On the Duration of an Epidemic

A stochastic SIR (Susceptible, Infected, Recovered) model for the spread of a non-lethal disease is considered. The size of the population is constant. The problem of computing the moment-generating function of the random time until all members of the population are recovered is solved in special ca...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 32; no. 4; pp. 1241 - 1251
Main Author Lefebvre, Mario
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.10.2024
Springer Nature B.V
Subjects
Boundary conditions
Computer Science
Engineering
Epidemics
Mathematics
Mathematics and Statistics
Original Research
Partial differential equations
Similarity solutions
Kolmogorov backward equation
Similarity solutions
Primary 60J70
Special functions
Secondary 92D30
Epidemiology
Online AccessGet full text
ISSN0971-3514
0974-6870
DOI10.1007/s12591-022-00626-7

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Summary:A stochastic SIR (Susceptible, Infected, Recovered) model for the spread of a non-lethal disease is considered. The size of the population is constant. The problem of computing the moment-generating function of the random time until all members of the population are recovered is solved in special cases. The expected duration of the epidemic is also computed, as well as the probability that the whole population will be either cured or immunized before every member is infected. The method of similarity solutions is used to solve the various Kolmogorov partial differential equations, subject to the appropriate boundary conditions.
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ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-022-00626-7