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  1. ModelSim Population Biology Unit

    18 May 2015 | Teaching & Reference Material

    This resource has been updated - find the current version here: https://qubeshub.org/qubesresources/publications/902This resource provides rich student modeling activities and materials, teacher resources, and much more, in the realm of agent based models applied to population biology....

  2. The preferential attachment model

    10 May 2015 | Teaching & Reference Material | 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...

  3. The preferential attachment model

    10 May 2015 | Teaching & Reference Material | 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...

  4. Exploring distances with IONTW

    10 May 2015 | Teaching & Reference Material | 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...

  5. Exploring distances with IONTW

    10 May 2015 | Teaching & Reference Material | 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...

  6. The friendship paradox

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar

    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...

  7. The friendship paradox

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar

    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...

  8. The replacement number

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar, Ying Xin

    In this module we introduce the important notion of the replacement number, which generalizes the basic reproductive number R0. We investigate how this number behaves near the start of an outbreak in models based on the uniform mixing assumption and in models that assume a contact network that is...

  9. The replacement number

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar, Ying Xin

    In this module we introduce the important notion of the replacement number, which generalizes the basic reproductive number R0. We investigate how this number behaves near the start of an outbreak in models based on the uniform mixing assumption and in models that assume a contact network that is...

  10. Differential equation models of disease transmission

    10 May 2015 | Teaching & Reference Material | 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...

  11. Differential equation models of disease transmission

    10 May 2015 | Teaching & Reference Material | 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...

  12. Exploring random regular graphs with IONTW

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar

    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...

  13. Exploring random regular graphs with IONTW

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar

    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...

  14. Exploring Erdős-Rényi random graphs with IONTW

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar

    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...

  15. Exploring Erdős-Rényi random graphs with IONTW

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar

    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...

  16. Exploring contact patterns between two subpopulations

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar

    In this module we introduce a construction of generic random graphs for a given degree sequence or degree distribution and explore whether mixing between hosts who belong to different subpopulations is assortative or disassortative.Level: Undergraduate students of biology or...

  17. Exploring contact patterns between two subpopulations

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar

    In this module we introduce a construction of generic random graphs for a given degree sequence or degree distribution and explore whether mixing between hosts who belong to different subpopulations is assortative or disassortative.Level: Undergraduate students of biology or...

  18. A brief review of basic probability theory

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just

    The spread of infectious diseases is inherently a stochastic process and the materials posted at this web site heavily rely on probability theory. Here we review some basic concepts of probability theory for easy reference. The material is restricted to notions that are used in teaching...

  19. A brief review of basic probability theory

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just

    The spread of infectious diseases is inherently a stochastic process and the materials posted at this web site heavily rely on probability theory. Here we review some basic concepts of probability theory for easy reference. The material is restricted to notions that are used in teaching...

  20. Network-based models of transmission of infectious diseases: a brief overview

    10 May 2015 | Teaching & Reference Material | Contributor(s): Winfried Just, Hannah Lea Callender, Drew LaMar

    The main purpose of this document is to give a brief but mathematically rigorous description of the network-based models of transmission of infectious diseases that are studied on this web site. Readers will be able to find a much more detailed development of this material in our book chapters...