Anderson DF, Mattingly JC (2007) Propagation of fluctuations in biochemical systems, II: nonlinear chains. IET Syst Biol 1(6):313–325
[DOI:
10.1049/iet-syb]
Anderson DF, Mattingly JC, Frederik Nijhout H, Reed MC (2007) Propagation of fluctuations in biochemical systems, I: Linear SSC networks. Bull Math Biol 69(6):1791–1813
[DOI:
10.1007/s11538-007-9192-2]
Bao J-D, Jia Y (2004) Determination of fission rate by mean last passage time. Phys Rev C 69(2):027602
[DOI:
10.1103/PhysRevC.69.027602]
Bena I (2006) Dichotomous markov noise: exact results for out-of-equilibrium systems. Int J Mod Phys B 20(20):2825–2888
[DOI:
10.1142/S0217979206034881]
Browning AP, Jenner AL, Baker RE, Maini PK (2023) Smoothing in linear multicompartment biological processes subject to stochastic input. arXiv preprint arXiv:2305.09004
Campbell A (2003) The future of bacteriophage biology. Nat Rev Genet 4(6):471–477
[DOI:
10.1038/nrg1089]
Carr EJ, Simpson MJ (2019) New homogenization approaches for stochastic transport through heterogeneous media. J Chem Phys 150(4)
Clark ED, Lawley SD (2023) How drug onset rate and duration of action affect drug forgiveness. J Pharmacokin Pharmacodyn (in press)
Clark ED, Lawley SD (2022) Should patients skip late doses of medication? A pharmacokinetic perspective. J Pharmacokinet Pharmacodyn 49(4):429–444
[DOI:
10.1007/s10928-022-09812-0]
Comtet A, Cornu F, Schehr G (2020) Last-passage time for linear diffusions and application to the emptying time of a box. J Stat Phys 181(5):1565–1602
[DOI:
10.1007/s10955-020-02637-6]
Counterman ED, Lawley SD (2021) What should patients do if they miss a dose of medication? A theoretical approach. J Pharmacokinet Pharmacodyn 48(6):873–892
[DOI:
10.1007/s10928-021-09777-6]
Counterman ED, Lawley SD (2022) Designing drug regimens that mitigate nonadherence. Bull Math Biol 84(1):1–36
[DOI:
10.1007/s11538-021-00976-3]
Félix M-A, Barkoulas M (2015) Pervasive robustness in biological systems. Nat Rev Genet 16(8):483–496
[DOI:
10.1038/nrg3949]
Felmlee MA, Morris ME, Mager DE (2012) Mechanism-based pharmacodynamic modeling. In: Computational toxicology, pp 583–600. Springer
Fermín LJ, Lévy-Véhel J (2017) Variability and singularity arising from poor compliance in a pharmacokinetic model ii: the multi-oral case. J Math Biol 74(4):809–841
[DOI:
10.1007/s00285-016-1041-1]
Fill JA (2009) The passage time distribution for a birth-and-death chain: strong stationary duality gives a first stochastic proof. J Theor Probab 22(3):543–557
[DOI:
10.1007/s10959-009-0235-5]
Gibaldi M, Perrier D (1982) Pharmacokinetics, 2nd edn. Marcelly Dekker, New York
[DOI:
10.1201/b14095]
Haynes RB, McDonald HP, Garg A, Montague P (2002) Interventions for helping patients to follow prescriptions for medications. Cochrane Database Syste Rev 2
Huang C, Ferrell JE (1996) Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc Natl Acad Sci USA 93(19):10078–10083
[DOI:
10.1073/pnas.93.19.10078]
Kloeden PE, Platen E (1992) Numerical solution of stochastic differential equations, corrected edition. Springer, Berlin
[DOI:
10.1007/978-3-662-12616-5]
Lévy-Véhel P-E, Lévy-Véhel J (2013) Variability and singularity arising from poor compliance in a pharmacokinetic model i: the multi-iv case. J Pharmacokinet Pharmacodyn 40(1):15–39
[DOI:
10.1007/s10928-012-9284-y]
Li J, Nekka F (2007) A pharmacokinetic formalism explicitly integrating the patient drug compliance. J Pharmacokinet Pharmacodyn 34(1):115–139
[DOI:
10.1007/s10928-006-9036-y]
Li J, Nekka F (2009) A probabilistic approach for the evaluation of pharmacological effect induced by patient irregular drug intake. J Pharmacokinet Pharmacodyn 36(3):221–238
[DOI:
10.1007/s10928-009-9119-7]
Liu L, Liu X, Yao DD (2004) Analysis and optimization of a multistage inventory-queue system. Manag Sci 50(3):365–380
[DOI:
10.1287/mnsc.1030.0196]
Louten J (2016) Virus structure and classification. In: Essential human virology, pp 19
McAllister N, Lawley S (2022) A pharmacokinetic and pharmacodynamic analysis of drug forgiveness. J Pharmacokinet Pharmacodyn 49:1–17
[DOI:
10.1007/s10928-022-09808-w]
Meyer B, Chevalier C, Voituriez R, Bénichou O (2011) Universality classes of first-passage-time distribution in confined media. Phys Rev E 83(5):051116
[DOI:
10.1103/PhysRevE.83.051116]
Michael J (2007) Conceptual assessment in the biological sciences: a national science foundation-sponsored workshop
Morgan DO (2007) The cell cycle: principles of control. New Science Press, Beijing
Norris JR (1998) Markov chains, statistical & probabilistic mathematics. Cambridge University Press, Cambridge
Osterberg L, Blaschke T (2005) Adherence to medication. N Engl J Med 353(5):487–497
[DOI:
10.1056/NEJMra050100]
Osterberg LG, Urquhart J, Blaschke TF (2010) Understanding forgiveness: minding and mining the gaps between pharmacokinetics and therapeutics. Clin Pharmacol Therapeutics 88(4):457–459
[DOI:
10.1038/clpt.2010.171]
Pavliotis GA (2014) Stochastic processes and applications: diffusion processes, the Fokker-Planck and Langevin equations, vol 60. Springer, Berlin
Rosenbaum SE (2016) Basic pharmacokinetics and pharmacodynamics: an integrated textbook and computer simulations. Wiley, Hoboken
Sabaté E, Sabaté E et al (2003) Adherence to long-term therapies: evidence for action. World Health Organization, Geneva
Simpson EH (1949) Measurement of diversity. Nature 163(4148):688–688
[DOI:
10.1038/163688a0]
