Lecture
Lab instructions and code
Lab solutions are available here. Feel free to reference these as you work, but also code it up yourself! (Even just copy-pasting chunks of code is good—it might seem silly, but it’s a good first step to learning how things work!)
Input-output equation solutions for the SIR model (pdf from Mathematica)
Fisher information matrix calculation code: MATLAB version, R version
Profile likelihood code: MATLAB version, R version
Lab datasets
SIR model data set: MATLAB version, R version
Cholera data set (Angola, 2006): MATLAB version, R version
Additional useful references
Raue, Andreas, et al. “Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood.” Bioinformatics 25.15 (2009): 1923-1929.
Meshkat, Nicolette, Christine Er-zhen Kuo, and Joseph DiStefano III. “On finding and using identifiable parameter combinations in nonlinear dynamic systems biology models and COMBOS: a novel web implementation.” PLoS One 9.10 (2014): e110261.
Meshkat, Nicolette, and Seth Sullivant. “Identifiable reparametrizations of linear compartment models.” Journal of Symbolic Computation 63 (2014): 46-67.
Constantine, Paul G. Active subspaces: Emerging ideas for dimension reduction in parameter studies. Vol. 2. SIAM, 2015.
Smith, Ralph C. Uncertainty quantification: theory, implementation, and applications. Vol. 12. Siam, 2013.
Stuff from our group:
For more information about the cholera example: Eisenberg MC, Robertson SL, Tien JH. 2013. Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease. J. Theor. Biol. 324: 84-102.
Brouwer, Andrew F., and Marisa C. Eisenberg. “The underlying connections between identifiability, active subspaces, and parameter space dimension reduction.” arXiv preprint arXiv:1802.05641 (2018).
Eisenberg, Marisa C., and Harsh V. Jain. “A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study.” Journal of theoretical biology 431 (2017): 63-78.
Eisenberg, Marisa C., and Michael AL Hayashi. “Determining identifiable parameter combinations using subset profiling.” Mathematical biosciences 256 (2014): 116-126.