Predicting population extinction or disease outbreaks with stochastic models
Models of exponential growth, logistic growth and epidemics are common applications in undergraduate differential equation courses. The corresponding stochastic models are not part of these courses, although when population sizes are small their behaviour is often more realistic and distinctly diffe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Intercollegiate Biomathematics Alliance
2017-01-01
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| Series: | Letters in Biomathematics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/23737867.2016.1264870 |
| _version_ | 1818382878691557376 |
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| author | Linda J. S. Allen Sophia R. Jang Lih-Ing Roeger |
| author_facet | Linda J. S. Allen Sophia R. Jang Lih-Ing Roeger |
| author_sort | Linda J. S. Allen |
| collection | DOAJ |
| description | Models of exponential growth, logistic growth and epidemics are common applications in undergraduate differential equation courses. The corresponding stochastic models are not part of these courses, although when population sizes are small their behaviour is often more realistic and distinctly different from deterministic models. For example, the randomness associated with births and deaths may lead to population extinction even in an exponentially growing population. Some background in continuous-time Markov chains and applications to populations, epidemics and cancer are presented with a goal to introduce this topic into the undergraduate mathematics curriculum that will encourage further investigation into problems on conservation, infectious diseases and cancer therapy. MATLAB programs for graphing sample paths of stochastic models are provided in the Appendix. |
| first_indexed | 2024-12-14T02:57:28Z |
| format | Article |
| id | doaj.art-dc780d93d98144a694af5d3769e7f8b5 |
| institution | Directory Open Access Journal |
| issn | 2373-7867 |
| language | English |
| last_indexed | 2024-12-14T02:57:28Z |
| publishDate | 2017-01-01 |
| publisher | Intercollegiate Biomathematics Alliance |
| record_format | Article |
| series | Letters in Biomathematics |
| spelling | doaj.art-dc780d93d98144a694af5d3769e7f8b52022-12-21T23:19:36ZengIntercollegiate Biomathematics AllianceLetters in Biomathematics2373-78672017-01-014112210.1080/23737867.2016.12648701264870Predicting population extinction or disease outbreaks with stochastic modelsLinda J. S. Allen0Sophia R. Jang1Lih-Ing Roeger2Texas Tech UniversityTexas Tech UniversityTexas Tech UniversityModels of exponential growth, logistic growth and epidemics are common applications in undergraduate differential equation courses. The corresponding stochastic models are not part of these courses, although when population sizes are small their behaviour is often more realistic and distinctly different from deterministic models. For example, the randomness associated with births and deaths may lead to population extinction even in an exponentially growing population. Some background in continuous-time Markov chains and applications to populations, epidemics and cancer are presented with a goal to introduce this topic into the undergraduate mathematics curriculum that will encourage further investigation into problems on conservation, infectious diseases and cancer therapy. MATLAB programs for graphing sample paths of stochastic models are provided in the Appendix.http://dx.doi.org/10.1080/23737867.2016.1264870Exponential growthlogistic growthcontinuous-time Markov chainSIR epidemicstochastic process |
| spellingShingle | Linda J. S. Allen Sophia R. Jang Lih-Ing Roeger Predicting population extinction or disease outbreaks with stochastic models Letters in Biomathematics Exponential growth logistic growth continuous-time Markov chain SIR epidemic stochastic process |
| title | Predicting population extinction or disease outbreaks with stochastic models |
| title_full | Predicting population extinction or disease outbreaks with stochastic models |
| title_fullStr | Predicting population extinction or disease outbreaks with stochastic models |
| title_full_unstemmed | Predicting population extinction or disease outbreaks with stochastic models |
| title_short | Predicting population extinction or disease outbreaks with stochastic models |
| title_sort | predicting population extinction or disease outbreaks with stochastic models |
| topic | Exponential growth logistic growth continuous-time Markov chain SIR epidemic stochastic process |
| url | http://dx.doi.org/10.1080/23737867.2016.1264870 |
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