Predicting CoronaVirus with Math
Let me ask you guys a question, in this situation we are facing right now is there a possible way that you can predict the spread of Covid-19 in your country by using Math? If you answer yes, then you are completely right. Just by using this mathematical model developed by an Argentinian Engineered you can have a useful tool in order to see if in your country things are ameliorating or sagging.
Sample graph used for explanation
So let’s see what we have in the graph, let’s imagine that you search the number of confirmed cases per day ever since it started in your country. The Y-axis as demonstrated in the graph means the number of infected people on that day, in the X-axis it is each day. For example, I3 (I= infected people), meaning the quantity of infected people on day 3. In = would be a general case meaning that it is the quantity of infected people in an determined n or day. So now how do we find the number of cases for the next day? Well, first of all, let’s define some things. Assuming that from one day to another there’s not the same amount of infected people, for example, I3to I4, we can just simply indicate that this increase in the number of infected people as ΔI3 these would be new cases that are detected in the course of day 3. Now let’s think, how do we calculate the newly infected cases in the course of day 3, this is the answer simply by this equation ΔI3=I4–I3 giving us the new cases. Of course this was easy, because we had the information, but what if we don’t?
Finding New Cases
Now let’s ask the question mathematically, ΔIn depends on what? Meaning how many new cases I have after the day has fully passed, what are the factors that contribute to this? Let me give an example, if we are all in our houses and we don’t have any contact with people infected, are we going to get infected? The answer is unlikely. With this I mean that ΔIn is directly proportional to the level of exposure that we have and the probability of getting the virus, for example if you don’t wash your hands or don’t have a strong immune system. It also depends on how many people are infected in the country, because it’s more probable that they would infect other people. In more mathematical terms this equation would end up being ΔIn=E*P*In. Using the example from before ΔI3=I4–I3; we can state that ΔIn=In+1–In. Meaning In+a=next day. Now let’s put it all together In+1–In=E*P*In. Now lets leave In+1 alone. In+1=E*P*In+In then we factor, In+1=(EP+1)In. So now, what does this mean? Well it’s the answer of what must happen in order to fight coronavirus correctly. If this constant(EP+1) is equal to 1, would mean that In+1=In , that would mean that the quantity of infected people in the next day is the same as the day before, meaning that there’s no new infected people meaning stability. If this (EP+1)grows the quantity of infected people would also grow, that’s why it’s in our duty to try to make it as close to 1 as possible. Now let’s rename this (EP+1) as a problematic factor or just F. F=(EP+1). Now how to know what factor you have in your country? Well it’s just simply as the quantity of infected people in the next day divided by the quantity of confirmed cases in the previous day. So with this you will know if your country and people are taking the necessary adjustments to prevent the spread of the Covid-19.
The final equation found by the Argentinian Engineered is :
With this you can simply find an approximation to future cases and see if your country is doing quite okay.
Now, i’ve created a table with every single confirmed case per day and found this
F=In+1/In for Bolivia.
With this I concluded that F= 1.18on average. Finally using the equation from before it was predicted that by the end of March 22, there would be about 28 cases. According to information given by John Hopkins University webpage which demonstrates all confirmed cases in Bolivia. There are 27. Which means that I was pretty close to finding the confirmed cases for this day. Meaning that something has to be done and we as citizens have to start caring about this issue and do not expose ourselves to the danger.