Diffusion and Discrete Temporal Models of the Growth of Free-Ranging Cats in Urban Areas

TL;DR

This paper develops a reaction-diffusion and complex dynamical model to analyze the population growth and dispersal of feral cats in urban areas, emphasizing the importance of control strategies.

Contribution

It introduces a novel combined reaction-diffusion and complex dynamical system model incorporating social factors and stochasticity for feral cat population analysis.

Findings

Population reaches equilibrium without intervention

Dispersal ability depends on biological and social factors

Control measures are necessary for sustainability

Abstract

The survival of the domestic cat (Felis catus) in various ecosystems has become increasingly relevant due to its impact on wildlife, public health, and society. In countries like Mexico, social factors such as abandonment have led to the feralization of the species and an unexpected increase in its population in urban areas. To design and implement effective population control methods, a thorough analysis of the species' population dynamics, along with the social factors influencing it, is necessary. We propose a reaction-diffusion model to simulate the natural dispersal of the population within a bounded domain. After exploring the species' spreading ability, we construct a complex dynamical system based on the biological characteristics of cats and their intraspecific and interspecific interactions, which we explain and study in detail. Both deterministic and stochastic parameters are considered to enhance the realism of the simulations. Our results indicate that the population reaches equilibrium, highlighting the need for control methods combined with social regulations to achieve sustainability in the system.