Moment closure methods appear in myriad scientific disciplines in the modelling of complex
systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled …

Over the past decade, the use of networks has led to a new modelling paradigm combining
several branches of science, including physics, mathematics, biology and social sciences …

Recently, research that focuses on the rigorous understanding of the relation between
simulation and/or exact models on graphs and approximate counterparts has gained lots of …

In this paper we use comparison theorems from classical ODE theory in order to rigorously
show that the N-Intertwined Mean-Field Approximation (NIMFA) model provides an upper …

We extrapolate from the exact master equations of epidemic dynamics on fully connected
graphs to non-fully connected by keeping the size of the state space N+ 1, where N is the …

A large system of ordinary differential equations is approximated by a parabolic partial
differential equation with dynamic boundary condition and a different one with Robin …

Mean-field models are often used to approximate Markov processes with large state-spaces.
One-step processes, also known as birth-death processes, are an important class of such …

Deterministic limit of a class of continuous time Markov chains is considered based purely
on differential equation techniques. Starting from the linear system of master equations …

Using operator semigroup methods, we show that Fokker-Planck type second-order PDE-s
can be used to approximate the evolution of the distribution of a one-step process on $ N …

A differenciálegyenletek kvalitatív elméletének kezdeteit rendszerint Poincaré
munkásságáig vezetik vissza, amikor a természettudományokban (akkor elsősorban a …