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

- 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.

**Mathematical model for alopecia areata Atanaska Dobreva, Ralf Paus, N.G. Cogan**

Alopecia areata (AA) is an autoimmune disease, and its clinical phenotype is characterized by the formation of distinct hairless patterns on the scalp or other parts of the body. In most cases hair falls out in round patches. A well-established hypothesis for the pathogenesis of AA states that collapse of hair follicle immune privilege is one of the essential elements in disease development. To investigate the dynamics of alopecia areata, we develop a mathematical model that incorporates immune system components and hair follicle immune privilege agents whose involvement in AA has been confirmed in clinical studies and experimentally. We perform parameter sensitivity analysis in order to determine which inputs have the greatest effect on outcome variables. Our findings suggest that, among all processes reflected in the model, immune privilege guardians and the pro-inflammatory cytokine interferon-γ govern disease dynamics. These results agree with the immune privilege collapse hypothesis for the development of AA.

**Global sensitivity analysis used to interpret biological experimental results Angela M. Jarrett, Yaning Liu, N. G. Cogan, M. Yousuff Hussaini**

Modeling host/pathogen interactions provides insight into immune defects that allow bacteria to overwhelm the host, mechanisms that allow vaccine strategies to be successful, and illusive interactions between immune components that govern the immune response to a challenge. However, even simplified models require a fairly high dimensional parameter space to be explored. Here we use global sensitivity analysis for parameters in a simple model for biofilm infections in mice. The results indicate which parameters are insignificant and are ‘frozen’ to yield a reduced model. The reduced model replicates the full model with high accuracy, using approximately half of the parameter space. We used the sensitivity to investigate the results of the combined biological and mathematical experiments for osteomyelitis. We are able to identify parts of the compartmentalized immune system that were responsible for each of the experimental outcomes. This model is one example for a technique that can be used generally.

**Effect of Periodic Disinfection on Persisters in a One-Dimensional Biofilm Model**(with B. Szomolay and M. Dindos)

It is well known that disinfection methods that successfully kill suspended bacterial populations often fail to eliminate bacterial biofilms. Recent efforts to understand biofilm survival have focused on the existence of small, but very tolerant, subsets of the bacterial population termed persisters. In this investigation, we analyze a mathematical model of disinfection that consists of a susceptible-persister population system embedded within a growing domain. This system is coupled to a reaction-diffusion system governing the antibiotic and nutrient. We analyze the effect of periodic and continuous dosing protocols on persisters in a one-dimensional biofilm model, using both analytic and numerical method. We provide sufficient conditions for the existence of steady-state solutions and show that these solutions may not be unique. Our results also indicate that the dosing ratio (the ratio of dosing time to period) plays an important role. For long periods, large dosing ratios are more effective than similar ratios for short periods. We also compare periodic to continuous dosing and find that the results also depend on the method of distributing the antibiotic within the dosing cycle.

**Publications**:

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