epiverse-trace · avallecam · Apr 2, 2025
diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd
@@ -336,9 +336,9 @@ In the lines above, we described how to specify the offspring distribution and g
 
 ### Stopping criteria
 
-This is an customisable feature of `{epichains}`. By default, branching process simulations end when they have gone extinct. For long-lasting transmission chains, in `simulate_chains()` you can add the `stat_max` argument. 
+This is an customisable feature of `{epichains}`. By default, branching process simulations end when they have gone extinct. For long-lasting transmission chains, in `simulate_chains()` you can add the `stat_threshold` argument. 
 
-For example, if we set an stopping criteria for `statistic = "size"` of `stat_max = 500`, no more offspring will be produced after a chain of size 500.
+For example, if we set an stopping criteria for `statistic = "size"` of `stat_threshold = 500`, no more offspring will be produced after a chain of size 500.
 
 :::::::::::::::::::::::::::
 

diff --git a/episodes/delays-functions.Rmd b/episodes/delays-functions.Rmd

 If you need it, read in detail about the [R probability functions for the normal distribution](https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/docs/lectures/lecture13.htm#probfunc), each of its definitions and identify in which part of a distribution they are located!

 ![The four probability functions for the normal distribution ([Jack Weiss, 2012](https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/docs/lectures/lecture13.htm#probfunc))](fig/fig5a-normaldistribution.png)

 ::::::::::::::::::::


 Estimating $R_t$ requires data on the daily number of new infections. Due to lags in the development of detectable viral loads, symptom onset, seeking care, and reporting, these numbers are not readily available. All observations reflect transmission events from some time in the past. In other words, if $d$ is the delay from infection to observation, then observations at time $t$ inform $R_{t−d}$, not $R_t$. [(Gostic et al., 2020)](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008409#sec007)

 ![**Timeline for chain of disease reporting, the Netherlands.** Lab, laboratory; PHA, public health authority. From [Marinović et al., 2015](https://wwwnc.cdc.gov/eid/article/21/2/13-0504_article)](fig/disease-reporting.jpg)

 The **delay distribution** could be inferred jointly with the underlying times of infection or estimated as the sum of the [incubation period](../learners/reference.md#incubation) distribution and the distribution of delays from symptom onset to observation from line list data ([reporting delay](../learners/reference.md#reportingdelay)). For `{EpiNow2}`, we can specify these two complementary delay distributions in the `delays` argument.

diff --git a/episodes/quantify-transmissibility.Rmd b/episodes/quantify-transmissibility.Rmd

 Refer to the prior probability distribution and the [posterior probability](https://en.wikipedia.org/wiki/Posterior_probability) distribution.

 In the ["`Expected change in reports`" callout](#expected-change-in-daily-cases), by "the posterior probability that $R_t < 1$", we refer specifically to the [area under the posterior probability distribution curve](https://www.nature.com/articles/nmeth.3368/figures/1). 

 ::::::::::::::::::::::::::::::::::::::::::::::::

 estimates_regional$summary$plots$R
 ```

 ![](fig/quantify-transmissibility-regional.png)

 ::::::::::::

diff --git a/episodes/delays-access.Rmd b/episodes/delays-access.Rmd

 Infectious diseases follow an infection cycle, which usually includes the following phases: presymptomatic period, symptomatic period and recovery period, as described by their [natural history](../learners/reference.md#naturalhistory). These time periods can be used to understand transmission dynamics and inform disease prevention and control interventions.

 ![Definition of key time periods. From [Xiang et al, 2021](https://www.sciencedirect.com/science/article/pii/S2468042721000038)](fig/time-periods.jpg)


 ::::::::::::::::: callout

 The generation time, jointly with the reproduction number ($R$), provide valuable insights on the strength of transmission and inform the implementation of control measures. Given a $R>1$, the shorter the generation time, the earlier the incidence of disease cases will grow.

 ![Video from the MRC Centre for Global Infectious Disease Analysis, Ep 76. Science In Context - Epi Parameter Review Group with Dr Anne Cori (27-07-2023) at <https://youtu.be/VvpYHhFDIjI?si=XiUyjmSV1gKNdrrL>](fig/reproduction-generation-time.png)

 In calculating the effective reproduction number ($R_{t}$), the *generation time* distribution is often approximated by the [serial interval](../learners/reference.md#serialinterval) distribution.
 This frequent approximation is because it is easier to observe and measure the onset of symptoms than the onset of infectiousness.

 ![A schematic of the relationship of different time periods of transmission between an infector and an infectee in a transmission pair. Exposure window is defined as the time interval having viral exposure, and transmission window is defined as the time interval for onward transmission with respect to the infection time ([Chung Lau et al., 2021](https://academic.oup.com/jid/article/224/10/1664/6356465)).](fig/serial-interval-observed.jpeg)

 However, using the *serial interval* as an approximation of the *generation time* is primarily valid for diseases in which infectiousness starts after symptom onset ([Chung Lau et al., 2021](https://academic.oup.com/jid/article/224/10/1664/6356465)). In cases where infectiousness starts before symptom onset, the serial intervals can have negative values, which is the case for diseases with pre-symptomatic transmission ([Nishiura et al., 2020](https://www.ijidonline.com/article/S1201-9712(20)30119-3/fulltext#gr2)).


 When we calculate the *serial interval*, we see that not all case pairs have the same time length. We will observe this variability for any case pair and individual time period, including the [incubation period](../learners/reference.md#incubation) and [infectious period](../learners/reference.md#infectiousness).

 ![Serial intervals of possible case pairs in (a) COVID-19 and (b) MERS-CoV. Pairs represent a presumed infector and their presumed infectee plotted by date of symptom onset ([Althobaity et al., 2022](https://www.sciencedirect.com/science/article/pii/S2468042722000537#fig6)).](fig/serial-interval-pairs.jpg)

 To summarise these data from individual and pair time periods, we can find the **statistical distributions** that best fit the data ([McFarland et al., 2023](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2023.28.27.2200806)).

 <!-- add a reference about good practices to estimate distributions -->

 ![Fitted serial interval distribution for (a) COVID-19 and (b) MERS-CoV based on reported transmission pairs in Saudi Arabia. We fitted three commonly used distributions, Log normal, Gamma, and Weibull distributions, respectively ([Althobaity et al., 2022](https://www.sciencedirect.com/science/article/pii/S2468042722000537#fig5)).](fig/seria-interval-fitted-distributions.jpg)

 Statistical distributions are summarised in terms of their **summary statistics** like the *location* (mean and percentiles) and *spread* (variance or standard deviation) of the distribution, or with their **distribution parameters** that inform about the *form* (shape and rate/scale) of the distribution. These estimated values can be reported with their **uncertainty** (95% confidence intervals).

 - Which one would be harder to control? 
 - Why do you conclude that?

 ![Serial interval of novel coronavirus (COVID-19) infections overlaid with a published distribution of SARS. ([Nishiura et al., 2020](https://www.ijidonline.com/article/S1201-9712(20)30119-3/fulltext))](fig/serial-interval-covid-sars.jpg)

 ::::::::::::::::: hint

	If you need it, read in detail about the [R probability functions for the normal distribution](https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/docs/lectures/lecture13.htm#probfunc), each of its definitions and identify in which part of a distribution they are located!

	![The four probability functions for the normal distribution ([Jack Weiss, 2012](https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/docs/lectures/lecture13.htm#probfunc))](fig/fig5a-normaldistribution.png)
Check warning on line 115 in episodes/delays-functions.Rmd GitHub Actions / Build markdown source files if valid `[image missing alt-text]: fig/fig5a-normaldistribution.png`

	::::::::::::::::::::


	Estimating $R_t$ requires data on the daily number of new infections. Due to lags in the development of detectable viral loads, symptom onset, seeking care, and reporting, these numbers are not readily available. All observations reflect transmission events from some time in the past. In other words, if $d$ is the delay from infection to observation, then observations at time $t$ inform $R_{t−d}$, not $R_t$. [(Gostic et al., 2020)](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008409#sec007)

	![Timeline for chain of disease reporting, the Netherlands. Lab, laboratory; PHA, public health authority. From [Marinović et al., 2015](https://wwwnc.cdc.gov/eid/article/21/2/13-0504_article)](fig/disease-reporting.jpg)
Check warning on line 401 in episodes/delays-functions.Rmd GitHub Actions / Build markdown source files if valid `[image missing alt-text]: fig/disease-reporting.jpg`

	The delay distribution could be inferred jointly with the underlying times of infection or estimated as the sum of the [incubation period](../learners/reference.md#incubation) distribution and the distribution of delays from symptom onset to observation from line list data ([reporting delay](../learners/reference.md#reportingdelay)). For `{EpiNow2}`, we can specify these two complementary delay distributions in the `delays` argument.

	Refer to the prior probability distribution and the [posterior probability](https://en.wikipedia.org/wiki/Posterior_probability) distribution.

	In the ["`Expected change in reports`" callout](#expected-change-in-daily-cases), by "the posterior probability that $R_t < 1$", we refer specifically to the [area under the posterior probability distribution curve](https://www.nature.com/articles/nmeth.3368/figures/1).
Check warning on line 102 in episodes/quantify-transmissibility.Rmd GitHub Actions / Build markdown source files if valid `[missing anchor]: [" Expected change in reports " callout](#expected-change-in-daily-cases)`

	::::::::::::::::::::::::::::::::::::::::::::::::

	estimates_regional$summary$plots$R
	```

	![](fig/quantify-transmissibility-regional.png)
Check warning on line 574 in episodes/quantify-transmissibility.Rmd GitHub Actions / Build markdown source files if valid `[image missing alt-text]: fig/quantify-transmissibility-regional.png`

	::::::::::::

	Infectious diseases follow an infection cycle, which usually includes the following phases: presymptomatic period, symptomatic period and recovery period, as described by their [natural history](../learners/reference.md#naturalhistory). These time periods can be used to understand transmission dynamics and inform disease prevention and control interventions.

	![Definition of key time periods. From [Xiang et al, 2021](https://www.sciencedirect.com/science/article/pii/S2468042721000038)](fig/time-periods.jpg)
Check warning on line 38 in episodes/delays-access.Rmd GitHub Actions / Build markdown source files if valid `[image missing alt-text]: fig/time-periods.jpg`


	::::::::::::::::: callout

	The generation time, jointly with the reproduction number ($R$), provide valuable insights on the strength of transmission and inform the implementation of control measures. Given a $R>1$, the shorter the generation time, the earlier the incidence of disease cases will grow.

	![Video from the MRC Centre for Global Infectious Disease Analysis, Ep 76. Science In Context - Epi Parameter Review Group with Dr Anne Cori (27-07-2023) at <https://youtu.be/VvpYHhFDIjI?si=XiUyjmSV1gKNdrrL>](fig/reproduction-generation-time.png)
Check warning on line 110 in episodes/delays-access.Rmd GitHub Actions / Build markdown source files if valid `[image missing alt-text]: fig/reproduction-generation-time.png`

	In calculating the effective reproduction number ($R_{t}$), the generation time distribution is often approximated by the [serial interval](../learners/reference.md#serialinterval) distribution.
	This frequent approximation is because it is easier to observe and measure the onset of symptoms than the onset of infectiousness.

	![A schematic of the relationship of different time periods of transmission between an infector and an infectee in a transmission pair. Exposure window is defined as the time interval having viral exposure, and transmission window is defined as the time interval for onward transmission with respect to the infection time ([Chung Lau et al., 2021](https://academic.oup.com/jid/article/224/10/1664/6356465)).](fig/serial-interval-observed.jpeg)
Check warning on line 115 in episodes/delays-access.Rmd GitHub Actions / Build markdown source files if valid `[image missing alt-text]: fig/serial-interval-observed.jpeg`

	However, using the serial interval as an approximation of the generation time is primarily valid for diseases in which infectiousness starts after symptom onset ([Chung Lau et al., 2021](https://academic.oup.com/jid/article/224/10/1664/6356465)). In cases where infectiousness starts before symptom onset, the serial intervals can have negative values, which is the case for diseases with pre-symptomatic transmission ([Nishiura et al., 2020](https://www.ijidonline.com/article/S1201-9712(20)30119-3/fulltext#gr2)).


	When we calculate the serial interval, we see that not all case pairs have the same time length. We will observe this variability for any case pair and individual time period, including the [incubation period](../learners/reference.md#incubation) and [infectious period](../learners/reference.md#infectiousness).

	![Serial intervals of possible case pairs in (a) COVID-19 and (b) MERS-CoV. Pairs represent a presumed infector and their presumed infectee plotted by date of symptom onset ([Althobaity et al., 2022](https://www.sciencedirect.com/science/article/pii/S2468042722000537#fig6)).](fig/serial-interval-pairs.jpg)
Check warning on line 127 in episodes/delays-access.Rmd GitHub Actions / Build markdown source files if valid `[image missing alt-text]: fig/serial-interval-pairs.jpg`

	To summarise these data from individual and pair time periods, we can find the statistical distributions that best fit the data ([McFarland et al., 2023](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2023.28.27.2200806)).

	<!-- add a reference about good practices to estimate distributions -->

	![Fitted serial interval distribution for (a) COVID-19 and (b) MERS-CoV based on reported transmission pairs in Saudi Arabia. We fitted three commonly used distributions, Log normal, Gamma, and Weibull distributions, respectively ([Althobaity et al., 2022](https://www.sciencedirect.com/science/article/pii/S2468042722000537#fig5)).](fig/seria-interval-fitted-distributions.jpg)
Check warning on line 133 in episodes/delays-access.Rmd GitHub Actions / Build markdown source files if valid `[image missing alt-text]: fig/seria-interval-fitted-distributions.jpg`

	Statistical distributions are summarised in terms of their summary statistics like the location (mean and percentiles) and spread (variance or standard deviation) of the distribution, or with their distribution parameters that inform about the form (shape and rate/scale) of the distribution. These estimated values can be reported with their uncertainty (95% confidence intervals).

	- Which one would be harder to control?
	- Why do you conclude that?

	![Serial interval of novel coronavirus (COVID-19) infections overlaid with a published distribution of SARS. ([Nishiura et al., 2020](https://www.ijidonline.com/article/S1201-9712(20)30119-3/fulltext))](fig/serial-interval-covid-sars.jpg)
Check warning on line 167 in episodes/delays-access.Rmd GitHub Actions / Build markdown source files if valid `[image missing alt-text]: fig/serial-interval-covid-sars.jpg`

	::::::::::::::::: hint