This review provides a pedagogic and self-contained introduction to master equations and
to their representation by path integrals. Since the 1930s, master equations have served as …

We study multicellular tumor spheroids by introducing a new three-dimensional agent-based
Voronoi-Delaunay hybrid model. In this model, the cell shape varies from spherical in thin …

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in
low-dimensional and disordered media such as biological membranes. We present Monte …

We study the general properties of stochastic two-species models for predator-prey
competition and coexistence with Lotka–Volterra type interactions defined on ad …

We introduce a simple model of population dynamics which considers reproducing
individuals or particles with birth and death rates depending on the number of other …

Mathematical methods in Biology are of increasing relevance for understanding the control
and the dynamics of biological systems with medical relevance. In particular, agent-based …

We study multicellular tumour spheroids with a continuum model based on partial differential
equations (PDEs). The model includes viable and necrotic cell densities, as well as oxygen …

Complex systems are composed of many particles or agents that move and interact with one
another. The underlying mathematical framework to model many of these systems must …

We study a simple chemical reaction system and effects of the internal noise. The chemical
reaction system causes the same transition phenomenon discussed by Togashi and Kaneko …

We study a stochastic lattice predator–prey system by means of Monte Carlo simulations that
do not impose any restrictions on the number of particles per site, and discuss the …