Author's Hypothesis: 2
If the long-term immune-amnesia predicted by the authors is true, there should be a measurable difference, detectable in the population-level data, to prove this hypothesis. The authors' will show this by accounting for the length of time that the immune system remains impaired due to the immune-amnesia or immuno-modulation as they also refer to it. They suggest that this immuno-amnesia is like a measles "Shadow" that remains even after the measles epidemic has ended. At a population level, it can be accounted for as an accumulation of past measles cases or epidemics.
For example, if there is a very large amount of measles (a high incidence of measles) in year 1, and the immune-amnesia following measles lasts for 3 years, then for up to three years after this large measles epidemic there might be a noticeable increase in other infectious diseases due to the impaired immune resistance from the immune-amnesia.
So, if the amnesia lasts for 3 years, then during year 2, for example, the amount of other infectious diseases during that year will be proportional not only to the amount of measles that happened during year 2, but rather to the amount of measles that happened during both years 1 and 2. Similarly, during year three, the amount of non-measles infections will be a reflection of the amount of measles that happened in that year, year 3, as well as years 2 and 1. However, because we said that the immune-amnesia in this example lasts for 3 years only, then if we look at the amount of non-measles infections in year 4, it will be a reflection of the amount of measles that happened in that year, year 4, plus year 3 and year 2. It will not however reflect the large measles epidemic that happened in year 1 anymore, because those children would no longer have immune amnesia by year 4.