Madi Yerlanov

Journal article Nonlinear Analysis Real World Applications · February 1, 2027 This paper introduces a reaction-advection-diffusion system that models interactions among three actors: a target, a partaker, and an inhibitor. The framework is versatile, capturing phenomena ranging from the emergence and movement of crime hotspots in ur ... Full text Cite

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

Preprint · March 26, 2026 In populations with community structure, the formation of consensus requires both alignment within and diffusion of beliefs across groups, processes that evolve on distinct time scales. How do modularity, asymmetry, and polarization shape this process? We ... Link to item Cite

Global bifurcations and pattern formation in target–offender–guardian crime models

Journal article European Journal of Applied Mathematics · January 1, 2026 We study a reaction–advection–diffusion model of a target–offender–guardian system designed to capture interactions between urban crime and policing. Using Crandall–Rabinowitz bifurcation theory and spectral analysis, we establish rigorous conditions for b ... Full text Cite

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

Preprint · October 17, 2025 This paper introduces a reaction-advection-diffusion system that models interactions among three actors: a target, a partaker, and a guardian. The framework is versatile, capturing phenomena ranging from the emergence and movement of crime hotspots in urba ... Link to item Cite

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

Preprint · September 15, 2025 We study a reaction-advection-diffusion model of a target-offender-guardian system designed to capture interactions between urban crime and policing. Using Crandall-Rabinowitz bifurcation theory and spectral analysis, we establish rigorous conditions for b ... Link to item Cite

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

Journal article Chaos (Woodbury, N.Y.) · June 2025 We analyze a system of partial differential equations introduced as a model for urban crime with law enforcement. This system is known to obtain spatially localized patterns representing crime hotspots. In this work, we obtain the amplitude equations that ... Full text Cite

Effective population size in simple infectious disease models.

Journal article Journal of mathematical biology · November 2023 Almost all models used in analysis of infectious disease outbreaks contain some notion of population size, usually taken as the census population size of the community in question. In many settings, however, the census population is not equivalent to the p ... Full text Cite

Estimates for evolutionary partial differential equations in classical function spaces

Journal article Forum of Mathematics Sigma · September 1, 2023 We establish new local and global estimates for evolutionary partial differential equations in classical Banach and quasi-Banach spaces that appear most frequently in the theory of partial differential equations. More specifically, we obtain optimal (local ... Full text Cite

Algebraic sets defined by the commutator matrix

Journal article Journal of Algebra · January 1, 2022 In this paper we study algebraic sets of pairs of matrices defined by the vanishing of either the diagonal of their commutator matrix or its anti-diagonal. We find systems of parameters for the coordinate rings of these two sets and their intersection and ... Full text Cite

Event-specific interventions to minimize COVID-19 transmission.

Journal article Proceedings of the National Academy of Sciences of the United States of America · December 2020 COVID-19 is a global pandemic with over 25 million cases worldwide. Currently, treatments are limited, and there is no approved vaccine. Interventions such as handwashing, masks, social distancing, and "social bubbles" are used to limit community transmiss ... Full text Cite

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

Journal article PLoS computational biology · December 2020 Extensive non-pharmaceutical and physical distancing measures are currently the primary interventions against coronavirus disease 2019 (COVID-19) worldwide. It is therefore urgent to estimate the impact such measures are having. We introduce a Bayesian epi ... Full text Cite

Algebraic sets defined by the commutator matrix

Preprint · June 24, 2020 In this paper we study algebraic sets of pairs of matrices defined by the vanishing of either the diagonal of their commutator matrix or its anti-diagonal. We find a system of parameters for the coordinate rings of these two sets and their intersection and ... Link to item Cite