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- Title
Predicting population extinction or disease outbreaks with stochastic models.
- Authors
Allen, Linda J. S.; Jang, Sophia R.; Roeger, Lih-Ing
- Abstract
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.
- Subjects
BIOLOGICAL extinction; DISEASE outbreaks; CANCER treatment; STOCHASTIC analysis; MARKOV processes
- Publication
Letters in Biomathematics, 2017, Vol 4, Issue 1, p1
- ISSN
2373-7867
- Publication type
Article
- DOI
10.1080/23737867.2016.1264870