 We will take up some sample models and scenarios and try to perform sensitivity analysis and policy analysis and I will walk through on how I end up doing these sensitivity analysis and you can adopt it and further improve it to ensure that we are able to do these things in a proper manner. Let us look first example is infectious diseases dynamics. It builds on whatever model we did, the debugged disease model that we had yesterday. Now, we like to take the sensitivity of infectious diseases model to say 50 percent increase in recovery time or 50 percent increase in contact rate on the initial number of infected people instead of 1 it can be 10 or 100. We want to see what happens to the dynamics and we need to have a base case against which we want to compare the same. So, let me just quickly go over how we can do sensitivity analysis, you know, so let me open. So, this is our model, we have lot of things happening. So, first I am just going to save as into a new model. So, first we have to check whether our model is, this thing is open infectious diseases model which I have saved. One, if you actually go to the control panel, data sets there will be lot of data sets you might have used in the previous cases, it is best to get rid of all of that, so that we have only the base case. So, first is to write here the base case, simulate it and keep it ready. So, that is the base case against which we are going to compare. So, now to do sensitivity analysis and since all these parameter, all these are parameter changes, we can actually do it without trying to using what is called as the SIM setup, without trying to open and save all the settings. So, what we are going to do is I am going to just click this SIM setup. So, first case we are going to do is doubling the recovery time, right. So, let us just call it ID, recovery time, now instead of, so recovery time originally was 0.35 weeks, we are going to double it, so it is going to be 0.7, right. So, let us just call it 07, I am just some names, right. Then you click recovery time, so as soon as you click the recovery time, when I first I click SIM-SIM, then I got this, I change the name title. Once you click recovery time, it will show 0.35, we changed it to 0.7, right. And then you can enter, then when you click simulate, it is already simulated with this one setting, that is, so now if you actually open recovery time, you will find that it is still 0.35. Meaning 0.7 was only used for that simulation run, but you did not change your fundamental base model, which is quite useful because sensitivity analysis, then if you end up changing many things, then it you would not know what combination is you are actually comparing with that after some point, right. So, this is the only change that has occurred. Now, to actually see the results, if we click infected population and click graph, now you can see both the graphs, base case as well as this IDR T04 is what I gave in recovery time 0.7. So, it will collect for 50 percent increase or double the increase from 0.35 to 0.7, it actually increased about say 5000, 500 to 7000 would be what about 25 percent increase in the infected population, okay. We will do more, so even if you did not see it, the previous one we can see it now. Let us just check, okay. So, actually it is not double the, we ran double the recovery time, actually the scenario given is 50 percent increase in recovery time. So, recovery time is 2.5 days, 50 percent increase would be how much? 1.25, so 2, 3, 3.75 days. So, 3.75 by 7 would be 0.5, 0.525. So, that is the setting that we should have simulated. So, let us just do that. So, again 50 percent increase. So, I am going to click SIM setup RT, say 55, click recovery time instead of 0.35 write 0.52, what was it? Try 2, 5. So, this is 50 percent increase in the time in the recovery time, then I click enter and then I have to click display button, I click infected population. So, this was doubling the recovery time, we just want 50 percent increase, so I am just removed that graph. So, 50 percent increase in the recovery time cause just to peak at much higher. So, recovery time is longer that means people are taking more time to get, I mean being infected, right and that is adversely affecting how? How many new people are getting infected? There is infected persons that increases about 10 percent, 5,500 to 6,500 to 20 percent. Now, let us do 50 percent increase in contact rate, the current contact rate is 20, 50 percent increase means it should be become 30. So, let us just SIM setup, the contact rate 30, then contact rate 20, I change it to 30. Remember when I change this, what is the recovery time we are using? Recovery time is still 0.35, since exit analysis we change only one parameter at a time and this helps us avoid other errors. I click play, I infected population, I plot it, let me again remove this ID07. So, compared to the base case when the contact rate increases also we are getting similar peak, but much earlier. So, if contact rate increase 50 percent or the recovery rate increase 50 percent, the total infected is the same. That is interesting, that is one. Two, in this case more contact rate happens, more people are getting infected earlier. So, the peak shifts by a few days here which can have impact on our policy in the sense of how much you want to have base and things like that. So, this is how sensitivity we do and say how much, then we compare how much reduction in days is about 2 to 2 and a half days has reduced and peak has increased by 25 percent. For 50 percent increase in these changes it result 25 percent, these changes is how we record it. What is the next one? Initial number of infected people are 10 and 100. So, let us see what happens to that. But, infected people if you look at the function it is actually written as a variable inside. If it is inside that then we cannot change it when we do since the same it does not allow us to change the initial value of stock. To make it change we need to introduce a new variable that has got call it initial infected, creating initial infected, I am connecting an arrow connecting initial infected to initial population. Click equation and make the initial value as initial infected. Click ok, go to the equation, keep this as 1. So, if this as 1 is already the base case we have. So, now we can again send this in, I R initial 10. So, change initial infected to 10, let us run it and let us do initial infected to 10. I just ran 2 runs with different values of initial infected. If you look at the infected population you get all sorts of interesting graphs in this spot which is the base case which is this purple line. So, when initial 10 from the base case the initial was 10 the peak actually shifted. So, as more initial people were there the peak is now occurring earlier because now the probability of meeting infected person is much higher. So, peak so more people get infected early on. So, peak just shifts left when initial is 100 it peaks it moves left even more. But the maximum continues remain the same, it does not change. So, look at recovering population you can observe that whatever the value you had put the number of people who recovered as all those same 1000 which does not change eventually everybody gets infected because the very basic model and this has settled followed 0 the only changes are the trajectories that has happened compared to the base case which is in purple here. So, there are some scenarios which delayed delayed the recovery versus there are some scenarios which resulted in more people getting recovered much earlier that is speaking much more. As expected when you double the recovery time it takes longer to people to recover right. For all other cases there are more people already infected. So, they will recover faster I mean in the same amount of time. So, only that is why we are getting this right. So, this is an example how we can do basic substitute analysis using SIM setup where we are all using Vensim student edition there is a Vensim pro edition which allows you to automate it to some extent where you can give the range of these parameters it will do all this runs for you and give it because you have to pay for it. So, I am not showing that. So, there will be an additional set of icons for doing automated sensitivity analysis this is the manual version, but the logic is to understand how to do it automation comes later. Now, we have all these settings. Now, let us go back to a model let us do policy analysis on the same model. Analyze the impact of following policies with the base case. Policy on recovered population does not pose any threat of spreading infected disease as they are quarantined. Once they recover they leave the place or something or they got immune so much that they are not spreading disease anymore. Once you got the disease there are so much say antibodies in you that you are not able to you are not spreading the disease that is an policy. Policy 2's fatality ratio could have been reduced 15% if 100% of population are given antibiotics coverage upfront in anticipation. Currently the fatality ratio is 90%. So, recall the question. What it says is all the people who are given antibiotic injection major driver happened then the fatality ratio will come to 15%. So, when these two policies we want to implement or policy 3 is combined policy 1 and 2 meaning recovered population of shell quarantined and we are doing antibiotics coverage we are incurring double the cost this thing happen. But what will be dynamics? The less people get infected will take much longer or shorter will the peak be taller or shorter. So, these are questions we want to understand and based on these policies recommend which is the best ones or people can actually implement it in the field. So, let us go back to our model. First one says that recovered population does not pose any threat as their quarantine. So, how do we change the model to reflect that? So, now it is said that the recovering population does not affect new people getting infected. So, this link should disappear that is policy 1. Second one was this fatality ratio. It is said that if we do 15% to 100% of people get antibiotics and fatality ratio goes from current 0.990% to 15% 1.5. So, this is a parameter change quite easy we can do it. But this is a structural change we want to enable right. So, to do that let us just create a new variable called policy of quarantined recover I am going to have a big name policy of quarantined recovering population. Let us just link it or we are just looking at the model. So, infected population the total population is infected plus recovering plus susceptible. So, I am just going to move this case here. So, now recovering population I am going to multiply by the policy of quarantined recovering population. This policy let us set it to 0 with the comments and 0 indicates people are quarantined. 1 indicates people are not quarantined and recovered people. So, I am just introducing a new variable there. So, 0 indicates they are being quarantined. So, that means the policy is in effect when it is 0. It is up to us to define whether policy is on or off and what it is to be. So, I am just defining it that way. So, this helps us understand what is a better modeling factors. Now, I can again use a SIM setup tool to set the policies. Let us do SIM setup and let us call it ID policy 1. The policy of quarantine instead of 0 let us just make it. So, 0 means it is already quarantined. Let me escape it, stop it. What is the base case we want? We want the base case to be 1 indicates recovered people are not quarantined. So, let us just call that as the base case. Again, as you can observe, we are using the comment box to do the documentation. So, it becomes easier for us to figure out what is happening. Now, let us do SIM policy of quarantine. So, if I put 0 that means people are being quarantined. Policy 1 happens. Let us play it. Now, for policy 2 let us SIM and fatality ratio goes to 15 percent. So, I am changing fatality ratio to 0.15, clicking enter and running it. And policy 3 is people are quarantined that is become 0 and fatality ratio is 0.15. Both the changes has occurred. I am going to simulate it. I have three different runs, three different policies are evaluated. Go to infected population. All our sensitivity runs are there. I am going to just comment it all out so that we can compare what we actually want. This is the changes we see if we have the base case which is right here. Now, let us do one policy at a time. Policy 1 actually had no impact. Even if I removed the recovered population it did not have any impact. It did not have any impact. It is almost the same. Policy 2 it reduced the peak infected because that means putting antibiotics is much more effective. When I did policy 3 when all are there again there does not need to be any impact. That is quite interesting. We get the policies right. Policy 4 and time initially it is 1. Let me just simulate the base case again. Policy 3. We expect policy 3 to be similar to policy 1 right at least. It should be similar but it did not. Let me just let us again check policy 3. Let me call it B. Now, since I am not happy with sim sim what I am going to do is I am going to hard change it here. People are quarantined and fatality ratio is 0.15. I am going to hard change in this model so that I can run it. Base case and policy. Policy 3. Doing both seems to have an adverse effect which is quite counterintuitive result that we are getting. We ensured fatality is small and we quarantined people. That means once they are going to recover then they are not influencing. If fatality is high then more people go into disease stock and disease stock does not affect our population. We know that disease stock is not affecting or the number of people are getting infected. But when they go into recovered mode then and we are removing them from that still they should have this similar impact. But interestingly showing this one. Let us try say recovering population graph. Now, we are getting some very interesting results. Base case is here. In policy 3. Of course, policy 3 B is the same. More people are recovering. Of course, because we gave them the injection I guess the antibiotics. Policy 2 also more people are recovering which is again because the antibiotics suffered. In policy 1 the number of people compared to the baseline. Policy 1 just mimics the same baseline case the same number of people that are recovering. So, it is quite counterintuitive result that we are able to get even in such a simple model. That the number of people who are just providing them with antibiotics. There is a subtle change here if you observe with policy. We are going to remove base case. Between policy 2 and policy 3 there is a subtle difference. So, including or excluding the recovered population affecting them did not matter antibiotics had a much better effect. So, doing antibiotics and quarantining people did not have much effect. That is one of the interesting thing that comes out with this model. So, we have done this housing stock dynamics. We can also check sensitivity of model to say for example, one parameter time to build houses 6 to 5 months or time to build houses increases from 6 months to 7 months. And we can analyze impact of one new policy also saying due to change in FSI rules. Authorities are considering replacing every demolished house with 1.25 new houses from month 20 onwards to meet the new demand. So, look at the model the number of houses, desired number of houses increases 50,000 units in month 20. So, along with it there is a policy also being considered. So, why don't you work on this?