Work

Mathematical Modeling of Serial Killer Dynamics and its Prevention Using Machine Learning Based Physics Informed Neural Networks

Year: 2026

Type: article

Abstract: Serial killer activity is a complex social threat that traditional criminology often struggles to predict quantitatively. To better understand this phenomenon, we propose a mathematical modeling framework inspired by epidemiology. The population is divided into four compartments: at-risk individuals (A), active serial killers (S), prevention programs (P), and law enforcement (L). Their interactions are described by a system of nonlinear differential equations representing the spread and control of criminal behavior. We first establish fundamental analyticalproperties of the model, including positivity and boundedness of solutions. Two equilibrium states are identified: a crime-free equilibrium and a persistent (endemic) crime state. A threshold parameter, the basic reproduction number R0, determines stability; the crime-free state is stable when R0 < 1. We further apply Physics-Informed Neural Networks (PINNs) to estimate model parameters from data, demonstrating accurate recovery with errors below 5%. This combined analytical-computational approach provides a novel framework for studying criminal dynamics.

Source: Applied Mathematical Biosystems

DOI: 10.67029/j.amb.2026.0021.16

Authors: Tshering Dorjee Bhutia, Biswadip Pal, Purnendu Sardar, Santosh Biswas, Krishna Pada Das

Institutions: Ramakrishna Mission Residential College, Jadavpur University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

SDG: Peace, justice, and strong institutions

Open Access status: hybrid

Funder: University Grants Commission