Structured parametric epidemic models |
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| Authors: | B Cantó C Coll E Sánchez |
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| Affiliation: | 1. Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, 14. 46022 Valencia, Spainbcanto@mat.upv.es;3. Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, 14. 46022 Valencia, Spain |
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| 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 ?0 and the stability of the model in the equilibrium is studied using ?0 in terms of the model parameters. |
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| Keywords: | epidemic model identifiability basic reproduction number Beverton–Holt function equilibrium |
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