On the quasi-stationary distribution of the stochastic logistic epidemic
An approximation is derived for the quasi-stationary distribution of the stochastic logistic epidemic in the intricate case where the transmission factor R 0 lies in the transition region near the deterministic threshold value 1. An approximation for the expected time to extinction from quasi-statio...
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| Published in | Mathematical biosciences Vol. 156; no. 1; pp. 21 - 40 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
United States
Elsevier Inc
01.03.1999
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| Abstract | An approximation is derived for the quasi-stationary distribution of the stochastic logistic epidemic in the intricate case where the transmission factor
R
0 lies in the transition region near the deterministic threshold value 1. An approximation for the expected time to extinction from quasi-stationarity in the same parameter region is also given.
Mathematics subject classification: 60J27; 92D30 |
|---|---|
| AbstractList | An approximation is derived for the quasi-stationary distribution of the stochastic logistic epidemic in the intricate case where the transmission factor
R
0 lies in the transition region near the deterministic threshold value 1. An approximation for the expected time to extinction from quasi-stationarity in the same parameter region is also given.
Mathematics subject classification: 60J27; 92D30 An approximation is derived for the quasi-stationary distribution of the stochastic logistic epidemic in the intricate case where the transmission factor R0 lies in the transition region near the deterministic threshold value 1. An approximation for the expected time to extinction from quasi-stationarity in the same parameter region is also given.An approximation is derived for the quasi-stationary distribution of the stochastic logistic epidemic in the intricate case where the transmission factor R0 lies in the transition region near the deterministic threshold value 1. An approximation for the expected time to extinction from quasi-stationarity in the same parameter region is also given. An approximation is derived for the quasi-stationary distribution of the stochastic logistic epidemic in the intricate case where the transmission factor R0 lies in the transition region near the deterministic threshold value 1. An approximation for the expected time to extinction from quasi-stationarity in the same parameter region is also given. |
| Author | Nåsell, Ingemar |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/10204386$$D View this record in MEDLINE/PubMed |
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| Keywords | Transition region Quasi-stationary distribution Asymptotic approximation SIS model Time to extinction |
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| References | I. Nåsell, On the time to extinction in recurrent epidemics, to appear in J. Roy. Stat. Soc., Series B Nåsell (BIB2) 1996; 28 Bartholomew (BIB4) 1976; 4 Weiss, Dishon (BIB3) 1971; 11 Jacquez, Simon (BIB9) 1993; 117 Norden (BIB7) 1982; 14 I. Nåsell, The threshold concept in stochastic epidemic and endemic models. in: D. Mollison (Ed.), Epidemic Models: Their Structure and Relation to Data, Cambridge University, Cambridge, 1995 Kryscio, Lefèvre (BIB8) 1989; 26 Oppenheim, Shuler, Weiss (BIB5) 1977; 88 Cavender (BIB6) 1978; 10 R. Ross, The Prevention of Malaria, 2nd ed., John Murray, London, 1911 M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965 Andersson, Djehiche (BIB10) 1998; 35 Oppenheim (10.1016/S0025-5564(98)10059-7_BIB5) 1977; 88 10.1016/S0025-5564(98)10059-7_BIB1 Cavender (10.1016/S0025-5564(98)10059-7_BIB6) 1978; 10 Nåsell (10.1016/S0025-5564(98)10059-7_BIB2) 1996; 28 Andersson (10.1016/S0025-5564(98)10059-7_BIB10) 1998; 35 Weiss (10.1016/S0025-5564(98)10059-7_BIB3) 1971; 11 Jacquez (10.1016/S0025-5564(98)10059-7_BIB9) 1993; 117 Bartholomew (10.1016/S0025-5564(98)10059-7_BIB4) 1976; 4 Kryscio (10.1016/S0025-5564(98)10059-7_BIB8) 1989; 26 10.1016/S0025-5564(98)10059-7_BIB13 Norden (10.1016/S0025-5564(98)10059-7_BIB7) 1982; 14 10.1016/S0025-5564(98)10059-7_BIB12 10.1016/S0025-5564(98)10059-7_BIB11 |
| References_xml | – volume: 4 start-page: 187 year: 1976 ident: BIB4 article-title: Continuous time diffusion models with random duration of interest publication-title: J. Math. Sociol. – volume: 88 start-page: 191 year: 1977 ident: BIB5 article-title: Stochastic theory of nonlinear rate processes with multiple stationary states publication-title: Physica A – reference: I. Nåsell, On the time to extinction in recurrent epidemics, to appear in J. Roy. Stat. Soc., Series B – volume: 14 start-page: 687 year: 1982 ident: BIB7 article-title: On the distribution of the time to extinction in the stochastic logistic population model publication-title: Adv. Appl. Prob. – volume: 26 start-page: 685 year: 1989 ident: BIB8 article-title: On the extinction of the S–I–S stochastic logistic epidemic publication-title: J. Appl. Prob. – reference: I. Nåsell, The threshold concept in stochastic epidemic and endemic models. in: D. Mollison (Ed.), Epidemic Models: Their Structure and Relation to Data, Cambridge University, Cambridge, 1995 – volume: 35 start-page: 662 year: 1998 ident: BIB10 article-title: A threshold limit theorem for the stochastic logistic epidemic publication-title: J. Appl. Prob. – volume: 11 start-page: 261 year: 1971 ident: BIB3 article-title: On the asymptotic behavior of the stochastic and deterministic models of an epidemic publication-title: Math. Biosci. – volume: 10 start-page: 570 year: 1978 ident: BIB6 article-title: Quasi-stationary distributions of birth-and-death processes publication-title: Adv. Appl. Prob. – reference: M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965 – volume: 117 start-page: 77 year: 1993 ident: BIB9 article-title: The stochastic SI model with recruitment and deaths. I. Comparisons with the closed SIS model publication-title: Math. Biosci. – volume: 28 start-page: 895 year: 1996 ident: BIB2 article-title: The quasi-stationary distribution of the closed endemic SIS model publication-title: Adv. Appl. Prob. – reference: R. Ross, The Prevention of Malaria, 2nd ed., John Murray, London, 1911 – volume: 10 start-page: 570 year: 1978 ident: 10.1016/S0025-5564(98)10059-7_BIB6 article-title: Quasi-stationary distributions of birth-and-death processes publication-title: Adv. Appl. Prob. doi: 10.2307/1426635 – volume: 26 start-page: 685 year: 1989 ident: 10.1016/S0025-5564(98)10059-7_BIB8 article-title: On the extinction of the S–I–S stochastic logistic epidemic publication-title: J. Appl. Prob. doi: 10.2307/3214374 – volume: 11 start-page: 261 year: 1971 ident: 10.1016/S0025-5564(98)10059-7_BIB3 article-title: On the asymptotic behavior of the stochastic and deterministic models of an epidemic publication-title: Math. Biosci. doi: 10.1016/0025-5564(71)90087-3 – ident: 10.1016/S0025-5564(98)10059-7_BIB1 – volume: 35 start-page: 662 year: 1998 ident: 10.1016/S0025-5564(98)10059-7_BIB10 article-title: A threshold limit theorem for the stochastic logistic epidemic publication-title: J. Appl. Prob. doi: 10.1239/jap/1032265214 – volume: 88 start-page: 191 year: 1977 ident: 10.1016/S0025-5564(98)10059-7_BIB5 article-title: Stochastic theory of nonlinear rate processes with multiple stationary states publication-title: Physica A doi: 10.1016/0378-4371(77)90001-2 – volume: 117 start-page: 77 year: 1993 ident: 10.1016/S0025-5564(98)10059-7_BIB9 article-title: The stochastic SI model with recruitment and deaths. I. Comparisons with the closed SIS model publication-title: Math. Biosci. doi: 10.1016/0025-5564(93)90018-6 – ident: 10.1016/S0025-5564(98)10059-7_BIB13 – volume: 28 start-page: 895 year: 1996 ident: 10.1016/S0025-5564(98)10059-7_BIB2 article-title: The quasi-stationary distribution of the closed endemic SIS model publication-title: Adv. Appl. Prob. doi: 10.2307/1428186 – volume: 4 start-page: 187 year: 1976 ident: 10.1016/S0025-5564(98)10059-7_BIB4 article-title: Continuous time diffusion models with random duration of interest publication-title: J. Math. Sociol. doi: 10.1080/0022250X.1976.9989853 – volume: 14 start-page: 687 year: 1982 ident: 10.1016/S0025-5564(98)10059-7_BIB7 article-title: On the distribution of the time to extinction in the stochastic logistic population model publication-title: Adv. Appl. Prob. doi: 10.2307/1427019 – ident: 10.1016/S0025-5564(98)10059-7_BIB11 – ident: 10.1016/S0025-5564(98)10059-7_BIB12 |
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| Snippet | An approximation is derived for the quasi-stationary distribution of the stochastic logistic epidemic in the intricate case where the transmission factor
R
0... An approximation is derived for the quasi-stationary distribution of the stochastic logistic epidemic in the intricate case where the transmission factor R0... |
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| SubjectTerms | Asymptotic approximation Endemic Diseases Epidemiology Humans Logistic Models Models, Biological Quasi-stationary distribution SIS model Stochastic Processes Time to extinction Transition region |
| Title | On the quasi-stationary distribution of the stochastic logistic epidemic |
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