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Mathematical models and theorems
out of 5 stars
01 Feb 2017 | | Contributor(s):: Winfried Just
In this module we introduce and compare various types of deterministic and stochastic mathematical models of disease transmission. We then illustrate how one can derive predictions of these models in the form of mathematical theorems.Level: Advanced undergraduate and graduate students of...
William J Heuett
The preferential attachment model
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar, Ying Xin
Many empirically studied networks have approximately so-called power-law or scale-free degree distributions. In Section 1 we formally define such distributions and explore some of their properties. We also introduce and briefly compare two methods for constructing random...
Exploring distances with IONTW
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar
Section 1 is purely conceptual and invites readers to critically evaluate popular claims based on Stanley Milgram's famous experiment that gave birth to the phrases small-world property and six degrees of separation. In Section 2 we use IONTW to explore distances between nodes in several...
The friendship paradox
In this module we introduce the so-called friendship paradox and illustrate how it affects disease transmission on networks that exhibit this phenomenon.You also need to download the input file degreesFP.txt that will be used in this module.Level: Advanced undergraduate and graduate...
Differential equation models of disease transmission
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender
In this module we explore ODE models of disease transmission and compare some of their predictions with those of agent-based models. Parts of this material will be referenced in later modules.Level: Advanced undergraduate and graduate students of mathematics or biology.DownloadStudent copy (no...
Exploring random regular graphs with IONTW
In this module we introduce and explore the structure of random regular graphs. Moreover, we compare the predictions of SIR-models on random regular contact networks with the predictions of corresponding models on Erdős-Rényi networks.Level: Undergraduate students of biology or...
Exploring Erdős-Rényi random graphs with IONTW
In this module we explore in detail the distribution of the sizes of connected components of Erdős-Rényi random graphs and discover the reasons for the similarities and differences between disease transmission on Erdős-Rényi networks and complete graphs that were observed in...
Exploring Disease Transmission on Networks with NetLogo
10 May 2015 | | Contributor(s):: Winfried Just, Ying Xin
A quick tour of IONTW
30 Jan 2015 | | Contributor(s):: Winfried Just, Ying Xin
In this module we guide you through some of the capabilities of IONTW. Highlights include the types of networks supported, setting up various types of models of disease transmission, observing the resulting dynamics, and collecting statistics on the outcomes. Along the way, the module also...