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

• Disease progression:
  • Susceptible
  • Exposed/latent (i.e., will go on to infection)
  • Infectious
  • Recovered
• Infection process
  • There are a finite number of generations
    • Start with 4: index infection (i.e., generation 0), generation 1 (contacts), generation 2 (contacts of contacts), and generation 3 (potential escaping infections)
    • In general, this number could be varied
  • Number of infections generated by infected people
    • Assume branching process (i.e., each infections yields an i.i.d. number of offspring)
    • Assume it's 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 passive detection
  • 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 being 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) has an independent probability of triggering contact tracing
  • Contact tracing has an independent probability of detecting each infection caused by the detected infection
    • N.B.: Contact tracing goes only forward and only one generation. For example, say index infects A infects B infects C, and the is passively 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.
    • Make this an input parameter, and for convenience, display $R_0 = \mathrm{rate} / E[t_\mathrm{inf}]$ in the widget as a derived parameter
  • Network/contact structure: see above; these are i.i.d. Poisson
  • Passive detection probability and delay distribution: Dirac delta
  • Contact tracing probability and delay distribution: Dirac delta
• Initialization: Seed a single infection (e.g., exposed via travel)
• Outputs
  • Number of detected and undetected infections in each generation
  • Event log, including:
    • Who infected whom
    • Timing of detections, disease state transitions, etc.

Out of scope

• Could we make a correlated draw of infections in each generation sufficient to describe certain network parameters? Or do you also need timing?
• If two people in generation $g$ contact an infection in generation $g+1$, and both of the $g$ infections are detected, does the $g+1$ infection get two chances for contact tracing to work?

Analysis

• Define a "successful" simulation as one with zero 4th-generation infections

Project Admins

• Scott Olesen (CDC/CFA) [email protected]
• Andy Magee (CDC/CFA) [email protected]
• Paige Miller (CDC/CFA) [email protected]

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