Bulletin of Mathematical Biology

, Volume 40, Issue 4, pp 483–498 | Cite as

A stochastic approach to predator-prey models

  • Stephen C. Smeach
  • Albert Rust


A deterministic investigation of a linear differential equation system which describes predator vs prey behavior as a function of equilibrium densities and reproductive rates is given. A more realistic structure of this model in a stochastic framework is presented. The reproductive rates and initial population sizes are considered to be random variables and their probabilistic behavior characterized by various joint probability distributions. The deterministic behaviors of the prey and predator species as functions of time are compared with the mean behaviors in the stochastic model.


Stochastic Differential Equation Deterministic Model Reproductive Rate Stochastic Approach Joint Probability Density Function 
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  1. Bellman, R. E. and R. E. Kalaba. 1965.Quasilinearitation and Nonlinear Boundary-Value Problem. New York: Elsevier.Google Scholar
  2. Brauer, F. and J. A. Nohel. 1969.Qualitative Theory of Ordinary Differential Equation. New York: W. A. Benjamin, Inc.Google Scholar
  3. May, R. M. 1973.Stability and Complexity in Model Ecosystems. Princeton: Princeton University Press.Google Scholar
  4. Smith, J. M. 1968.Mathematical Ideas in Biology. London: Cambridge University Press.Google Scholar
  5. — 1974.Models in Ecology. London: Cambridge University Press.Google Scholar
  6. Soong, T. T. 1971. “Pharmacokinetics with Uncertainties in Rate Constants.”Math. Biosci.,12, 235–243.CrossRefGoogle Scholar
  7. — 1973.Random Differential Equations in Science and Engineering. New York: Academic Press.Google Scholar

Copyright information

© Society for Mathematical Biology 1978

Authors and Affiliations

  • Stephen C. Smeach
    • 1
  • Albert Rust
    • 1
  1. 1.Department of MathematicsUniversity of South FloridaTampaU.S.A.

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