From bb95bebf5d002ef55c38491464d9c5008f9bd65f Mon Sep 17 00:00:00 2001 From: Amanda Minter Date: Thu, 21 Dec 2023 10:52:49 +0000 Subject: [PATCH] distinguish parameter definitions from process descriptions in flow diagram --- episodes/simulating-transmission.Rmd | 30 ++++++++++++---------------- 1 file changed, 13 insertions(+), 17 deletions(-) diff --git a/episodes/simulating-transmission.Rmd b/episodes/simulating-transmission.Rmd index 93c271eb..d0888c36 100644 --- a/episodes/simulating-transmission.Rmd +++ b/episodes/simulating-transmission.Rmd @@ -155,9 +155,7 @@ By the end of this tutorial, learners should be able to replicate the above imag To generate predictions of infectious disease trajectories, we must first select a mathematical model to use. There is a library of models to choose from in `epidemics`. Models in `epidemics` are prefixed with `model` and suffixed by the name of infection (e.g. Ebola) or a different identifier (e.g. default), and whether the model has a R or [C++](../learners/reference.md#cplusplus) code base. -In this tutorial, we will use the default model in `epidemics`, `model_default_cpp()` which is an age-structured SEIR model described by a system of [ordinary differential equations](../learners/reference.md#ordinary). For each age group $i$, individuals are classed as either susceptible $S$, infected but not yet infectious $E$, infectious $I$ or recovered $R$. - -The schematic below shows the flow of individuals between the disease states $S$, $E$, $I$ and $R$ and parameters that describe the processes. +In this tutorial, we will use the default model in `epidemics`, `model_default_cpp()` which is an age-structured SEIR model described by a system of [ordinary differential equations](../learners/reference.md#ordinary). For each age group $i$, individuals are classed as either susceptible $S$, infected but not yet infectious $E$, infectious $I$ or recovered $R$. The schematic below shows the processes which describe the flow of individuals between the disease states $S$, $E$, $I$ and $R$ and the key parameters for each process. ```{r diagram, echo = FALSE, message = FALSE} DiagrammeR::grViz("digraph { @@ -182,22 +180,14 @@ DiagrammeR::grViz("digraph { # edges ####### - S -> E [label = ' infection (β)'] - E -> I [label = ' onset of \ninfectiousness (α)'] - I -> R [label = ' recovery (γ)'] + S -> E [label = ' infection \n(transmissibility β)'] + E -> I [label = ' onset of infectiousness \n(infectiousness rate α)'] + I -> R [label = ' recovery \n(recovery rate γ)'] }") ``` - -The model parameters definitions are : - -- transmission rate or transmissibility $\beta$, -- [contact matrix](../learners/reference.md#contact) $C$ containing the frequency of contacts between age groups (a square $i \times j$ matrix), -- infectiousness rate $\alpha$ (preinfectious period ([latent period](../learners/reference.md#latent)) =$1/\alpha$), -- recovery rate $\gamma$ (infectious period = $1/\gamma$). - ::::::::::::::::::::::::::::::::::::: callout ### Model parameters : rates @@ -209,9 +199,7 @@ We can use knowledge of the natural history of the disease to inform our values :::::::::::::::::::::::::::::::::::::::::::::::: - - -For each disease state ($S$, $E$, $I$ and $R$) and age group ($i$), we have an ordinary differential equation describing the rate of change with respect to time. The contact matrix $C$ allows for heterogeneity in contacts between age groups. Individuals in age group ($i$) move from the susceptible state ($S_i$) to the exposed state ($E_i$) via age group specific contact with the infectious individuals in their own and other age groups $\beta S_i \sum_j C_{i,j} I_j$. They then move to the infectious state at a rate $\alpha$ and recover at a rate $\gamma$. There is no loss of immunity (there are no flows out of the recovered state). +For each disease state ($S$, $E$, $I$ and $R$) and age group ($i$), we have an ordinary differential equation describing the rate of change with respect to time. $$ \begin{aligned} @@ -221,6 +209,14 @@ $$ \frac{dR_i}{dt} &=\gamma I_i \\ \end{aligned} $$ +Individuals in age group ($i$) move from the susceptible state ($S_i$) to the exposed state ($E_i$) via age group specific contact with the infectious individuals in their own and other age groups $\beta S_i \sum_j C_{i,j} I_j$. The contact matrix $C$ allows for heterogeneity in contacts between age groups. They then move to the infectious state at a rate $\alpha$ and recover at a rate $\gamma$. There is no loss of immunity (there are no flows out of the recovered state). + +The model parameters definitions are : + +- transmission rate or transmissibility $\beta$, +- [contact matrix](../learners/reference.md#contact) $C$ containing the frequency of contacts between age groups (a square $i \times j$ matrix), +- infectiousness rate $\alpha$ (preinfectious period ([latent period](../learners/reference.md#latent)) =$1/\alpha$), +- recovery rate $\gamma$ (infectious period = $1/\gamma$). ::::::::::::::::::::::::::::::::::::: callout