Mathematical Biosciences and Engineering (MBE)

On the usefulness of set-membership estimation in the epidemiology of infectious diseases
Pages: 141 - 152, Issue 1, February 2018

doi:10.3934/mbe.2018006      Abstract        References        Full text (414.1K)           Related Articles

Andreas Widder - ORCOS, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria (email)

1 C. L. Althaus, Estimating the reproduction number of Ebola virus (EBOV) during the 2014 outbreak in West Africa, PLOS Currents Outbreaks, (2014).
2 C. L. Althaus, N. Low, E. O. Musa, F. Shuaib and S. Gsteiger, Ebola virus disease outbreak in Nigeria: Transmission dynamics and rapid control, Epidemics, 11 (2015), 80-84.
3 H. Andersson and T. Britton, Stochastic Epidemic Models and Their Statistical Analysis, Lecture Notes in Statistics, 151. Springer-Verlag, New York, 2000.       
4 R. Baier and M. Gerdts, A computational method for non-convex reachable sets using optimal control, in 2009 European Control Conference (ECC), IEEE, 2009, 97-102.
5 D. P. Bertsekas, Dynamic Programming and Optimal Control, Athena Scientific, 1995.
6 A. Bhargava and F. Docquier, HIV pandemic, medical brain drain, and economic development in Sub-Saharan Africa, The World Bank Economic Review, 22 (2008), 345-366.
7 A. Blake, M. T. Sinclair and G. Sugiyarto, Quantifying the impact of foot and mouth disease on tourism and the UK economy, Tourism Economics, 9 (2003), 449-465.
8 A. Capaldi, S. Behrend, B. Berman, J. Smith, J. Wright and A. L. Lloyd, Parameter estimation and uncertainty quantication for an epidemic model, Mathematical Biosciences and Engineering, 9 (2012), 553-576.       
9 O. Diekmann, H. Heesterbeek and T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics, Princeton University Press, 2013.       
10 J. Hsu, Multiple Comparisons: Theory and Methods, CRC Press, 1996.       
11 M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals, Princeton University Press, 2008.       
12 A. B. Kurzhanski and P. Varaiya, Dynamics and Control of Trajectory Tubes, Springer, 2014.       
13 P. E. Lekone and B. F. Finkenst├Ądt, Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study, Biometrics, 62 (2006), 1170-1177.       
14 N.-A. M. Molinari, I. R. Ortega-Sanchez, M. L. Messonnier, W. W. Thompson, P. M. Wortley, E. Weintraub and C. B. Bridges, The annual impact of seasonal influenza in the US: Measuring disease burden and costs, Vaccine, 25 (2007), 5086-5096.
15 E. Polak, Computational Methods in Optimization: A Unified Approach, vol. 77, Academic Press, New York-London, 1971.       
16 E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, Second edition. Texts in Applied Mathematics, 6. Springer-Verlag, New York, 1998.       
17 M. R. Thomas, G. Smith, F. H. Ferreira, D. Evans, M. Maliszewska, M. Cruz, K. Himelein and M. Over, The economic impact of Ebola on Sub-Saharan Africa: Updated estimates for 2015, World Bank Group.
18 T. Toni, D. Welch, N. Strelkowa, A. Ipsen and M. P. Stumpf, Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems, Journal of the Royal Society Interface, 6 (2009), 187-202.
19 T. Tsachev, V. M. Veliov and A. Widder, Set-membership estimation for the evolution of infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 74 (2017), 1081-1106.       
20 V. Veliov and A. Widder, Modelling and estimation of infectious diseases in a population with heterogeneous dynamic immunity, Journal of Biological Dynamics, 10 (2016), 457-476.       
21 A. Widder, Matlab files for set-membership estimation, Zenodo, 2016.

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