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I am trying to understand a formula in this paper (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5444538/#:~:text=Low%20Risk%20of%20International%20Zika,the%202016%20Olympics%20in%20Brazil). In the legend of the Figure, there is a formula:

"probability of an individual becoming infected over t days" = 1 - e^((-λ)(t/365))

In which λ is the incidence rate. However, the authors of this paper didn't mention or reference how this equation came about. Can someone help guide me in interpreting the rationale behind this?

I am able to rearrange the formula by isolating the λ (or incidence rate) term.

λ = -ln(1-(probability of an individual becoming infected over t days)/(t/365)

Does -ln(1-(probability of an individual becoming infected over t days) refers to incident cases observed over t days? If so, why?

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