Characterising model dynamics using sparse grid interpolation: Parameter estimation of cholera

References

• O. Akman and E. Schaefer, An evolutionary computing approach for parameter estimation investigation of a model for cholera, J. Biol. Dyn 9 (2015), pp. 147–158.
   Google Scholar
• V. Barthelmann, E. Novak, and K. Ritter, High dimensional polynomial interpolation on sparse grids, Adv. Comput. Math. 12 (2000), pp. 273–288.
   Google Scholar
• J.N. Bazil, G.T. Buzzard, and A.E. Rundell, A global parallel model based design of experiments method to minimize model output uncertainty, Bull. math. biol. 74 (2012), pp. 688–716.
   Google Scholar
• L.M.A. Bettencourt and R.M. Ribeiro, Real time bayesian estimation of the epidemic potential of emerging infectious diseases, PLoS ONE 3 (2008). pp. e2185.
   Google Scholar
• H.J. Bungartz and M. Griebel, Sparse grids, Acta Numer. 13 (2004), pp. 147–269.
   Google Scholar
• A. Camacho, M. Bouhenia, R. Alyusfi, A. Alkohlani, M.A.M. Naji, X. de Radiguès, A.M. Abubakar, A. Almoalmi, C. Seguin, M.J. Sagrado, M. Poncin, M. McRae, M. Musoke, A. Rakesh, K. Porten, C. Haskew, K.E. Atkins, R.M. Eggo, A.S. Azman, M. Broekhuijsen, M.A. Saatcioglu, L. Pezzoli, M.L. Quilici, A.R. Al-Mesbahy, N. Zagaria, and F.J. Luquero, Cholera epidemic in Yemen, 2016–18: An analysis of surveillance data, Lancet Glob. Health 6 (2018), pp. e680–e690.
   Google Scholar
• G. Chowell, Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts, Infect. Dis. Model. 2 (2017), pp. 379–398.
   Google Scholar
• C.T. Codeço, Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir, BMC Infect. Dis. 1 (2001), pp. 209.
   Google Scholar
• F.C. Coelho, C.T. Codeço, and M.G.M. Gomes, A Bayesian framework for parameter estimation in dynamical models, PLoS ONE 6 (2011), pp. 1–6.
   Google Scholar
• M.M. Donahue and G.T. Buzzard, Parameter identification with adaptive sparse grid-based optimization for models of cellular processes, Methods Bioeng. (2009), pp. 1–32.
   Google Scholar
• M.M. Donahue, G.T. Buzzard, and A.E. Rundell, Robust parameter identification with adaptive sparse grid-based optimization for nonlinear systems biology models, in 2009 American Control Conference, St. Louis, MI, USA. IEEE, 2009, pp. 5055–5060.
   Google Scholar
• I.C.H. Fung, Cholera transmission dynamic models for public health practitioners, Emerg. Themes Epidemiol. 11 (2014), pp. 1–11.
   Google Scholar
• T. Gerstner and M. Griebel, Numerical integration using sparse grids, Numer. Algorithms 18 (1998), pp. 209–232.
   Google Scholar
• T. Gerstner and M. Griebel, Dimension-adaptive tensor-product quadrature, Computing 71 (2003), pp. 65–87.
   Google Scholar
• T. Gerstner and M. Griebel, Sparse grids, in Encyclopedia of Quantitative Finance, Vol. 13, John Wiley & Sons, Ltd, Chichester, UK, 2010, pp. 147–269.
   Google Scholar
• Y.H. Grad, J.C. Miller, and M. Lipsitch, Cholera Modeling, Epidemiology 23 (2012), pp. 523–530.
   Google Scholar
• D. He, X. Wang, D. Gao, and J. Wang, Modeling the 2016-2017 Yemen cholera outbreak with the impact of limited medical resources, J. Theor. Biol. 451 (2018), pp. 80–85.
   Google Scholar
• L. Held, Bayesian Methods in Epidemiology, in Handbook of Epidemiology, Springer New York, New York, NY, 2014, pp. 1161–1193.
   Google Scholar
• G. Katriel, R. Yaari, A. Huppert, U. Roll, and L. Stone, Modelling the initial phase of an epidemic using incidence and infection network data: 2009 H1N1 pandemic in Israel as a case study, J. R. Soc. Interface 8 (2011), pp. 856–867.
   Google Scholar
• A. Klimke, Sparse grid interpolation toolbox user's guide, Tech. Rep., 2008.
   Google Scholar
• A. Klimke and B. Wohlmuth, Algorithm 847: spinterp: Piecewise multilinear hierarchical sparse grid interpolation in MATLAB, ACM Trans. Math. Softw. 31 (2005), pp. 561–579.
   Google Scholar
• J.C. Lagarias, J.A. Reeds, M.H. Wright, and P.E. Wright, Convergence properties of the nelder–mead simplex method in low dimensions, SIAM J. Optim. 9 (1998), pp. 112–147.
   Google Scholar
• E.C. Lee, M.R. Kelly, B.M. Ochocki, S.M. Akinwumi, K.E. Hamre, J.H. Tien, and M.C. Eisenberg, Model distinguishability and inference robustness in mechanisms of cholera transmission and loss of immunity, J. Theor. Biol. 420 (2017), pp. 68–81.
   Google Scholar
• T. Mdluli, G.T. Buzzard, and A.E. Rundell, Efficient optimization of stimuli for model-based design of experiments to resolve dynamical uncertainty, PLOS Comput. Biol. 11 (2015), pp. e1004488.
   Google Scholar
• C.G. Moles, P. Mendes, and J.R. Banga, Parameter estimation in biochemical pathways: A comparison of global optimization methods, Genome res. 13 (2003), pp. 2467–74.
   Google Scholar
• Z. Mukandavire, S. Liao, J. Wang, H. Gaff, D.L. Smith, and J.G. Morris, Estimating the reproductive numbers for the 2008–2009 cholera outbreaks in Zimbabwe, Proc. Natl. Acad. Sci. 108 (2011), pp. 8767–8772.
   Google Scholar
• J.A. Nelder and R. Mead, A simplex method for function minimization, Comput. J. 7 (1965), pp. 308–313.
   Google Scholar
• H. Nishiura, S. Tsuzuki, and Y. Asai, Forecasting the size and peak of cholera epidemic in Yemen, 2017, Future Microbiol. 13 (2018), pp. 399–402.
   Google Scholar
• H. Nishiura, S. Tsuzuki, B. Yuan, T. Yamaguchi, and Y. Asai, Transmission dynamics of cholera in Yemen, 2017: A real time forecasting, Theor. Biol. Med. Model. 14 (2017), pp. 1316.
   Google Scholar
• A. Rinnooy Kan and G. Timmer, Stochastic global optimization methods part i: Clustering methods, Math. Programming 39 (1987), pp. 27–56.
   Google Scholar
• A. Smirnova and G. Chowell, A primer on stable parameter estimation and forecasting in epidemiology by a problem-oriented regularized least squares algorithm, Infect. Dis. Model. 2 (2017), pp. 268–275.
   Google Scholar
• S. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Sov. Math., Dokl. 4 (1963), pp. 240–243.
   Google Scholar
• J. Sun, J.M. Garibaldi, and C. Hodgman, Parameter estimation using meta-heuristics in systems biology: A comprehensive review, IEEE/ACM Trans. Comput. biol. bioinformatics/IEEE, ACM 9 (2012), pp. 185–202.
   Google Scholar
• L.F. White and M. Pagano, Transmissibility of the influenza virus in the 1918 pandemic, PLoS ONE3 (2008). pp. e1498
   Google Scholar
• L.F. White, J. Wallinga, L. Finelli, C. Reed, S. Riley, M. Lipsitch, and M. Pagano, Estimation of the reproductive number and the serial interval in early phase of the 2009 influenza A/H1N1 pandemic in the USA, Influenza Respir. Viruses 3 (2009), pp. 267–276.
   Google Scholar
• WHO, Situation report no. 40 - Yemen conflict, Tech. Rep. 40, 2017.
   Google Scholar
• WHO, Weekly Epidemiological Bulletin - W52 2017 (Dec 25 - Dec 31), Tech. Rep., 2017.
   Google Scholar
• R. Yaari, G. Katriel, L. Stone, E. Mendelson, M. Mandelboim, and A. Huppert, Model-based reconstruction of an epidemic using multiple datasets: Understanding influenza A/H1N1 pandemic dynamics in Israel, J. R. Soc. Interface 13 (2016), pp. 20160099.
   Google Scholar
• H. Yserentant, Sparse grids, adaptivity, and symmetry, Computing (Vienna/New York) 78 (2006), pp. 195–209.
   Google Scholar