### Abstract

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 language | English (US) |
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Journal | Bulletin of Mathematical Biology |

DOIs | |

State | Accepted/In press - Jan 1 2018 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Neuroscience(all)
- Immunology
- Mathematics(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Environmental Science(all)
- Pharmacology
- Agricultural and Biological Sciences(all)
- Computational Theory and Mathematics

### Cite this

**Universal Statistics of Incubation Periods and Other Detection Times via Diffusion Models.** / Bakhtin, Yuri.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Universal Statistics of Incubation Periods and Other Detection Times via Diffusion Models

AU - Bakhtin, Yuri

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Conditional exit times

KW - Cumulants

KW - Diffusion

KW - First passage times

KW - Gumbel distribution

KW - Incubation periods

KW - Right skew

UR - http://www.scopus.com/inward/record.url?scp=85058780023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85058780023&partnerID=8YFLogxK

U2 - 10.1007/s11538-018-00558-w

DO - 10.1007/s11538-018-00558-w

M3 - Article

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

ER -