Discussed a list of relevant terms which were discussed during the project. I will solidify my understanding of the terms in question and then begin to craft an outline for a presentation which gives mention to most of the terms listed while taking into consideration the audience at hand.
Concepts to be discussed:

• Statistical Likelihood
• Generating Functions

Notes:
April 27 Title submission
May 2nd Pre Presentation meeting
Desired figures for presentation (perhaps more to come):

• SIR figures to assist in explaining the choice of basic reproduction number as mean for offspring distributions
• Plots comparing Poisson vs Negative Binomial distributions on most developed models (I.E. model with initial population and immunity)
• SIR model graph to compare with branching process figures

(Push notebook for figures with "@marlinfiggins" in pull requests 1 at a time for review)

• Add agent tracking
• Generate transmission tree
• Think about mathematics behind branching process, specifically extinction probability

Meeting Summary: Discussed some important changes needed for the branching process and clarified some misconceptions about immunity. Plotted data, and verified implementation of negative binomial distribution. Generated thoughts on the takeaways I valued most from the project, which will act as anchor points for the presentation.

During our meeting we discussed next steps for the project, specifically what to focus on during the coming weeks as the presentation approaches. First step is to flesh out the Galton Watson branching process implementation:

• Negative Binomial Distribution Implementation (SciPyStats)
• Freeze distributions (size of previous generation)
• Batch simulations, running multiple realizations simultaneously
  Extensions of the GW branching process could be
• Simulating finite population and/or some form of immunity
• Simulating infectious period
• Changing offspring distributions
  Think about producing estimates for the following:
• Extinction probability
• Time to extinction
• Exponential Growth Rate

I think it's important to make sure that we're keeping track of what we're reading and skills gained over the course of the project.

Hello,

We should fix the README since it appears to misspell both our names and that is a bit embarrassing (for me).

This week we'll work on simulating a Galton-Watson Branching Process in Python for different offspring distributions.

The idea currently is to look how changes in the offspring distribution affect our simulated epidemics as well as their probability of extinction.

For the first two candidates, I would use the Poisson distribution and Negative Binomial distribution. You'll find this section on the Poisson-Gamma mixture particularly helpful for motivating why we're doing this.

Let's first work on getting simulations running with each of these offspring distribution with $R_{0} = 1.5$.

Tasks

• Simulate offspring distributions with mean $R_{0}$ for both Poisson and Negative Binomial.
• Run branching process simulation for 10 generations and 50 realizations

Things to think about

• What aspects of the process does changing the over-dispersion affect?
• Why might over-dispersion matter in real life?
• What are the limitations of the Galton-Watson model when modeling real life infectious diseases?

• Reading chapter 1 of the epidemiology book: Really interested in the jacobian analysis of the ODE the author uses would love to discuss that further
• Phylo tree of Ebola looks interesting in terms of how the virus seems to mutate rapidly and with longevity in particular areas as opposed to others. As a side note, I assume a lack of mutations in a virus doesn't directly imply a lack of further spread, but I would guess are the two factors are correlated?