Ring vaccination widget

Overview

This repo contains code for investigating the potential efficacy of ring vaccination for a disease interactively via a streamlit app.

Model description

The model is a branching process with the following description. Note that we the model does not track (and indeed has no notion of) susceptibles.

• Disease progression:
  • Exposed/latent (i.e., will go on to infection)
  • Infectious
  • Recovered
• Infection process
  • There are a finite number of generations
  • Default is 3 (beyond the index infection, i.e., generation 0): generation 1 (contacts), generation 2 (contacts of contacts), and generation 3 (potential escaping infections)
  • Number and timing of infections generated by infected people
  • Assumed to be a Poisson process: draw inter-infection times from $\mathrm{Exp}(1/\lambda)$ until infectious period ends or infection is detected
    • N.B.: All "contacts" here are effective contacts, i.e., encounters that result in transmission
• Passive detection (i.e., self-detection)
  • Each infection has an independent probability of potential passive detection
  • N.B.: To actually be passively detected, the detection must occur at a time before recovery and before being detected by other means.
  • If passively detected, detection occurs at some time distribution since exposure.
  • Start with Dirac delta distribution (i.e., all passively-detected infections are detected at some fixed delay after exposure)
  • N.B.: This assumes that progression of infectiousness and symptoms are independent. We could not say that, e.g., symptoms begin immediately upon onset of infectiousness, and the delay to self-detection is some time after that.
  • N.B.: There is no assumption that index case is passively detected. If the index case does not self-detect, this is not an automatic fail, since they might not infect anyone, or their infectees might self-detect.
• Contact tracing (i.e., active detection)
  • Every detected infection (whether passive or active) automatically contact tracing
  • Contact tracing has an independent probability of detecting each infection caused by the detected infection
  • N.B.: To actually be actively detected, the detection must occur at a time before recovery and before being detected by other means.
  • N.B.: Contact tracing goes only forward and only one generation. For example, say index infects A infects B infects C, and the index is not detected, but A is passively detected. Then this creates an chance to actively detect B, but not the index or C (although C might be detected if the detection of A leads to contact tracing that detects B that in turn leads to contact tracing that detects C).
  • N.B.: "Detection" here means detection and successful intervention. We do not separately model the detected infection's probability of divulging contact information, the ability of public health to find that contact, or the probability of that contact to comply with quarantine/isolation.
  • There is a distribution of times between triggering detection and contact tracing completion. Start with Dirac delta.
• Input parameters/assumptions for this model
  • Latent period $t_\mathrm{latent}$ distribution (time from contact to onset of infectiousness). Start with Dirac delta.
  • Infectious period $t_\mathrm{inf}$ distribution. Start with Dirac delta.
  • Infectious rate. Start with identical for all people.
  • Passive detection probability and delay distribution: Dirac delta
  • Active detection probability and delay distribution: Dirac delta
• Initialization: Seed a single infection (e.g., exposed via travel)
• Outputs
  • High-level aggregate summaries of all simulations
  • Visual of history of each individual simulation.

Scope

The scope of this repo is a model which is a (1) branching processes where (2) the offspring distribution (including the times at which subsequent infections are caused) for any infection depends only on the history of the process up until the time at which they are infected. For practical purposes, this most likely means the scope can be considered to be density-independent branching processes.

The model implemented herein may be iterated upon subject to preserving this basic structure. For example, any model which requires tracking susceptibles or a network structure is out of scope. But replacing Dirac delta distributions with other probability distributions for disease history would be in scope.

Analysis

• Define a "successful" simulation as one with zero 3rd-generation infections (i.e., no infected contacts-of-contacts-of-contacts)

Project Admins

• Scott Olesen (CDC/CFA) ulp7@cdc.gov
• Andy Magee (CDC/CFA) rzg0@cdc.gov

General Disclaimer

This repository was created for use by CDC programs to collaborate on public health related projects in support of the CDC mission. GitHub is not hosted by the CDC, but is a third party website used by CDC and its partners to share information and collaborate on software. CDC use of GitHub does not imply an endorsement of any one particular service, product, or enterprise.

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