Open AccessStability and estimation problems related to a stage-structured epidemic model
Author(s) -
M. L. Diouf,
Abderrahman Iggidr,
Max O. Souza
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019220
Subject(s) - observability , observer (physics) , estimator , kalman filter , stability (learning theory) , epidemic model , mathematics , stage (stratigraphy) , class (philosophy) , estimation , covariate , econometrics , exponential stability , control theory (sociology) , computer science , statistics , artificial intelligence , medicine , population , control (management) , biology , engineering , paleontology , physics , environmental health , systems engineering , quantum mechanics , nonlinear system , machine learning
In this work, we consider a class of stage-structured Susceptible-Infectious (SI) epidemic models which includes, as special cases, a number of models already studied in the literature. This class allows for n different stages of infectious individuals, with all of them being able to infect susceptible individuals, and also allowing for different death rates for each stage-this helps to model disease induced mortality at all stages. Models in this class can be considered as a simplified modelling approach to chronic diseases with progressive severity, as is the case with AIDS for instance. In contradistinction to most studies in the literature, we consider not only the questions of local and global stability, but also the observability problem. For models in this class, we are able to construct two different state-estimators: the first one being the classical high-gain observer, and the second one being the extended Kalman filter. Numerical simulations indicate that both estimators converge exponentially fast, but the former can have large overshooting, which is not present in the latter. The Kalman observer turns out to be more robust to noise in measurable data.