This research was supported by NSF Awards #0612467, and #1510743 #1122378

- The focus of my research is on mathematical biology. In
particular,
I am interested in fluid/solid interaction, chemical transport, bacterial physiology. I have spent the past several years researching biological processes where each of the topics above plays a fundamental role. As in many areas of applied mathematics, the mathematical methods that I use are very diverse. Deriving and analysing mathematical models requires familiarity with the biology of the problem, but also with multiphase flow, non-Newtonian fluid dynamics and nonlinear dynamics. I also employ computational methods, perturbation analysis, sensitivity/UQ and nonlinear PDE theory to answer specific, biologically motivated problems.

I have several students working on a variety of problems including spatial aspects of biofilm infections, host/bacteria interactions, immune disease, micro filtration. I am also working on several other projects. Below I have listed some abstracts papers that have recently appeared or are to appear.

**A framework for model analysis across multiple experiment regimes: Investigating effects of zinc on***Xylella fastidiosa*as a case study Manu Aggarwal, M.Y.Hussaini, Leonardo De La Fuente, Fernando Navarrete, and N.G.Cogan Journal of theoretical biology 457, 88-100

Mathematical models are ubiquitous in analyzing dynamical biological systems. However, it might not be possible to explicitly account for the various sources of uncertainties in the model and the data if there is limited experimental data and information about the biological processes. The presence of uncertainty introduces problems with identifiability of the parameters of the model and determining appropriate regions to explore with respect to sensitivity and estimates of parameter values. Since the model analysis is likely dependent on the numerical estimates of the parameters, parameter identifiability should be addressed beforehand to capture biologically relevant parameter space. Here, we propose a framework which uses data from different experiment regimes to identify a region in the parameter space over which subsequent mathematical analysis can be conducted. Along with building confidence in the parameter estimates, it provides us with variations in the parameters due to changes in the experimental conditions. To determine significance of these variations, we conduct global sensitivity analysis, allowing us to make testable hypothesis for effects of changes in the experimental conditions on the biological system. As a case study, we develop a model for growth dynamics and biofilm formation of a bacterial plant pathogen, and use our framework to identify possible effects of zinc on the bacterial populations in different metabolic states. The framework reveals underlying issues with parameter identifiability and identifies a suitable region in the parameter space, sensitivity analysis over which informs us about the parameters that might be affected by addition of zinc. Moreover, these parameters prove to be identifiable in this region.

**Computational Investigation of Ripple Dynamics in Biofilms in Flowing Systems, Nicholas G.Cogan, Jian Li, Stefania Fabbri, Paul Stoodley Biophysical journal 115 (7), 1393-1400**

Biofilms are collections of microorganisms that aggregate using a self-produced matrix of extracellular polymeric substance. It has been broadly demonstrated that many microbial infections in the body, including dental plaque, involve biofilms. While studying experimental models of biofilms relevant to mechanical removal of oral biofilms, distinct ripple patterns have been observed. In this work, we describe a multiphase model used to approximate the dynamics of the biofilm removal process. We show that the fully nonlinear model provides a better representation of the experimental data than the linear stability analysis. In particular, we show that the full model more accurately reflects the relationship between the apparent wavelength and the external forcing velocities, especially at mid-to-low velocities at which the linear theory neglects important interactions. Finally, the model provides a framework by which the removal process (presumably governed by highly nonlinear behavior) can be studied.

**The Ups and Downs of**Staphylococcus aureus infections are a growing concern worldwide due to the increasing number of strains that exhibit antibiotic resistance. Recent studies have indicated that some percentage of people carry the bacteria in the nasal cavity and therefore are at a higher risk of subsequent, and more serious, infections in other parts of the body. However, individuals carrying the infection can be classified as only intermittent carriers versus persistent carriers, being able to eliminate the bacteria and later colonized again. Using a model of bacterial colonization of the anterior nares, we investigate oscillatory patterns related to intermittent carriage of S. aureus. Following several studies using global sensitivity analysis techniques, various insights into the model’s behaviour were made including interacting effects of the bacteria’s growth rate and movement in the mucus, suggesting parameter connections associated with biofilm-like behaviour. Here the bacterial growth rate and bacterial movement are explicitly connected, leading to expanded oscillatory behaviour in the model. We suggest possible implications that this oscillatory behaviour can have on the definition of intermittent carriage and discuss differences in the bacterial virulence dependent upon individual host health. Furthermore, we show that connecting the bacterial growth and movement also expands the region of the parameter space for which the bacteria are able to survive and persist.*S. aureus*nasal carriage AM Jarrett, NG Cogan Mathematical Medicine and Biology: a Journal of the IMA

**Publications**:

50.) A framework for model analysis across multiple experiment regimes: Investigating effects of zinc on Xylella fastidiosa as a case study M Aggarwal, MY Hussaini, L De La Fuente, F Navarrete, NG Cogan Journal of theoretical biology 457, 88-100

49.) Computational investigation of ripple dynamics in biofilms in flowing systems NG Cogan, J Li, S Fabbri, P Stoodley Biophysical journal 115 (7), 1393-1400

48.) The ups and downs of S. aureus nasal carriage AM Jarrett, NG Cogan Mathematical medicine and biology: a journal of the IMA

47.) A mathematical model for the determination of mouse excisional wound healing parameters from photographic data NG Cogan, AP Mellers, BN Patel, BD Powell, M Aggarwal, KM Harper, ... Wound Repair and Regeneration

46.) Uncertainty propagation in a model of dead-end bacterial microfiltration using fuzzy interval analysis NG Cogan, MY Hussaini, S Chellam Journal of Membrane Science 546, 215-224

45.) Short-Term Antiretroviral Treatment Recommendations Based on Sensitivity Analysis of a Mathematical Model for HIV Infection of CD4+T Cells AM Croicu, AM Jarrett, NG Cogan, MY Hussaini Bulletin of mathematical biology 79 (11), 2649-2671

44.) Fluid‐driven interfacial instabilities and turbulence in bacterial biofilms S Fabbri, J Li, RP Howlin, A Rmaile, B Gottenbos, M De Jager, EM Starke, ... Environmental microbiology 19 (11), 4417-4431

43.) Combining two methods of global sensitivity analysis to investigate MRSA nasal carriage model AM Jarrett, NG Cogan, MY Hussaini Bulletin of mathematical biology 79 (10), 2258-2272

42.) Global parametric sensitivity analysis of a model for dead-end microfiltration of bacterial suspensions NG Cogan, S Chellam Journal of Membrane Science 537, 119-127

41.) Analysing the dynamics of a model for alopecia areata as an autoimmune disorder of hair follicle cycling A Dobreva, R Paus, NG Cogan Mathematical medicine and biology: a journal of the IMA

40.) Exploring an autoimmune hair loss condition through mathematical modeling and sensitivity analysis A Dobreva, R Paus, N Cogan

39.) Optimal backwashing in dead-end bacterial microfiltration with irreversible attachment mediated by extracellular polymeric substances production NG Cogan, J Li, AR Badireddy, S Chellam Journal of Membrane Science 520, 337-344

38.) Theoretical and experimental evidence for eliminating persister bacteria by manipulating killing timing NG Cogan, H Rath, N Kommerein, SN Stumpp, M Stiesch FEMS microbiology letters 363 (23)

37.) Predictive Computer Models for Biofilm Detachment Properties in Pseudomonas aeruginosa NG Cogan, JM Harro, P Stoodley, ME Shirtliff Mbio 7 (3), e00815-16

36.) Sensitivity analysis of a pharmacokinetic model of vaginal anti-HIV microbicide drug delivery AM Jarrett, Y Gao, MY Hussaini, NG Cogan, DF Katz Journal of pharmaceutical sciences 105 (5), 1772-1778

35.) Shocks and rarefactions arise in a two-phase model with logistic growth DA Ekrut, NG Cogan Applied Mathematics Letters 52, 4-8

34.) A Two-Dimensional Multiphase Model of Biofilm Formation in Microfluidic Chambers M Whidden, N Cogan, M Donahue, F Navarrete, L De La Fuente Bulletin of mathematical biology 77 (12), 2161-2179

33.) Mathematical model for alopecia areata A Dobreva, R Paus, NG Cogan Journal of theoretical biology 380, 332-345

32.) Mathematical model for MRSA nasal carriage AM Jarrett, NG Cogan, MY Hussaini Bulletin of mathematical biology 77 (9), 1787-1812

31.) Global sensitivity analysis used to interpret biological experimental results AM Jarrett, Y Liu, NG Cogan, MY Hussaini Journal of mathematical biology 71 (1), 151-170

30.) B Szomolay, NG Cogan (2015) Modelling mechanical and chemical treatment of biofilms with two phenotypic resistance mechanisms, Environmental microbiology

29.) A Dobreva, R Paus, NG Cogan (2015) Mathematical model for alopecia areata Journal of theoretical biology 380, 332-345

28.) DA Ekrut, NG Cogan (2015) A Particular Solutions for a Two-Phase Model with a Sharp Interface BIOMATH 4 (1), Article ID: 1503081

This one is sort of irritating - there are a couple of errors in this paper, most importantly the example is incorrect (although the methodology is correct). The journal will not accept errata, so I am posting one here. If you see people reference this paper, can you please point them to the corrections…

Errata for Shocks and Rarefactions Arise in a Two-Phase Model with Logistic Growth

27.) A. M. Jarrett, Y. Liu, N.G. Cogan and M. Y. Hussaini (2015) Global sensitivity analysis used to interpret biological experimental results, Journal of Mathematical Biology, in press.

26.) Angela M. Jarret, N. G. Cogan and M. E. Shirtliff (2014), Model of Inflammatory Host Response to a Bacterial Infection, Mathematical Medicine and Biology, in press. (Winner of the Best Paper Prize)

25.) N.G. Cogan and S. Chellam (2014) A method for determining the optimal back-washing frequency and duration for dead-end microfiltration, Journal of Membrane Science, 469, 410-417.

24.) N. G. Cogan (2013), Concepts in Bacterial Disinfection (Review), Mathematical Biosciences, 245(2), 111-125.

23.) N. G. Cogan, M. R. Donahue, Mark Whidden and Leonardo De La Fuente (2013), Pattern Formation Exhibited by Biofilm Formation within Microfluidic Chambers, Biophysical Journal, 104(9), 1867-1874.

22.) N. G. Cogan, Barbara Szomolay and Martin Dindos (2013), Effect of Periodic Disinfection on Persisters in a One-Dimensional Biofilm Model, Bulletin of Mathematical Biology,75(1), 94-123

21.) N. G. Cogan, Matthew Donahue and Mark Whidden (2012), Marginal Stability and Traveling Fronts in Two-Phase Mixtures, Phys. Rev. E., 86(5): 056204.

20.) N.G. Cogan, Jason Brown, Kyle Darres, Katherine Petty (2012), Optimal Control Strategies for Disinfection of Bacterial Populations with Persister/Susceptible Dynamics, Antimicrobial Agents and Chemotherapy, 56(9) pp: 4816-4826.

19.) Chellam, S. and N.G. Cogan (2011). Colloidal and Bacterial Fouling during Constant Flux Microfiltration: Comparison of Classical Blocking Laws with a Unified Model Combining Pore Blocking and EPS Secretion, Journal of Membrane Science, 382(1-2) 148-157.

18.) Cogan, N. G. (2011), Computational exploration of disinfection of bacterial biofilms in partially blocked channels. International Journal for Numerical Methods in Biomedical Engineering. doi: 10.1002/cnm.1451

17.) Cogan, N. G., Gunn, J. S. and Wozniak, D. J. (2011), Biofilms and infectious diseases: biology to mathematics and back again. FEMS Microbiology Letters, 322: 1?.

16.) R.D. Guy and N.G. Cogan, Multiphase flow models of biogels from crawling cells to bacterial biofilms. HFSP Journal, 4(11) (2010).

15.) N.G. Cogan and Charles W. Wolgemuth, Two-Dimensional Patterns in Bacterial Veils Arise from Self-generated, Three-Dimensional Fluid Flows, Bulletin of Mathematical Biology (2010).

14.) N. G. Cogan, An Extension of the Boundary Integral Method Applied to Periodic Disinfection of a Dynamic Biofilm, SIAM J. Appl. Math., 70(7), pp. 2281-2307 (2010).

13.) N.G. Cogan and Shankar Chellam, Incorporating pore blocking, cake filtration and EPS production in a model for constant pressure bacterial fouling during dead-end microfiltration, Journal of Membrane Science, 345(1-2), 81-89 (2009).

12.) Patrick DeLeenheer and N.G. Cogan, Failure of antibiotic treatment in microbial populations , Journal of Mathematical Biology, 59(4), 563-579 (2009).

11.) N. G. Cogan and Shankar Chellam, Regularized Stokeslets Solution for 2-D Flow in Dead-end Microfiltration: Application to Bacterial Deposition and Fouling, Journal of Membrane Science 318(1-2) pp: 379-386 (2008)

10.) Tianyu Zhang, N. G. Cogan and Qi Wang, Field-Phase Models for Biofilms. II. 2-D Numerical Simulations of Biofilm-Flow Interaction, Communications in Computational Physics, 4(1) pp: 72-101 (2008)

9.) Tianyu Zhang, N. G. Cogan and Qi Wang, Phase-Field Models for Biofilm. I. Theory and 1-D Simulations, SIAM J. Appl. Math 69(3), pp. 641-669 (2008)

8.) N. G. Cogan, A Two-Fluid Model of Biofilm Disinfection , Bulletin of Mathematical Biology, 70(3) pp. 800-819 (2008)

7.) Nicholas G. Cogan, Hybrid Numerical Treatment of Two Fluid Problems with Passive Interfaces , COMM. APP. MATH. AND COMP. SCI. Vol 2., No. 1, pp. 117-133 2007

6.) N. G. Cogan Incorporating Toxin Hypothesis into a Mathematical Model of Persister Formation and Dynamics , Journal of Theoretical Biology 248 (2007): 340-349

5.) N.G. Cogan, Effects of Persister Formation on Bacterial Response to Dosing , Journal of Theoretical Biology 238(3): 694-703 (2006)

4.) N. G. Cogan and C.W. Wolgemuth, Pattern Formation in Bacterial Veils, Biophysical Journal 88, 2525-2529 (2005)

3.) N.G. Cogan, Ricardo Cortez and Lisa J. Fauci, Modeling Physiological Resistence in Bacterial Biofilms, Bulletin of Mathematical Biology 67 (4): 831-853 (2005)

2.) N.G. Cogan and James P. Keener, Channel Formation in Gels , SIAM J. Appl. Math., Vol. 65, N0. 6, pp. 1839-1854.

1.) N.G. Cogan and James P. Keener, The Role of the Biofilm Matrix in Structural Development Mathematical Medicine and Biology 21(2),147-166 (2004)

**Simulations**(quicktime):

**Stripe 0**: Veil on the borderline of stripesStripe0 **Stripe 1**: Veil in stripe regime with tight colormapStripe1 **Stripe 1a**: Same regime with broad colormapStripe 1a **Fingering instability**: Production of polymer induces gradients in osmotic pressure. Expansion of the biofilm gel leads to a surface instability.Mushroom **Disinfection**: Dynamic disinfection zones with no external flow. The disifectant reacts with a component of the biofilm, destroying both the disinfectant and the nuetralizer.No Flow **Fluid Visualization**: Movie showing advective transport of a passive marker dye. There is no explicit diffusion, although the numerical method is diffusive.Fluid Visual **Disinfection**: Disinfection simulation indicating that physiological resistance cannot be the only resistance mechanism employed by biofilms.Disinfection **Moving Cluster**with advection of a dye. (NOTE: this is an animated GIF and takes a loooong time to load:Cluster **Moving Circle-centered**: Simulation of a blob of viscous fluid immeresed in water with a parabolic background flow.Circle - centered **Moving Circle-off center**: Simulation of a blob of viscous fluid immeresed in water with a parabolic background flow.Circle - off center **One Cluster**: One cluster in a parabolic background flowCluster **Two Clusters**:Two initially identical clusters in parabolic background flowTwo Clusters **One Cluster**: Growth and response to fluidGrowing Biofilm **Two Clusters**: Growth and response to fluidGrowing Biofilm