Research interests:

I am still finding my niche in the science world. In general, I am interested in making biological/ecological/sociological/medical modeling more interpretable and understandable. At the same time, I would like to explore how other aspects of "pure math" might help provide deeper insights in this field.  

Publications:

1. A study of general reaction-advection-diffusion equations describing dynamics between target, partaker, and inhibitor.

Madi Yerlanov, Nancy Rodriguez. Nonlinear Analysis: Real World Applications. 2027.

2. Global Bifurcations and Pattern Formation in Target-Offender-Guardian Crime Models.

Madi Yerlanov, Qi Wang, Nancy Rodriguez. EJAM. 2026.

3. Formation and suppression of hotspots in urban crime models with law enforcement. 

Madi Yerlanov, Qi Wang, Nancy Rodriguez. Chaos. 2025.

4. Effective population size in simple infectious disease models. 

Madi Yerlanov, Piyush Agarwal, Caroline Colijn, Jessica E. Stockdale. Journal of Mathematical Biology. 2023.

5. Estimates for evolutionary partial differential equations in classical function spaces.

Alejandro Castro Castilla, Anders Israelsson, Wolfgang Staubach, Madi Yerlanov.  Forum of Mathematics, Sigma. 2023.

6. Algebraic sets defined by the commutator matrix.

Zhibek Kadyrsizova, Madi Yerlanov.  Journal of Algebra. 2022.

7. Event-specific interventions to minimize COVID-19 transmission.

Paul Tupper, Madi Yerlanov, Himani Boury, Caroline Colijn. PNAS. 2020.

8. Quantifying the impact of COVID-19 control measures using a Bayesian model of physical distancing.

Sean C Anderson, Andrew M Edwards, Madi Yerlanov, Nicola Mulberry, Jessica Stockdale, Sarafa A Iyaniwura, Rebeca C Falcao, Michael C Otterstatter, Michael A Irvine, Naveed Z Janjua, Daniel Coombs, Caroline Colijn. medRxiv. PLOS Computational Biology. 2020.

Preprints:

1. Modularity, asymmetry, and polarization shape consensus speed in the voter model.

Madi Yerlanov, Zachary Kilpatrick, Nancy Rodriguez. arxiv. 2026.

Theses:

1. Reaction-Advection-Diffusion Systems as a Tool to Explore Social Dynamics: Modeling, Analysis, and Extensions.

Madi Yerlanov. PhD dissertation. 2026. 

2. Effective population size in infectious disease models.

Madi Yerlanov. MSc thesis. 2021.

3. Frobenius Singularities of Algebraic Sets of Matrices.

Madi Yerlanov. Capstone project. 2019.  

Some code repositories:

1. Global Bifurcations and Pattern Formation in Target-Offender-Guardian Crime Models.

Matlab.

2. Formation and Suppression of Hotspots in Urban Crime Models with Law Enforcement.

Matlab, Mathematica.

3. Effective population size in simple infectious disease models.

Julia, R.