Merge branch 'main' of https://github.com/cdcent/cfa-scenarios-model …

…into priors-visualizer

README.md

@@ -1,12 +1,18 @@
 # CFA Scenarios Model
+
 [Overview](#overview) |
 [Model Structure](#model-structure) |
 [Quick Start](#quick-start) |
 [Data Sources](#data-sources) |
 [Project Admins](#project-admins) |
 [Fine Text and Disclaimers](#general-disclaimer)
+
 ## Overview
 
+> [!IMPORTANT]
+> This repository is under active development and will be substantially refactored in the near future.
+> Please look around, but we advise against working with this code until it has stabilized.
+
 This repository is for the design and implementation of a Scenarios forecasting model, built by the Scenarios team within CFA-Predict.
 
 Currently, we aim to use this code to forecast different disease tranmission scenarios with a compartmental mechanistic ODE model.  This model is under development with transmission of SARS-CoV-2 as our primary focus.  We plan to apply this model to the transmission of other respiratory viruses such as influenza and RSV.  We aim to provide enough flexibility for the code users to explore a variety of scenarios, but also making certain design decisions that allow for fast computation and fitting as well as code readability.

ode_model.md

@@ -12,45 +12,45 @@ The SEIP (Susceptible-Exposed-Infectious-Partially Immune) model presented here
 
 The model also includes seasonal vaccination effects, where individuals in the highest vaccination tier are periodically reset to the next highest tier, simulating annual vaccination campaigns. The mathematical representation of the model follows:
 
-$
+```math
 \frac{dS_{i,j,k,m}}{dt} =
 -\left(\sum_{\ell}\lambda_{i,\ell}(t)\right) S_{i,j,k,m}
 - (1-\delta_{m=0}\delta_{k=K}) \min\left(\frac{\nu_{i,k}(t)\mathcal{N}_{i}}{\sum_{j,m'} S_{i,j,k,m'}}, 1\right) S_{i,j,k,m}
-$
+```
 
-$
+```math
 + \delta_{m=0}(1-\delta_{k=0})\min \left(\frac{\nu_{i,k-1}(t)\mathcal{N}_{i}}{\sum_{j,m'} S_{i,j,k-1,m'}}, 1\right)\sum_{m'} S_{i,j,k-1,m'}
-$
+```
 
-$
+```math
 + \delta_{m=0}\delta_{k=K} \min \left(\frac{\nu_{i,K}(t)\mathcal{N}_{i}}{\sum_{j,m'} S_{i,j,K,m'}}, 1\right)\sum_{m'} S_{i,j,K,m'}
-$
+```
 
-$
+```math
 + \delta_{m=0}\sum_{{(j',\ell ') \ | \ \eta(j',\ell ')=(j,\ell)}} \gamma_{\ell} I_{i,\eta(j',\ell'),k,\ell '}
 +\phi(t)(\delta_{k=K-1} S_{i,j,K,m}-\delta_{k=K} S_{i,j,K,m})
-$
+```
 
-$
+```math
 + (1-\delta_{m=0})\omega_{m-1} S_{i,j,k,m-1} - (1-\delta_{m=M})\omega_{m} S_{i,j,k,m}
-$
+```
 
-$
+```math
 \frac{dE_{i,j,k,\ell}}{dt} =
 \lambda_{i,\ell}(t) \sum_{m} S_{i,j,k,m} - \sigma_{\ell} E_{i,j,k,\ell}
 + \phi(t)(\delta_{k=K-1} E_{i,j,K,m}-\delta_{k=K} E_{i,j,K,m})
-$
+```
 
-$
+```math
 \frac{dI_{i,j,k,\ell}}{dt} =
 \sigma_{\ell} E_{i,j,k,\ell} - \gamma_{\ell} I_{i,j,k,\ell}
 + \phi(t)(\delta_{k=K-1} I_{i,j,K,m}-\delta_{k=K} I_{i,j,K,m})
-$
+```
 
-$
+```math
 \frac{dC_{i,j,k,\ell}}{dt} =
 \lambda_{i,\ell}(t) \sum_{m} S_{i,j,k,m}
-$
+```
 
 
 
@@ -83,17 +83,20 @@ $
 
 ### Relevant Parameters Representations
 
-$
+```math
 \phi(t) =
 \begin{cases}
 \left(\sin\left(\frac{2\pi (t + \tau)}{730}\right)\right)^{1000} & \text{during seasonal vaccination periods} \\
 0 & \text{otherwise}
 \end{cases}
-$for
+```
 
-$
+for
+
+```math
 \tau = 182.5 - \Delta_{t}.
-$
+```
+
 The function \(\eta\) determines a new immune state given the current state and the exposed strain using bitwise OR operations.
 
 Let:
@@ -109,9 +112,10 @@ The function performs the following steps:
 4. Return the new state as an integer.
 
 Formally, we define the new immune state function as:
-$
+
+```math
 \eta(x, y) = x \, | \, 2^{y}
-$
+```
 
 ## Example Calculations
 
@@ -171,40 +175,40 @@ If $N = 2$, possible states are:
 
 Lastly, we define a mathematical representation of the Force of infection for susceptible individuals in age group a and strain k is calculated as follows:
 
-$
+```math
 \Lambda_{a,k}(t) = \tilde{\lambda}_{a,k}(t) \cdot (1 - \text{WI}_{a,k})
-$
+```
 
 Where:
 
-$
+```math
 \tilde{\lambda}_{a,k}(t) = \frac{\beta \cdot \beta_{\text{coef}}(t) \cdot \sigma(t)}{P_a} \sum_{b,i,j} C_{ab} \cdot \left( I_{b,i,j,k}(t) + \mathcal{N}(\mu_i, \sigma_i) \cdot \phi_i \cdot P_b \right)
-$
+```
 
 And:
 
-$
+```math
 \text{WI}_{a,k} = \text{WIB}_{a,k} + \text{WIM}_{a,k}
-$
+```
 
-$
+```math
 \text{WIB}_{a,k} = \sum_{j} \text{II}_{a,j} \cdot \gamma_{jk}
-$
+```
 
-$
+```math
 \text{WIM}_{a,k} = (1 - \text{WIB}_{a,k}) \cdot \text{FI}_{a,k}
-$
+```
 
-$
+```math
 \text{FI}_{a,k} = \begin{cases}
 \mathcal{M}_{\text{HI}} & \text{if previously exposed to strain } k \\
 0 & \text{otherwise}
 \end{cases}
-$
+```
 
-$
+```math
 \text{II}_{a,k} = 1 - \sum_{j} \left( 1 - \chi_{k,j} \right) \left( 1 - \nu_{k,j} \right)
-$
+```
 
 | Symbol               | Description                                                                                |
 |----------------------|--------------------------------------------------------------------------------------------|
@@ -215,7 +219,7 @@ $
 | $\sigma(t)$        | Time-dependent seasonality coefficient                                                     |
 | $P_a$              | Population of age group a                                                              |
 | $C_{ab}$           | Contact matrix between age groups a and b                                          |
-| $\mathcal{N}(\mu__{i}, \sigma_{i})$ | Normal distribution for external infection centered at $\mu_{i}$ with scale $\sigma_{i}$ |
+| $\mathcal{N}(\mu_{i}, \sigma_{i})$ | Normal distribution for external infection centered at $\mu_{i}$ with scale $\sigma_{i}$ |
 | $\phi_{i}$           | Percentage of age group b for externally introduced strain i                        |
 | $\text{WI}_{a,k}$  | Waned immunity for age group a and strain k                                         |
 | $\text{WIB}_{a,k}$ | Waned immunity baseline for age group a and strain k                                |