Modeling and Numerical Considerations
  • J. Arino
  • P. van den Driessche
Part of the NATO Science Series book series (NAII, volume 205)


Continuous time deterministic epidemic models are traditionally formulated as systems of ordinary differential equations for the numbers of individuals in various disease states, with the sojourn time in a state being exponentially distributed. Time delays are introduced to model constant sojourn times in a state, for example, the infective or immune state. Models then become delay-differential and/or integral equations. For a review of some epidemic models with delay see van den Driessche [228]. More generally, an arbitrarily distributed sojourn time in a state, for example, the infective or immune state, is used by some authors (see [69] and the references therein).


Periodic Solution Hopf Bifurcation Sojourn Time Epidemic Model Delay Differential Equation 
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Copyright information

© Springer 2006

Authors and Affiliations

  • J. Arino
    • 1
  • P. van den Driessche
    • 2
  1. 1.Department of MathematicsUniversity of ManitobaWinnipegCanada
  2. 2.Department of Mathematics and StatisticsUniversity of Victoria BCCanada

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