Predicting population extinction or disease outbreaks with stochastic models

  • Linda J. S. Allen Texas Tech University
  • Sophia R. Jang
  • Lih-Ing Roeger
Keywords: Exponential growth, logistic growth, continuous-time Markov chain, SIR epidemic, stochastic process

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.

Published
2017-01-01
How to Cite
Allen, Linda J. S., Sophia R. Jang, and Lih-Ing Roeger. 2017. “Predicting Population Extinction or Disease Outbreaks With Stochastic Models”. Letters in Biomathematics 4 (1), 1-22. https://doi.org/10.1080/23737867.2016.1264870.
Section
Education