"QuizID"	"AppID"	"AppTitle"	"TaskID"	"TaskText"	"RecordID"	"Record"	"Type"	"Note"
"DSAIDE_reproductivenumber2"	"reproductivenumber2"	"Reproductive Number 2"	1	"In _Reproductive Number 1_, the focus was on a single outbreak. But the reproductive number concept is also useful in situations where a disease is endemic. As you learned in the _Patterns of ID_ app (if not, go do it before this one), to achieve an endemic state, we need replenishment of susceptibles through for instance births or waning immunity. We'll start with natural births and deaths. If births (and deaths) are present, you will be able to get multiple outbreaks and endemic states. Set the parameter values such that your hosts have approximately an average lifespan of 41 years (remember to convert to months before taking the inverse). Round to the first significant digit (i.e. 0.00X). Set birth rate such that the population is steady at 1000 in the absence of any infected hosts (if you need a reminder how that's done, revisit the _ID Patterns_ app). 

Now we'll introduce the disease. Set simulation time to around 500 years, 1 infected, _g_=5, _b_=0.015. Run the simulation, make sure you reach a steady state. Compare the steady state values for S (and optional I and R) from the simulation with those predicted from the SIR steady state equations (see _Patterns of ID_ app)."	"T1R1"	"The value you used for birth rate"	"Rounded_Integer"	"Report the rounded integer"
"DSAIDE_reproductivenumber2"	"reproductivenumber2"	"Reproductive Number 2"	1	"In _Reproductive Number 1_, the focus was on a single outbreak. But the reproductive number concept is also useful in situations where a disease is endemic. As you learned in the _Patterns of ID_ app (if not, go do it before this one), to achieve an endemic state, we need replenishment of susceptibles through for instance births or waning immunity. We'll start with natural births and deaths. If births (and deaths) are present, you will be able to get multiple outbreaks and endemic states. Set the parameter values such that your hosts have approximately an average lifespan of 41 years (remember to convert to months before taking the inverse). Round to the first significant digit (i.e. 0.00X). Set birth rate such that the population is steady at 1000 in the absence of any infected hosts (if you need a reminder how that's done, revisit the _ID Patterns_ app). 

Now we'll introduce the disease. Set simulation time to around 500 years, 1 infected, _g_=5, _b_=0.015. Run the simulation, make sure you reach a steady state. Compare the steady state values for S (and optional I and R) from the simulation with those predicted from the SIR steady state equations (see _Patterns of ID_ app)."	"T1R2"	"Number susceptible at steady state"	"Rounded_Integer"	"Report the rounded integer"
"DSAIDE_reproductivenumber2"	"reproductivenumber2"	"Reproductive Number 2"	2	"Figure out what the value for the reproductive number is at the endemic steady state. To that end, recall its definition (average number of new infectious persons created by one infectious person) and determine what has to be true if the number of infected neither increases nor decreases. How does that compare to the reproductive number at the peak of an outbreak, which you learned about before?"	"T2R1"	"Value of R at endemic steady state"	"Rounded_Integer"	"Report the rounded integer"
"DSAIDE_reproductivenumber2"	"reproductivenumber2"	"Reproductive Number 2"	3	"At steady state, you have the _R_ value you just figured out in the previous task and a fraction of the population is susceptible, namely  _S~f~_ / _S~0~_ where _S~f~_ is the number of susceptibles at steady state and _S~0~_ is the number of susceptibles at the beginning. You learned that the equation for the reproductive number for this model is _R~0~=bS~0~/(g+m)_. Use it to compute the reproductive number. Compare the value of _R~0~_ at the start (where the fraction of susceptible is 1) with the value of the fraction of susceptible and the R value at steady state. Can you figure out how they relate? It should confirm what you figured out about _R_ at steady state in the previous task."	"T3R1"	"Number susceptible left at steady state"	"Rounded_Integer"	"Report the rounded integer"
"DSAIDE_reproductivenumber2"	"reproductivenumber2"	"Reproductive Number 2"	3	"At steady state, you have the _R_ value you just figured out in the previous task and a fraction of the population is susceptible, namely  _S~f~_ / _S~0~_ where _S~f~_ is the number of susceptibles at steady state and _S~0~_ is the number of susceptibles at the beginning. You learned that the equation for the reproductive number for this model is _R~0~=bS~0~/(g+m)_. Use it to compute the reproductive number. Compare the value of _R~0~_ at the start (where the fraction of susceptible is 1) with the value of the fraction of susceptible and the R value at steady state. Can you figure out how they relate? It should confirm what you figured out about _R_ at steady state in the previous task."	"T3R2"	"The value for R~0~"	"Rounded_Integer"	"Report the rounded integer"
"DSAIDE_reproductivenumber2"	"reproductivenumber2"	"Reproductive Number 2"	4	"Next double the values for both natural birth and death rates. What do you get for the value of S at steady state? Is that surprising? If it is, take another look at the relation between _R~0~_ and S at steady state, and the equation for _R~0~_."	"T4R1"	"The value of S at steady state (end of simulation)"	"Rounded_Integer"	"Report the rounded integer"
"DSAIDE_reproductivenumber2"	"reproductivenumber2"	"Reproductive Number 2"	5	"A) Turn off births and deaths and instead assume immunity wanes over 10 months (convert to a rate). Run the simulation with the same transmission rate and recovery rate as task 1. Record the value of S at steady state. How does it compare to the value from the previous task? Is that surprising? Again, look at the equation for _R~0~_. 
B) Now double the initial number of susceptible. What is _R~0~_ now? What do you therefore expect for the number of susceptibles at steady state? Run the simulation to see what you get. If the numbers confuse you at first glance, think carefully about the relation between _R~0~_ and both number and fraction susceptible left at steady state. Also, compare what you find here with the way to get the steady state as discussed in _Patterns of ID_ and revisited in task 1 above."	"T5R1"	"Number susceptible at steady state (A)"	"Rounded_Integer"	"Report the rounded integer"
"DSAIDE_reproductivenumber2"	"reproductivenumber2"	"Reproductive Number 2"	5	"A) Turn off births and deaths and instead assume immunity wanes over 10 months (convert to a rate). Run the simulation with the same transmission rate and recovery rate as task 1. Record the value of S at steady state. How does it compare to the value from the previous task? Is that surprising? Again, look at the equation for _R~0~_. 
B) Now double the initial number of susceptible. What is _R~0~_ now? What do you therefore expect for the number of susceptibles at steady state? Run the simulation to see what you get. If the numbers confuse you at first glance, think carefully about the relation between _R~0~_ and both number and fraction susceptible left at steady state. Also, compare what you find here with the way to get the steady state as discussed in _Patterns of ID_ and revisited in task 1 above."	"T5R2"	"Number susceptible at steady state (B)"	"Rounded_Integer"	"Report the rounded integer"
"DSAIDE_reproductivenumber2"	"reproductivenumber2"	"Reproductive Number 2"	6	"One usually obtains R~0~ from the data/literature and uses it to pick values for the transmission parameter, _b_, which is otherwise very hard to estimate. Let's try that. Go online and find (approximate) values for the duration of the infectious period and _R~0~_ for SARS. Start with 1000 susceptible, 1 infected. Assume that for a single outbreak we can ignore births, deaths or waning immunity (all zer0). Use those values and the _R~0~_ equation to compute the transmission parameter, _b_. Then run a simulation with that value for _b_ (for 12 months). Recall from the _Reproductive Number 1_ app how you can use the fraction if suceptibles left at the end of an outbreak to compute _R~0~_. Do that here again to confirm that you get indeed (approximately) the value you started out with."	"T6R1"	"Nothing"	"None"	""
"DSAIDE_reproductivenumber2"	"reproductivenumber2"	"Reproductive Number 2"	7	"Let's repeat the same for a disease that causes an endemic state, tuberculosis (TB). Go online and find estimates for the basic reproductive number of TB. Note that TB is somewhat special: An infected and infectious person (someone with TB disease) might infect many others, but only some of those will go on to develop disease and become infectious. For R~0~, we always need to go from infectious individual to another infectious individual. Also find an estimate for the duration of the infectious period for TB. Then use these quantities to determine parameters _b_ and _g_ and run a simulation with 1000 susceptible and the same birth and death rates as in task 1 (m=0.002 and n=2). Check that the steady state levels of infected/infectious individuals matches with the R~0~ value you chose.

Note: The SIR model is not a good model for TB since for TB, the stage where individuals are infected but not yet infectious is long and important. So to really model TB, one would need to include such details. We are only using TB here for illustrative purposes."	"T7R1"	"Nothing"	"None"	""
