Interval observer for SIR epidemic model subject to uncertain seasonality

The issue of state estimation is considered for a SIR model with seasonal variations and uncertainties in the transmission rate. Assuming continuous measurement of the number of new infectives per unit time, a class of interval observers with estimate-dependent gain is constructed, and asymp-totic error bounds are provided. Mathematics Subject Classification (2000) Primary 92D30; Secondary 34C12, 93B07, 93D09, 93D30

[1]  V. Capasso.  Mathematical Structures of Epidemic Systems , 1993, Lecture Notes in Biomathematics.

[2]  C. Piccardi,et al.  Bifurcation analysis of periodic SEIR and SIR epidemic models , 1994, Journal of mathematical biology.

[3]  K. Dietz,et al.  The Incidence of Infectious Diseases under the Influence of Seasonal Fluctuations , 1976 .

[4]  M. Hirsch.  Stability and convergence in strongly monotone dynamical systems. , 1988 .

[5]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

[6]  A. Iggidr,et al.  On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients , 2014 .

[7]  Nacim Meslem,et al.  Interval Observers for Uncertain Nonlinear Systems. Application to bioreactors. , 2008 .

[8]  M. Keeling,et al.  Modeling Infectious Diseases in Humans and Animals , 2007 .

[9]  Jean-Luc Gouzé,et al.  Closed loop observers bundle for uncertain biotechnological models , 2004 .

[10]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[11]  R. Shorten,et al.  Quadratic and Copositive Lyapunov Functions and the Stability of Positive Switched Linear Systems , 2007, 2007 American Control Conference.

[12]  A. Iggidr,et al.  Observer design for a schistosomiasis model. , 2015, Mathematical biosciences.

[13]  Denis V. Efimov,et al.  Interval state observer for nonlinear time varying systems , 2013, Autom..

[14]  A. Berman.  CHAPTER 2 – NONNEGATIVE MATRICES , 1979 .