countries and overseas territories of the continent form the nodes of the network and air travel routes define the links [2]. The second application models the 2009 H1N1 outbreak between the municipalities of Sweden, with links between the municipalities indicating frequent travel routes.

Our first goal in both of these studies is to discover the relationship between the transmission risk between geographical units and a variety of travel, environmental, meteorological and socioeconomic risk factors. Our second goal is to estimate the risk of exportation and importation of the diseases for the territories involved in these studies. We will show that the GIIM model is able to identify the most critical risk factors in both scenarios, and in the influenza study, it is able make predictions about future outbreaks with good accuracy.

REFERENCE:

1. A. Bóta, L. M. Gardner: A generalized framework for the estimation of edge infection probabilities. arXiv:1706.07532 (2017)

2. L. M. Gardner, A. Bóta, N. D. Grubaugh, K. Gangavarapu, M. U. G. Kramer: Inferring the risk factors behind the geographical spread and transmission of Zika in the Americas.PLoS Neglected Tropical Diseases.

http://journals.plos.org/plosntds/article?id=10.1371/journal.pntd.0006194

You should understand…

• I am talking not as an expert but as a long-time university lecturer who likes distance teaching and learning.
• Due to unusual circumstances, we are all pushed into distance learning and distance teaching. This serves as a good excuse to talk about such unusual topic at mathematics seminar.
• Throughout our University there are many disscussions about choosing appropriate tools for teaching courses via internet.
• We can imagine that such discussions take place in many other places in Slovenia and elsewhere on Earth.

I am not going to…

• ... promote one system over another one.       [I hope some of you, will be able to do it soon at a similar seminar here or at some other location.]
• ... teach you how to use Powerpoint or Beamer, etc. for preparing your Seminar Talk.
• ... teach you how to organize your courses in moodle.
• ... teach you how to make and upload videos to Youtube on Vimeo.

So what I am going to do today?

• I will try to sketch a “theory” of communcation.
• Again, since I am not an expert in this area the word “theory” has to be taken cum grano salis.
• The goal of this talk is to give you enough theory that will explain
  1. why distance learning is difficult.
  2. why teaching large groups of students is more complicated than teaching small groups.
  3. why overusing colors and animation may be counter.

Everyone is welcome and encouraged to join the video-lecture via the following link:

https://zoom.us/j/479411024

A code is a subset of the vertex set of a graph. Given a code, the graph metric allows one to define an associated distance partition. Imposing combinatorial regularity conditions on the distance partition of a code leads to the definitions of the classes of s-regular and completely regular codes; analogously, algebraic symmetry conditions lead to the classes of s-neighbour-transitive and completely transitive codes. I will discuss previous results and current work related to characterising and classifying subclasses of 2-neighbour-transitive and completely transitive codes in Hamming graphs. All of the results I will discuss are part of ongoing effort to provide a full classification of completely transitive codes in Hamming graphs having minimum distance at least 5.