A Lie algebra approach to susceptible-infected-susceptible epidemics
The susceptible-infected-susceptible (SIS) epidemic model can be represented by a continuous-time Markov chain, which is governed by a set of deterministic differential equations (Kolmogorov forward equations). In this paper, a Lie algebra approach is applied to solve an SIS model where infectio...
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| Format: | Article |
| Language: | English |
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Texas State University
2012-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/233/abstr.html |
| _version_ | 1811309712101081088 |
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| author | Yilun Shang |
| author_facet | Yilun Shang |
| author_sort | Yilun Shang |
| collection | DOAJ |
| description | The susceptible-infected-susceptible (SIS) epidemic model can be represented by a continuous-time Markov chain, which is governed by a set of deterministic differential equations (Kolmogorov forward equations). In this paper, a Lie algebra approach is applied to solve an SIS model where infection rate and recovery rate are time-varying. The method presented here has been used widely in chemical and physical sciences but not in epidemic applications due to insufficient symmetries. |
| first_indexed | 2024-04-13T09:46:13Z |
| format | Article |
| id | doaj.art-f6eeaf17b2884810b28807412fe72934 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-13T09:46:13Z |
| publishDate | 2012-12-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-f6eeaf17b2884810b28807412fe729342022-12-22T02:51:45ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-12-012012233,17A Lie algebra approach to susceptible-infected-susceptible epidemicsYilun ShangThe susceptible-infected-susceptible (SIS) epidemic model can be represented by a continuous-time Markov chain, which is governed by a set of deterministic differential equations (Kolmogorov forward equations). In this paper, a Lie algebra approach is applied to solve an SIS model where infection rate and recovery rate are time-varying. The method presented here has been used widely in chemical and physical sciences but not in epidemic applications due to insufficient symmetries.http://ejde.math.txstate.edu/Volumes/2012/233/abstr.htmlEpidemic dynamicsLie algebraRiccati equationsusceptible-infected-susceptible |
| spellingShingle | Yilun Shang A Lie algebra approach to susceptible-infected-susceptible epidemics Electronic Journal of Differential Equations Epidemic dynamics Lie algebra Riccati equation susceptible-infected-susceptible |
| title | A Lie algebra approach to susceptible-infected-susceptible epidemics |
| title_full | A Lie algebra approach to susceptible-infected-susceptible epidemics |
| title_fullStr | A Lie algebra approach to susceptible-infected-susceptible epidemics |
| title_full_unstemmed | A Lie algebra approach to susceptible-infected-susceptible epidemics |
| title_short | A Lie algebra approach to susceptible-infected-susceptible epidemics |
| title_sort | lie algebra approach to susceptible infected susceptible epidemics |
| topic | Epidemic dynamics Lie algebra Riccati equation susceptible-infected-susceptible |
| url | http://ejde.math.txstate.edu/Volumes/2012/233/abstr.html |
| work_keys_str_mv | AT yilunshang aliealgebraapproachtosusceptibleinfectedsusceptibleepidemics AT yilunshang liealgebraapproachtosusceptibleinfectedsusceptibleepidemics |