Universal Statistics of Incubation Periods and Other Detection Times via Diffusion Models

Research output: Contribution to journalArticlepeer-review


We suggest an explanation of typical incubation times statistical features based on the universal behavior of exit times for diffusion models. We give a mathematically rigorous proof of the characteristic right skewness of the incubation time distribution for very general one-dimensional diffusion models. Imposing natural simple conditions on the drift coefficient, we also study these diffusion models under the assumption of noise smallness and show that the limiting exit time distributions in the limit of vanishing noise are Gaussian and Gumbel. Thus, they match the existing data as well as the other existing models do. The character of our models, however, allows us to argue that the features of the exit time distributions that we describe are universal and manifest themselves in various other situations where the times involved can be described as detection or halting times, for example response times studied in psychology.

Original languageEnglish (US)
Pages (from-to)1070-1088
Number of pages19
JournalBulletin of Mathematical Biology
Issue number4
StatePublished - Apr 15 2019


  • Conditional exit times
  • Cumulants
  • Diffusion
  • First passage times
  • Gumbel distribution
  • Incubation periods
  • Right skew

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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