Research

Students and postdocs

Current postdocs:

Hwai-Ray Tung

Current PhD students:

Tory Richardson

Former PhD students:

Samantha Linn, graduated 2025, now an NSF postdoc at Imperial College London
Anil Cengiz, graduated 2025, now a Machine Learning Engineer at PayPal
Elias Clark, graduated 2023, now at Metrum Research Group
Jacob Madrid, graduated 2023, now a postdoc at Duke University
Claire Plunkett, graduated 2023, now at Teledyne Scientific
Amanda Alexander, graduated 2022, now a postdoc at U of Houston

Current and former undergraduates:

Alex Gilsoul, Fall 2023
Guang Yang, Summer 2022
Brian Bettinson, Fall 2021

Noel McAllister, Spring 2021 & Summer 2021

Elijah Counterman, Fall 2020 & Spring 2021

Emma Coates, Fall 2020

Taylor Yates, Fall 2019

Hannah Choi, Fall 2017 & Spring 2018

Chong Wang, Summer 2017

Bo Zhu, Summer 2017

Jacob Madrid, Summer & Fall 2016

Daniel Armstrong, Spring 2016

Marie Tuft, Fall 2014 & Spring 2015

Oliver Richardson, Fall 2014 & Spring 2015

Braden Schaer, Fall 2014 & Spring 2015

Anand Singh, Fall 2014 & Spring 2015

Adela Yang, Summer 2014

Ana Martinez, Summer 2014

Jina Yun, Summer 2013

Andrew Gao, Summer 2013

Charnelle Bland, Summer 2012

Kirsten Bell, Summer 2012

Priyanka Nadar, Summer 2011

Molly Cinderella, Summer 2010

NSF DMS-2325258, 2023-2026: eMB: Collaborative Research: Stochasticity in ovarian aging and biotechnologies for menopause delay
NSF DMS-1944574, 2020-2025: CAREER: How diffusion, dimension, geometry, and redundancy affect cellular dynamics.
NSF DMS-1814832, 2018-2021: Diffusion in stochastic environments: analysis and biological applications.
SIAM Life Sciences Early Career Prize, 2018.
NSF DMS RTG-1148230, Co-PI 2016-2020: Research training in mathematical and computational biology.

Select research areas

Medication adherence

92. Mathematical modeling of medication nonadherence
SD Lawley, T Gibson, J Zheng
Frontiers in Pharmacology, 16, 2025

86. Less frequent dosing of GLP-1 receptor agonists as a viable weight maintenance strategy
CC Wu, A Cengiz, SD Lawley
Obesity, 33(7), 2025

85. Incretin mimetics for weight loss forgive nonadherence
A Cengiz, CC Wu, SD Lawley
Diabetes, Obesity and Metabolism, 27(8), 2025

81. How missed doses of antibiotics affect bacteria growth dynamics
HR Tung, SD Lawley
Bulletin of Mathematical Biology, 87(58), 2025

80. Alternative dosing regimens of GLP-1 receptor agonists may reduce costs and maintain weight loss efficacy
A Cengiz, CC Wu, SD Lawley
Diabetes, Obesity and Metabolism, 27(4), 2025

72. Understanding and quantifying network robustness to stochastic inputs
HR Tung, SD Lawley
Bulletin of Mathematical Biology, 86(55), 2024

67. How drug onset rate and duration of action affect drug forgiveness
ED Clark, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2024

58. Should patients skip late doses of medication? A pharmacokinetic perspective
ED Clark, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2022

56. A pharmacokinetic and pharmacodynamic analysis of drug forgiveness
NP McAllister, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2022

55. Designing drug regimens that mitigate nonadherence
ED Counterman, SD Lawley
Bulletin of Mathematical Biology, 84(20), 2022 (arXiv:2108.08358)
Awarded 2023 Lee A. Segel Best Student Paper Prize of the Society for Mathematical Biology

52. What should patients do if they miss a dose of medication? A theoretical approach
ED Counterman, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2021 (arXiv:2102.05442)

Ovarian aging and menopause timing and delay

88. On modeling ovarian aging and menopause timing
SD Lawley, N Santoro, J Johnson
Bulletin of Mathematical Biology, 87(104), 2025

87. Prolonging youth or prolonging perimenopause? Beware the monkey's paw
N Santoro, SD Lawley, MD Sammel, J Johnson
Menopause, 32(10), 2025

84. Modeling the extension of ovarian function after therapeutic targeting of the primordial follicle reserve
J Johnson, JW Emerson, A Smith, K Medina, EE Telfer, RA Anderson, SD Lawley
Human Reproduction Update, 31(5), 2025

70. Modeling delay of age at natural menopause with planned tissue cryopreservation and autologous transplantation
J Johnson, SD Lawley, JW Emerson, K Oktay
American Journal of Obstetrics & Gynecology, 2024
Try our menopause delay calculator

68. Mathematical recapitulation of the end stages of human ovarian aging
SD Lawley, MD Sammel, N Santoro, J Johnson
Science Advances, 10(2), 2024

63. Why is there an "oversupply" of human ovarian follicles?
SD Lawley, J Johnson
Biology of Reproduction, 108(5), 2023

64. Slowest first passage times, redundancy, and menopause timing
SD Lawley, J Johnson
Journal of Mathematical Biology, 86(90), 2023

60. Recapitulating human ovarian aging using random walks
J Johnson, JW Emerson, SD Lawley
PeerJ, 10:e13941, 2022

All publications

Submitted:

94. Small fluctuations induce rapid extinction in stochastic population models
JB Madrid, JP Keener, SD Lawley
Submitted

2025:

93. Passage times of fast inhomogeneous immigration processes
HR Tung, SD Lawley
Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(12), 2025 (arXiv:2508.14202)
Promoted as an "Editor's Pick" featured article.

92. Mathematical modeling of medication nonadherence
SD Lawley, T Gibson, J Zheng
Frontiers in Pharmacology, 16, 2025

91. Quantifying the transition from single file to Fickian diffusion
V Richardson, SD Lawley
Journal of Chemical Physics, 163(19), 2025

90. First passage times with fast immigration
HR Tung, SD Lawley
SIAM Journal on Applied Mathematics, 85(5), 2025 (arXiv:2502.10915)

89. Geometry controls diffusive target encounters and escape in tubular structures
JL Kim, SD Lawley, AI Brown
Physical Review E, 112(2), 2025

88. On modeling ovarian aging and menopause timing
SD Lawley, N Santoro, J Johnson
Bulletin of Mathematical Biology, 87(104), 2025

87. Prolonging youth or prolonging perimenopause? Beware the monkey's paw
N Santoro, SD Lawley, MD Sammel, J Johnson
Menopause, 32(10), 2025

86. Less frequent dosing of GLP-1 receptor agonists as a viable weight maintenance strategy
CC Wu, A Cengiz, SD Lawley
Obesity, 33(7), 2025

85. Incretin mimetics for weight loss forgive nonadherence
A Cengiz, CC Wu, SD Lawley
Diabetes, Obesity and Metabolism, 27(8), 2025

84. Modeling the extension of ovarian function after therapeutic targeting of the primordial follicle reserve
J Johnson, JW Emerson, A Smith, K Medina, EE Telfer, RA Anderson, SD Lawley
Human Reproduction Update, 31(5), 2025

83. Reaction kinetics of membrane receptors: a spatial modeling approach
A Cengiz, SD Lawley
Journal of Mathematical Biology, 90(57), 2025 (arXiv:2501.13837)

82. Cover times with stochastic resetting
S Linn, SD Lawley
Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(4), 2025 (arXiv:2406.12154)

81. How missed doses of antibiotics affect bacteria growth dynamics
HR Tung, SD Lawley
Bulletin of Mathematical Biology, 87(58), 2025

80. Alternative dosing regimens of GLP-1 receptor agonists may reduce costs and maintain weight loss efficacy
A Cengiz, CC Wu, SD Lawley
Diabetes, Obesity and Metabolism, 27(4), 2025

2024:

79. Competition of many searchers
SD Lawley
Invited chapter in Target Search Problems, editors: DS Grebenkov, R Metzler, G Oshanin (arXiv:2310.02157)

78. A reaction network model of microscale liquid-liquid phase separation reveals effects of spatial dimension
J Kim, SD Lawley, J Kim
Journal of Chemical Physics, 161(20), 2024

77. Narrow escape with imperfect reactions
A Cengiz, SD Lawley
Physical Review E, 110(5), 2024
Promoted as an "Editor's Suggestion" featured article

76. Fast decisions reflect biases; slow decisions do not
S Linn, SD Lawley, BR Karamched, ZP Kilpatrick, K Josic
Physical Review E, 110(2), 2024 (arXiv:2401.00306)
Press coverage in New Scientist

75. Hitting probabilities for fast stochastic search
S Linn, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 57(30), 2024 (arXiv:2404.01142)

74. Boundary homogenization for partially reactive patches
CE Plunkett, SD Lawley
Multiscale Modeling and Simulation, 22(2), 2024 (arXiv:2405.11310)

73. First hitting time of a one-dimensional Levy flight to small targets
D Gomez, SD Lawley
SIAM Journal on Applied Mathematics, 84(3), 2024 (arXiv:2307.06274)

72. Understanding and quantifying network robustness to stochastic inputs
HR Tung, SD Lawley
Bulletin of Mathematical Biology, 86(55), 2024

71. Cover times of many diffusive or subdiffusive searchers
H Kim, SD Lawley
SIAM Journal on Applied Mathematics, 84(2), 2024 (arXiv:2308.13417)

70. Modeling delay of age at natural menopause with planned tissue cryopreservation and autologous transplantation
J Johnson, SD Lawley, JW Emerson, K Oktay
American Journal of Obstetrics & Gynecology, 2024
Try our menopause delay calculator

69. Cover times of many random walkers on a discrete network
H Kim, SD Lawley
Physical Review E, 109(1), 2024 (arXiv:2310.07905)

68. Mathematical recapitulation of the end stages of human ovarian aging
SD Lawley, MD Sammel, N Santoro, J Johnson
Science Advances, 10(2), 2024

67. How drug onset rate and duration of action affect drug forgiveness
ED Clark, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2024

2023:

66. First passage times under frequent stochastic resetting
S Linn, SD Lawley
Physical Review E, 108(2), 2023

65. Extreme statistics of superdiffusive Levy flights and every other Levy subordinate Brownian motion
SD Lawley
Journal of Nonlinear Science, 33(53), 2023 (arXiv:2103.07851)

64. Slowest first passage times, redundancy, and menopause timing
SD Lawley, J Johnson
Journal of Mathematical Biology, 86(90), 2023

63. Why is there an "oversupply" of human ovarian follicles?
SD Lawley, J Johnson
Biology of Reproduction, 108(5), 2023

62. Boundary homogenization for patchy surfaces trapping patchy particles
CE Plunkett, SD Lawley
Journal of Chemical Physics, 158(9), 2023

2022:

61. Inferences from FRAP data are model dependent: a subdiffusive analysis
AM Alexander, SD Lawley
Biophysical Journal, 121(20), 2022

60. Recapitulating human ovarian aging using random walks
J Johnson, JW Emerson, SD Lawley
PeerJ, 10:e13941, 2022

59. Extreme hitting probabilities for diffusion
S Linn, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 55(34), 2022 (arXiv:2110.11277)

58. Should patients skip late doses of medication? A pharmacokinetic perspective
ED Clark, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2022

57. Spiracular fluttering decouples oxygen uptake and water loss: a stochastic PDE model of respiratory water loss in insects
SD Lawley, HF Nijhout, MC Reed
Journal of Mathematical Biology, 84(40), 2022

56. A pharmacokinetic and pharmacodynamic analysis of drug forgiveness
NP McAllister, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2022

55. Designing drug regimens that mitigate nonadherence
ED Counterman, SD Lawley
Bulletin of Mathematical Biology, 84(20), 2022 (arXiv:2108.08358)
Awarded 2023 Lee A. Segel Best Student Paper Prize of the Society for Mathematical Biology

2021:

54. Reaction-subdiffusion equations with species-dependent movement
AM Alexander, SD Lawley
SIAM Journal on Applied Mathematics, 81(6), 2021 (arXiv:2104.11151)

53. Singularities of invariant densities for random switching between two linear ODEs in 2D
Y Bakhtin, T Hurth, SD Lawley, JC Mattingly
SIAM Journal on Applied Dynamical Systems, 20(40), 2021 (arXiv:2009.01299)

52. What should patients do if they miss a dose of medication? A theoretical approach
ED Counterman, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2021 (arXiv:2102.05442)

51. Revising Berg-Purcell for finite receptor kinetics
G Handy, SD Lawley
Biophysical Journal, 120(11), 2021 (arXiv:2101.05956)

50. Extreme first passage times of piecewise deterministic Markov processes
SD Lawley
Nonlinearity, 34(5), 2021 (arXiv:1912.03438)

49. Bimolecular binding rates for pairs of spherical molecules with small binding sites
CE Plunkett, SD Lawley
Multiscale Modeling and Simulation, 19(1), 2021 (arXiv:2002.11703)

48. The effects of fast inactivation on conditional first passage times of mortal diffusive searchers
SD Lawley
SIAM Journal on Applied Mathematics, 81(1), 2021 (arXiv:2003.05515)

2020:

47. Extreme first passage times for random walks on networks
SD Lawley
Physical Review E, 102(6), 2020
Promoted as an "Editor's Suggestion" featured article

46. Subdiffusion-limited fractional reaction-subdiffusion equations with affine reactions: solution, stochastic paths, and applications
SD Lawley
Physical Review E, 102(4), 2020

45. Anomalous reaction-diffusion equations for linear reactions
SD Lawley
Physical Review E, 102(3), 2020

44. Extreme statistics of anomalous subdiffusion following a fractional Fokker-Planck equation: Subdiffusion is faster than normal diffusion
SD Lawley
Journal of Physics A: Mathematical and Theoretical, 53(38), 2020 (arXiv:2004.14994)

43. Competition between slow and fast regimes for extreme first passage times of diffusion
JB Madrid, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 53(33), 2020 (arXiv:2004.05414)

42. Receptor organization determines the limits of single-cell source location detection
SD Lawley, AE Lindsay, CE Miles
Physical Review Letters, 125(1), 2020

41. Asymptotic and numerical analysis of a stochastic PDE model of volume transmission
SD Lawley, V Shankar
Multiscale Modeling and Simulation, 18(2), 2020

40. Spiracular fluttering increases oxygen uptake
SD Lawley, MC Reed, HF Nijhout
PLOS ONE, 15(5), 2020

39. Interaction between switching diffusivities and cellular microstructure
P Murphy, PC Bressloff, SD Lawley
Multiscale Modeling and Simulation, 18(2), 2020

38. Distribution of extreme first passage times of diffusion
SD Lawley
Journal of Mathematical Biology, 80(7), 2020 (arXiv:1910.12170)

37. Effective permeability of a gap junction with age-structured switching
PC Bressloff, SD Lawley, P Murphy
SIAM Journal on Applied Mathematics, 80(1), 2020

36. Universal formula for extreme first passage statistics of diffusion
SD Lawley
Physical Review E, 101(1), 2020

35. A probabilistic approach to extreme statistics of Brownian escape times in dimensions 1, 2, and 3
SD Lawley, JB Madrid
Journal of Nonlinear Science, 2020 (arXiv:1907.07515)

2019:

34. Boundary homogenization for trapping patchy particles
SD Lawley
Physical Review E, 100(3), 2019

33. Diffusive search for diffusing targets with fluctuating diffusivity and gating
SD Lawley, CE Miles
Journal of Nonlinear Science, 29(6), 2019

32. How receptor surface diffusion and cell rotation increase association rates
SD Lawley, CE Miles
SIAM Journal on Applied Mathematics, 79(3), 2019

31. First passage time distribution of multiple impatient particles with reversible binding
SD Lawley, JB Madrid
Journal of Chemical Physics, 150(21), 2019
Promoted as an "Editor's Pick" featured article

30. Electrodiffusive flux through a stochastically gated ion channel
SD Lawley, JP Keener
SIAM Journal on Applied Mathematics, 79(2), 2019

29. Protein concentration gradients and switching diffusions
PC Bressloff, SD Lawley, P Murphy
Physical Review E, 99(3), 2019

28. Role of trap recharge time on the statistics of captured particles
G Handy, SD Lawley, A Borisyuk
Physical Review E, 99(2), 2019

2018:

27. Blowup from randomly switching between stable boundary conditions for the heat equation
SD Lawley
Communications in Mathematical Sciences, 16(4), 2018

26. Analysis of non-processive molecular motor transport using renewal reward theory
CE Miles, SD Lawley, JP Keener
SIAM Journal on Applied Mathematics, 78(5), 2018

25. Diffusion in an age-structured randomly switching environment
PC Bressloff, SD Lawley, P Murphy
Journal of Physics A: Mathematical and Theoretical, 51(31), 2018

24. A probabilistic analysis of volume transmission in the brain
SD Lawley
SIAM Journal on Applied Mathematics, 14(3), 2018

23. Receptor recharge time drastically reduces the number of captured particles
G Handy, SD Lawley, A Borisyuk
PLOS Computational Biology, 14(3), 2018

22. Smooth invariant densities for random switching on the torus
Y Bakhtin, T Hurth, SD Lawley, JC Mattingly
Nonlinearity, 31(4), 2018 (arXiv:1708.01390)

2017:

21. Diffusive transport in the presence of stochastically gated absorption
PC Bressloff, BR Karamched, SD Lawley, E Levien
Physical Review E, 96(2), 2017

20. Rebinding in biochemical reactions on membranes
SD Lawley, JP Keener
Physical Biology, 14(5), 2017

19. Hybrid colored noise process with space-dependent switching rates
PC Bressloff, SD Lawley
Physical Review E, 96(1), 2017

18. Mean first passage times for piecewise deterministic Markov processes and the effects of critical points
PC Bressloff, SD Lawley
Journal of Statistical Mechanics: Theory and Experiment, 063202, 2017

17. Temporal disorder as a mechanism for spatially heterogeneous diffusion
PC Bressloff, SD Lawley
Physical Review E - Rapid Communication, 95(6), 2017

16. Residence times of a Brownian particle with temporal heterogeneity
PC Bressloff, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 50(19), 2017

15. Dynamically active compartments coupled by a stochastically-gated gap junction
PC Bressloff, SD Lawley
Journal of Nonlinear Science, 27(5), 2017

2016:

14. Including rebinding reactions in well-mixed models of distributive biochemical reactions
SD Lawley, JP Keener
Biophysical Journal, 111(10), 2016

13. Diffusion on a tree with stochastically-gated nodes
PC Bressloff, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 49(24), 2016
Named to the journal's "Highlights of 2016" collection

12. Boundary value problems for statistics of diffusion in a randomly switching environment: PDE and SDE perspectives
SD Lawley
SIAM Journal on Applied Dynamical Systems, 15(3), 2016

11. Neurotransmitter concentrations in the presence of neural switching in one dimension
SD Lawley, J Best, MC Reed
Discrete and Continuous Dynamical Systems - Series B, 21(7), 2016

2015:

10. Stochastically gated diffusion-limited reactions for a small target in a bounded domain
PC Bressloff, SD Lawley
Physical Review E, 92(6), 2015

9. Escape from subcellular domains with randomly switching boundaries
PC Bressloff, SD Lawley
Multiscale Modeling and Simulation, 13(4), 2015

8. Coarse-graining intermittent intracellular transport: Two- and three-dimensional models
SD Lawley, M Tuft, HA Brooks
Physical Review E, 92(4), 2015

7. A new derivation of Robin boundary conditions through homogenization of a stochastically switching boundary
SD Lawley, JP Keener
SIAM Journal on Applied Dynamical Systems, 14(4), 2015

6. Escape from a potential well with a randomly switching boundary
PC Bressloff, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 48(22), 2015

5. Moment equations for a piecewise deterministic PDE
PC Bressloff, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 48(10), 2015
Chosen by editors as "Publisher's pick" featured article

4. Stochastic switching in infinite dimensions with applications to random parabolic PDE
SD Lawley, JC Mattingly, MC Reed
SIAM Journal on Mathematical Analysis, 47(4), 2015

2014:

3. Sensitivity to switching rates in stochastically switched ODEs
SD Lawley, JC Mattingly, MC Reed
Communications in Mathematical Sciences, 12(7), 2014

2. Mathematical modeling of the effects of glutathione on arsenic methylation
SD Lawley, J Yun, M Gamble, M Hall, MC Reed, HF Nijhout
Theoretical Biology and Medical Modelling, 11(20), 2014

2011:

1. Mathematical model insights into arsenic detoxification
SD Lawley, M Cinderella, M Hall, M Gamble, H F Nijhout, MC Reed
Theoretical Biology and Medical Modelling, 8(31), 2011