Structured parametric epidemic models

Abstract

A stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individuals in independent stages is formulated. In this analysis, an input interpreted as a birth function is considered. The structural identifiability is studied using the Markov parameters. Then, the unknown parameters are uniquely determined by the output structure corresponding to an observation of infection. Two different birth functions are considered: the linear case and the Beverton–Holt type to analyse the structured epidemic model. Some conditions on the parameters to obtain non-zero disease-free equilibrium points are given. The identifiability of the parameters allows us to determine uniquely the basic reproduction number ℛ₀ and the stability of the model in the equilibrium is studied using ℛ₀ in terms of the model parameters.

Keywords:

• epidemic model
• identifiability
• basic reproduction number
• Beverton–Holt function
• equilibrium

2010 AMS Subject Classifications:

• 93XX
• 93A30
• 93EXX

Acknowledgements

This work has been partially supported by MTM2010-18228. The authors wish to express their thanks to the reviewers for helpful comments and suggestions.