Bringing consistency to simulation of population models – Poisson Simulation as a bridge between micro and macro simulation

Abstract

Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro-and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.

Is it growing exponentially fast? – Impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics

“…Stochastic simulations of the generalized-growth model were generated through a Poisson simulation approach [11]. To assess the impact of assuming exponential growth in the context of near-exponential growth dynamics, we estimated the growth rate “ r ” for the exponential growth model for each of the 500 stochastic realizations to generate a distribution of the estimates of the growth rate “ r ”.…”

“…A total of 500 stochastic simulations were generated through a Poisson simulation approach [11]. The gray curves correspond to the ensemble of stochastic simulations.…”

A Guide to Population Modelling for Simulation

“…It also revealed a simple and direct relationship between discrete and continuous compartment models. Gustafsson and Sternad [23], based on [14], showed that agent-and entity-based and compartment-based models will produce fully consistent results if a number of simple rules are obeyed. In [24] this was extended to include situation-based models.…”

“…A brief presentation of stochastic compartment-based modelling using the Poisson Simulation approach is given in Appendix B. See also [23]. Constructions like queues of different kinds can easily be accomplished within compartment-based modelling by using Poisson Simulation, see [14].…”

Inferring Epidemic Network Topology from Surveillance Data

“…It has an advantage over the chain binomial models in the dynamic modeling of infectious disease spread. In the chain binomial models, varying the selection of can distort the dynamic patterns [31]. In contrast, the Poisson distribution can be freely adjusted with respect to without affecting the stochastic process due to the Poisson property.…”