Reproduction numbers for discrete-time epidemic models with arbitrary stage distributions

Abstract

Using an approach similar to that for continuous-time models, derivations of and for discrete-time epidemic models with arbitrary stage distribution are presented, and the formulas are shown to be consistent with those obtained from biological considerations. Both models with specific distributions for the infectious stage and models with an arbitrarily distributed (bounded) infectious stage are considered. Results show that the formulas for and can be expressed in terms of disease transmission rates and the means of stage distributions. Examples of Susceptible-Exposed-Infected-Recovered models as well as a model with disease control (e.g. isolation or hospitalization) are presented.

Keywords:

• reproduction number
• discrete-time model
• epidemics
• arbitrarily distributed stage durations

2000 Mathematics Subject Classification::

• 92D30
• 39A60
• 39A30

Acknowledgements

We thank the reviewers for their comments and suggestions that helped improve this paper. This research is supported in part by the NSF Grant DMS-1022758 to ZF, Mprime and an NSERC Discovery grant to PvdD.

Notes

1. [email protected]

2. [email protected]

Additional information

Notes on contributors

Nancy Hernández-Cerón

1

P. van den Driessche

2