update model description

README.md

@@ -8,123 +8,60 @@ app.
 
 ## Model description
 
-### Skateboard version
-
-- Disease progression: susceptible, exposed/latent (i.e., will go onto
-  infection), infectious, recovered
+- Disease progression:
+  - Susceptible
+  - Exposed/latent (i.e., will go on to infection)
+  - Infectious
+  - Recovered
 - Infection process
-  - Finite number of generations: index infection, generation 1 (contacts),
-    generation 2 (contacts of contacts), and generation 3
-  - Number of infections
-    - For first version, assume that all infections have i.i.d. number of
-      offspring (i.e., branching process)
-    - Index infection creates a number of generation 1 infections, drawn from
-      some distribution
-    - Generation 1 infections each create a number of generation 2 infections
-      - These values are drawn jointly (i.e., from a multivariate distribution)
-      - All network features are marginalized over this distribution
-      - The potential for correlations between numbers of infections (e.g., that
-        generation 2 infections might share contacts) are all baked into that
-        distribution
-    - Similarly for generations 2 and 3
-      - The distribution can vary between the three generations
-  - Timing of infections
-    - For first version, just space the infections uniformly in time
-    - For later versions, spacing them like for a Poisson 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
+  - Assume
+  - 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
 - 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
-  - (No assumption that index case is passively detected)
+    exposure. Start with Dirac delta distribution.
+  - (N.B.: No assumption that index case is passively detected)
 - 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
   - "Detection" means detection _and_ successful intervention
   - There is a distribution of times between triggering detection and contact
-    tracing completion
-- Input parameters/assumptions for this model
-  - Latent period $t_\mathrm{latent}$ distribution (time from contact to onset
-    of infectiousness)
-  - Infectious period $t_\mathrm{inf}$ distribution
-  - Infectious rate (which could be defined via $R_0 / E[t_\mathrm{inf}]$)
-  - Distribution of infections (start by making these independent, Poisson)
-  - Passive detection probability and delay distribution
-  - Contact tracing probability and delay distribution
-- Implementation/initialization
-  - Seed a single infection (e.g., exposed via travel)
-- Output/viz
-  - Some discrete realizations, showing the timelines of events for individuals
-    (e.g., how the different disease state periods line up in time)
-  - Distribution of number of undetected in generation 3
-
-### Fuller version
-
-- Disease progression: susceptible, exposed (i.e., will go onto infection),
-  infectious, recovered
-- Individuals make contacts on some network, with some effective (i.e.,
-  infection transmitting) contact rate. (Contact rates and effective contact
-  probability could be separated in parameter input, but they are perfectly
-  confounded in the model.)
-- Each infected individual can be detected. E.g., infected people might notice
-  their own symptoms.
-- When an infected person is detected, contact tracing and isolation are
-  initiated.
-  - Contact tracing
-    - Contact tracing can detect infections among contacts, contacts of
-      contacts, etc.
-    - Contact tracing has different performance characteristics for each "ring."
-      (The most straightforward choice would be to make second ring performance
-      equivalent to first ring, i.e., time from detecting infected contact to
-      infected contact-of-contact is identical to time from detecting index
-      infection to infected contact.)
-  - Isolation reduces transmission by some factor (which might be 100%) for that
-    individual.
+    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)
-  - Infectious period $t_\mathrm{inf}$ distribution
-  - Basic reproductive number $R_0$ (i.e., mean number of secondary infections
-    per index infection in the absence of intervention)
-    - Note: this defines some mean infectious rate $R_0 / E[t_\mathrm{inf}]$
-    - Assume that this infectious rate is constant over the period of
-      infectiousness. E.g., if perfectly effective isolation is implemented
-      halfway through an individual's infectious period, that halves their
-      number of expected secondary infections.
-    - Some distribution of number of secondary infections around $R_0$ (e.g.,
-      Poisson)
-    - Assume that the number of secondary infections is uncorrelated across
-      individuals (i.e., there is some kind of homogeneity in the contact
-      network).
-  - Per-infection detection (aka "passive" detection, in which individuals
-    identify their own symptoms)
-    - % of infections identified in this way (in the absence of contact tracing)
-    - Distribution of times from exposure to detection (or, equivalently, from
-      exposure to symptom onset and from symptom onset to detection)
-  - Contact tracing
-    - % of first ring (contacts) identified
-    - Distribution of times from index exposure to contact identification
-    - Time-varying performance of contact tracing (e.g., a simple assumption
-      would be that all infected contacts immediately stop infecting, i.e., that
-      the diagnostic test can identify infections with 100% sensitivity
-      immediately after exposure and isolation is 100% effective)
-    - % of second ring (contacts of contacts) identified, distribution of times,
-      etc.
-    - Third ring, etc.
+    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
 - Implementation/initialization
   - Seed a single infection (e.g., exposed via travel)
-  - **_Open question_**: How to deal with multiple rings?
-    - What are the network implications of treating undetected infections as new
-      index infections (with independent but identically distributed number of
-      secondary infections)?
-    - How hard would it be to simulate contacts on a simple network?
 - Output/viz
   - Some discrete realizations, showing the timelines of events for individuals
     (e.g., how the different disease state periods line up in time)
-  - Distribution of number of undetected
-- Assumptions of note
-  - Assuming independence is conservative: clustering helps you
+  - Distribution of number of undetected in generation 4 (contacts of contacts
+    of contacts)
+
+### Questions for future development
+
+- Is the correlated draw of infections in each generation sufficient to describe
+  certain network parameters? Or do you also need timing?
 
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