"QuizID"	"AppID"	"AppTitle"	"TaskID"	"TaskText"	"RecordID"	"Record"	"Type"	"Note"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	1	"Set numbers for initial uninfected cells, infected cells and virus to **U**=100000, **I**=0, and **V**=1. Set uninfected birth and death rates to *n*=10000 and *d~U~*=0.1, infected cell death rate to 1, and virus death rate to 2. Rate of infection should be set to 2e-5, virus production to 5, and conversion factor to 1. Start simulation at time 0 and run for 300 days, time step of 0.1 (that value doesn't matter much). Choose _p_ as the parameter to vary, between 1 and 10, do 10 different parameter values, linear spacing, and no log scales for plotting. 


Run the simulations; check to ensure all simulations reach steady state (see output message below plot). Then, reduce simulation time to 30 days, note how some simulations did not reach steady state and how that affects results."	"T1R1"	"Isteady for *p* = 7 and 300 days simulation time"	"Rounded_Integer"	"Report the rounded integer"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	1	"Set numbers for initial uninfected cells, infected cells and virus to **U**=100000, **I**=0, and **V**=1. Set uninfected birth and death rates to *n*=10000 and *d~U~*=0.1, infected cell death rate to 1, and virus death rate to 2. Rate of infection should be set to 2e-5, virus production to 5, and conversion factor to 1. Start simulation at time 0 and run for 300 days, time step of 0.1 (that value doesn't matter much). Choose _p_ as the parameter to vary, between 1 and 10, do 10 different parameter values, linear spacing, and no log scales for plotting. 


Run the simulations; check to ensure all simulations reach steady state (see output message below plot). Then, reduce simulation time to 30 days, note how some simulations did not reach steady state and how that affects results."	"T1R2"	"TRUE or FALSE: As *p* increases, **Vsteady** also increases."	"Logical"	"Report TRUE or FALSE"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	1	"Set numbers for initial uninfected cells, infected cells and virus to **U**=100000, **I**=0, and **V**=1. Set uninfected birth and death rates to *n*=10000 and *d~U~*=0.1, infected cell death rate to 1, and virus death rate to 2. Rate of infection should be set to 2e-5, virus production to 5, and conversion factor to 1. Start simulation at time 0 and run for 300 days, time step of 0.1 (that value doesn't matter much). Choose _p_ as the parameter to vary, between 1 and 10, do 10 different parameter values, linear spacing, and no log scales for plotting. 


Run the simulations; check to ensure all simulations reach steady state (see output message below plot). Then, reduce simulation time to 30 days, note how some simulations did not reach steady state and how that affects results."	"T1R3"	"Number of simulations that did not reach steady state for 30 days simulation time"	"Integer"	"Report the integer"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	1	"Set numbers for initial uninfected cells, infected cells and virus to **U**=100000, **I**=0, and **V**=1. Set uninfected birth and death rates to *n*=10000 and *d~U~*=0.1, infected cell death rate to 1, and virus death rate to 2. Rate of infection should be set to 2e-5, virus production to 5, and conversion factor to 1. Start simulation at time 0 and run for 300 days, time step of 0.1 (that value doesn't matter much). Choose _p_ as the parameter to vary, between 1 and 10, do 10 different parameter values, linear spacing, and no log scales for plotting. 


Run the simulations; check to ensure all simulations reach steady state (see output message below plot). Then, reduce simulation time to 30 days, note how some simulations did not reach steady state and how that affects results."	"T1R4"	"**Isteady** for *p* = 7 and 30 days simulation time"	"Rounded_Integer"	"Report the rounded integer"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	2	"Play around with the samples to run, i.e. the number of different parameter values. The higher the number, the more often the simulation runs, the longer it takes and the more detailed the results are. Also adjust the minimum and maximum, and linear or logarithmic spacing and plotting. Take a look at the model equations and diagram and see if by 'staring' at them, you can understand why you got the results you see. Some results might be expected; for instance, if you increase the rate at which infected cells produce virus, the virus peak goes up. Sometimes, results are less intuitive (see below). With enough practice, it is often possible to intuit specific results based on the underlying equations, but that requires a good bit of modeling practice. As models get more complicated, even experienced modelers can often not intuit what model behavior one should expect as specific parameters vary. Often, the only way to find out is by actually running the simulations."	"T2R1"	"Value for *p* when **Isteady** is approximately equal to **Usteady**, 96 samples, *p* to vary from 1 to 20 on a linear scale (Hint: use plotly to zoom-in)"	"Integer"	"Report the integer"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	2	"Play around with the samples to run, i.e. the number of different parameter values. The higher the number, the more often the simulation runs, the longer it takes and the more detailed the results are. Also adjust the minimum and maximum, and linear or logarithmic spacing and plotting. Take a look at the model equations and diagram and see if by 'staring' at them, you can understand why you got the results you see. Some results might be expected; for instance, if you increase the rate at which infected cells produce virus, the virus peak goes up. Sometimes, results are less intuitive (see below). With enough practice, it is often possible to intuit specific results based on the underlying equations, but that requires a good bit of modeling practice. As models get more complicated, even experienced modelers can often not intuit what model behavior one should expect as specific parameters vary. Often, the only way to find out is by actually running the simulations."	"T2R2"	"Number of values for *p* that are > 2 with 96 samples, *p* to vary from 1 to 20 on a linear scale"	"Integer"	"Report the integer"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	2	"Play around with the samples to run, i.e. the number of different parameter values. The higher the number, the more often the simulation runs, the longer it takes and the more detailed the results are. Also adjust the minimum and maximum, and linear or logarithmic spacing and plotting. Take a look at the model equations and diagram and see if by 'staring' at them, you can understand why you got the results you see. Some results might be expected; for instance, if you increase the rate at which infected cells produce virus, the virus peak goes up. Sometimes, results are less intuitive (see below). With enough practice, it is often possible to intuit specific results based on the underlying equations, but that requires a good bit of modeling practice. As models get more complicated, even experienced modelers can often not intuit what model behavior one should expect as specific parameters vary. Often, the only way to find out is by actually running the simulations."	"T2R3"	"Number of values for *p* that are > 2 with 96 samples, *p* to vary from 1 to 20 on a log scale"	"Integer"	"Report the integer"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	3	"The model we have here is so simple that we can in fact figure out how some of the outcomes depend on parameters without having to run simulations but instead by doing some math. Specifically, we can compute the steady states. You saw how that is done in the ___Basic Virus Model___ app. If this is unfamiliar to you or you need a refresher, (re)visit that app and go through the tasks. You found there (if you did the math) that the virus load at steady state is given by $V_s = (bnp-bd_Ign-d_Id_Ud_V)/bd_Id_V$. This equation suggests that as the rate at which infected cells produce virus increases, the virus load at steady state goes up, which you found above. It also suggests that the relation between virus load and the rate at which virus infects cell, *b*, is more complicated, since *b* shows up both in the numerator and denominator. If you have practice reading equations, you might be able to visualize how **V~s~** behaves as *b* is varied. You can always explore it numerically. Let's do that.


Set all parameters as previously, with _p_=5 and 300 days simulation time. Choose _b_ as the parameter to vary, between 1e-6 and 1e-3, do 20 different parameter values, log spacing for parameter values, and plot both axes on a logarithmic scale. Run the simulation. Observe the pattern you get for **V~s~** as a function of _b_ and see if it agrees with the equation (it should). 


We cannot compute similar mathematical expressions for the peak of the variables. In general, as soon as our model reaches a certain level of complexity (maybe around 5 equations and more), getting analytic/mathematical equations for most outcomes of interest is not possible and the numerical approach of running the simulations and looking at the results is the only option we have."	"T3R1"	"Using equation, **Vsteady** when *b* = 6.16e-6"	"Rounded_Integer"	"Report the rounded integer"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	3	"The model we have here is so simple that we can in fact figure out how some of the outcomes depend on parameters without having to run simulations but instead by doing some math. Specifically, we can compute the steady states. You saw how that is done in the ___Basic Virus Model___ app. If this is unfamiliar to you or you need a refresher, (re)visit that app and go through the tasks. You found there (if you did the math) that the virus load at steady state is given by $V_s = (bnp-bd_Ign-d_Id_Ud_V)/bd_Id_V$. This equation suggests that as the rate at which infected cells produce virus increases, the virus load at steady state goes up, which you found above. It also suggests that the relation between virus load and the rate at which virus infects cell, *b*, is more complicated, since *b* shows up both in the numerator and denominator. If you have practice reading equations, you might be able to visualize how **V~s~** behaves as *b* is varied. You can always explore it numerically. Let's do that.


Set all parameters as previously, with _p_=5 and 300 days simulation time. Choose _b_ as the parameter to vary, between 1e-6 and 1e-3, do 20 different parameter values, log spacing for parameter values, and plot both axes on a logarithmic scale. Run the simulation. Observe the pattern you get for **V~s~** as a function of _b_ and see if it agrees with the equation (it should). 


We cannot compute similar mathematical expressions for the peak of the variables. In general, as soon as our model reaches a certain level of complexity (maybe around 5 equations and more), getting analytic/mathematical equations for most outcomes of interest is not possible and the numerical approach of running the simulations and looking at the results is the only option we have."	"T3R2"	"Using plotly output, **Vsteady** when *b* is approximately equal to 6.16e-6"	"Rounded_Integer"	"Report the rounded integer"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	4	"Let's explore the impact of a different parameter. Set all variables as in task 1.


Choose _d~I~_ as the parameter to vary and set lower and upper limit to 0.25 and 5 and the number of samples to 20. Before you run the model, look at your equation for __V~s~__ and try to predict what you should see in the plot. Similarly, while you don't have an analytical solution, you can look at the model equations and try to intuit what you might expect __V~peak~__ and __I~peak~__ to do as you increase _d~I~_. 


Now run the model, compare the results with your expectations. How do they agree or disagree?"	"T4R1"	"**Vsteady** when _d~I~_ = 2.5"	"Rounded_Numeric"	"Report the rounded numeric to 2 decimal places"
"DSAIRM_basicvirusexploration"	"basicvirusexploration"	"Virus Model Exploration"	5	"Do the same explorations you did above for any other parameter you want to investigate. 


Note that here we focus on a single parameter at a time. With a little bit of coding effort, we could change the underlying simulation to loop over say 2 parameters and produce outcomes for sets of parameter values, e.g. _V~peak~_ as a function of _b_ and _p_. This can be done by writing 2 loops (or some equivalent way of doing it) to scan over various combinations of parameter values for _b_ and _p_ and run the simulation for each such combination and record the results. These results could be plotted as a 2-dimensional heatmap. While this could be extended to more than 2 parameters, it will become hard to visualize and long to run. If there are many parameters that could change, a different approach is useful, which you'll learn about in the ***Uncertainty and Sensitivity Analysis*** app."	"T5R1"	"Nothing"	"None"	""
