The color green: Where incidence meets prevalence

Figure 1. Money Flow

Does Figure 1 (right) look familiar?
The majority should relate to it as a continuously encountered event.

This similar image has been used to describe  incidence and prevalence and the relationship between the two (pebbles as representation). Incidence measures the frequency of events (such as the onset of illness) while prevalence  measures the proportion of people who have the illness right now.

The relationship between prevalence and incidence is related to duration or time, where prevalence would approximate incidence when the duration of disease is short.

Prevalence ≈ (incidence rate) × (average duration of illness).

So, if the duration of disease is short (like the common cold) prevalence approximates the incidence rate. Specifically, the inflow of disease approximates the outflow. Outflow is usually due to two main reasons: death or cure.

Now let's apply this concept to money flow into individual bank accounts, where after some pondering the prevalence equals incidence concept surprisingly could be very applicable.

Figure 2. Bank account before payday

The majority of people live from paycheck-to-paycheck, and most of our balance accounts (including mine) look like Figure 2. 

Using the following assumptions:

Dollar Incidence: Number of new dollars into balance on paycheck date (new disease). The incidence rate is usually calculated as the number of new cases within a specified time divided by the population at risk. I am not sure what the $$ at risk would be here or how to even think about computing it, so calculating a rate would be quite challenging, but for the sake of this analogy let's call new dollars as incidence (the unit of measurement is individual accounts).

Dollar Prevalence:  Is basically how much your bank account has at this moment. It is usually calculated by comparing the number of people who have a condition with the total number of people studied. Again, I will not dwell on whether it is possible to calculate a proportion here. The unit we are looking at is individual bank account...So, let us consider again that the amount of $$ right now is called prevalence.

Applying the formula of prevalence equals incidence above, inflow is your paycheck being posted and outflow could be, again, due to main reasons: expenses or investments. As such, a labeled Figure 1 would look like (Figure 3):

Figure 3.

Given that expenses strike the day of, if not the very day after, your paycheck, the duration in your account is really short. In individual bank accounts for the average person, dollar prevalence would approximate dollar incidence at that point in time.

Is it true that "it doesn't matter how fast color travels it is how fast you can see it"? I am not sure about the source of this saying, but green I think is very fast.