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)
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.