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so I have the definition of our not here and I'm just gonna take some quick notes it says the number of new cases that an existing case generates on average and it's over the infectious period in a susceptible population in here what they're kind of referring to is non-vaccinated population so the way to think about this is for me anyway is to kind of put it into math terms so if you have let's say I'm just gonna write these down here let's say you have existing cases here existing cases and you have new cases you literally can just take the two and just divide them by each other right you could say well new / existing existing is going to be my R naught equals R naught right so let's just go through a few scenarios so let's say R naught is less than 1 so if it's less than 1 let's think of how that might play out let's say you have two existing cases and you kind of come back and you say well how many new ones are there in my population well there's only one only one new person even though you used to have two and so you say okay well that's 1/2 equals 0.5 and that's less than 1 okay and what does that mean exactly well it means that if you have less than 1 over time you can see how this is basically this infection is going to die out right it's not gonna spread it's just gonna slowly die out because fewer and fewer people are gonna get it and and in this case maybe even just one generation down the road there will be no one to to potentially get this infection so these are always kind of the nice ones because they're gonna die out by themselves and that's always wonderful for Humanity when an infection dies out another scenario could be an R nought of 1 so in this case you might have two people with an infection and you follow them over time and you say well how many new people got infected with this infection you say well actually we found two new people I got infected so we had two old people two new people and so 2 divided by 2 equals 1 and just in terms of keeping track of of kind of this infection over time that means that basically this is a stable infection right it's not spreading numbers are basically always - and it's also not dying out what's the third scenario well the third one of course is going to be greater than one so if it's less than one an equal to one the third scenario is greater than one and you start out with two again let's just say and you say okay how many new people get this infection and this one let's say I'm just going to make this really really contagious let's say a lot of people get this infection let's say eight new people and how many existing well there were only two just like all the other examples so we have an R naught a four which is greater than one and so what is really happening here well this is an infection that's spreading so this infection is the one that we're worried about right it's spreading and we want to either kind of allow it to stabilize so one goal might be hey let's just get this at least stable right so that it's not infecting more and more people another goal might be let's actually eradicate this disease let's go all the way down to this theoretical are not of zero and what would our not of zero really what does that mean well it means that this number new is zero right the numerator is zero and and that means that there are no new cases and that would mean eradication so if you want to eradicate a disease like like smallpox for example this is what you have to do you have to figure out how to get all the way down to zero but for most diseases you just want to stop the spread you want to stop the spread and so if you want to stop the spread this is kind of the goal that you have to think about this is goal number one so let's put this in the context of a real infection so let's take the mumps virus and mumps causes you know fevers and headaches and kind of general lousy you know feelings but also it swells up your cheeks because it affects your saliva gland and it makes you look a little bit like a chipmunk so so mumps virus is not a pleasant virus and this infection when studied has an R nought of about four so it's actually it's perfectly modeled with this with this picture right here with two going to eight and fortunate for us we have an MMR vaccine and that stands for measles mumps and rubella and the measles mumps rubella vaccine is given to a lot of folks and it's going to help us kind of think through how to stop the spread of mumps for example so thinking through this if the goal is to stop the spread what does that mean well it means that our goal our not our goal our not is gonna be one in this case and what is our current or not what are we starting from well in this case it's gonna be four and so the proportion of people that are still gonna get sick I mean even with this wonderful goal the proportion that are still gonna get sick are 1/4 and I actually I can kind of maybe show them right here maybe these two will still get sick with mumps even if we're able to stop the spread because that's exactly what happened here right but the wonderful news and this is a the good part about this is that you're able to protect this many people with this goal at least right you're able to protect this many people and that basically is reflected as one minus one over four so one minus the goal are not over current are not right this is the math way to kind of represent this fraction so this represents this fraction right here and this represents this fraction right there so what proportion then what proportion need vaccination what proportion of our community let's say what proportion needs a vaccine to at least stop this spread you know that's the goal that we said we had right what proportion needs vaccine well we'd say well it's it's just what we laid out right it would be 1 minus the goal are not which is 1 divided by the current are not which is 4 so we'd say well this is 3/4 or 75% in other words if we are able to vaccinate 75% of people meaning these folks right 6 out of 8 is 75% then we basically have changed the way that mumps looks it no longer looks like an R not a 4 it looks like our goal R naught which is 1 now I'm gonna grab another example just to make sure we have a clear handle on how this works so measles has an arm of 18 put into words that means for every one existing case we see 18 new cases over the infectious period usually a few weeks in non vaccine in population so if that's the case how many people what proportion needs vaccine to stop the spread so we'd say okay well that means 1 - our goal is to stop the spread so 1 divided by we said they are not is 18 so this is the proportion that we need to vaccinate and that works out to about 94% holy cows that's much higher than what we saw with mumps right let's do one what one more example is do diphtheria so diphtheria kind of hard to spell but di ph th diphtheria has an R nought of let's say about 6 and these values 6:18 I said mumps was for you know really depends on which study you're looking at but most of these are presented as ranges but in case in if we accept the number 6 then we say ok it's 1 minus 1 because that's the goal R naught is 1 divided by 6 and that equals 83% so basically the higher that are not the better your vaccine coverage has to be in order to prevent an outbreak from happening and of course we're only talking about one way to protect folks and that's through vaccine the other way to protect folks of course is to try to limit the number of new cases by saying well let's just physically surround people and maybe put people in quarantine and and having people separated so if they can't actually catch infection like I'm doing here maybe doing that could also obviously prevent new cases from happening so I don't want to imply that vaccine is the only way but of course it's a very very effective way of preventing diseases from spreading