RESEARCH ON SIMULATION OF POPULATION MODELS
Signals and Systems Group, Dept. of Engineering Sciences,
The problem of modelling and simulating population modelsPopulation models are models of dynamic systems with an integer number of discrete entities (individuals), such as plants, animals, patients, vehicles, molecules, atoms, data packages or entities of any kind. Such models are frequently used in systems biology, ecology, epidemiology, demography and queuing systems, and are also important in physics, chemistry, traffic planning, production and many other fields.
In this project, we are constructing a systematic methodology for designing simulation models for population systems, a methodology that enables the user to pick an appropriate technique for the problem and purpose at hand.
The crucial task in population modelling is to preserve the characteristics of interest of the system under study, in particular four fundamental properties:
Poisson simulation: An efficient approach for stochastic macro simulationPoisson simulation is a technique for constructing macro models that can be used efficiently to simulate population models. It is a stochastic extension of (deterministic) Continuous System Simulation.
Poisson simulation is based on a form of differential/difference equation that models change in the number of entities in a compartment by Poisson processes that are fuctions of the state variables and time. Such a mechanism is appropriate in a very wide variety of situations. The method was first proposed by L. Gustafsson in 2000 ,  and is discussed further in the paper . It is there shown to be closely related to micro modelling, but it enables a much more efficient execution by aggregating entities. It therefore represents an additional useful tool in the modellers toolbox. The method is sometimes called the tau-leap method.
In the report [R1], Poisson simulation models are shown to be far superior to state-based Markov models in many respects, such as computational complexity and conceptual complexity.
Many application examples of using Poisson modelling and simulation
can be found in the book chapter  below. A Powersim implementation
for simulation and parameter estimation is described in [R3] and
a Matlab implementation is described in [R4].
Consistence between micro simulation, macro simulation and state-based (Markov) approachesAs outlined above, a population system can be modelled using a micro model focusing on the individual entities, a macro model where the entities are aggregated into compartments, or a state-based model where each possible discrete state in which the system can exist is represented.
However, the concepts, building blocks, procedural mechanisms and the time handling for theses approaches are very different. For the results and conclusions from studies based on micro, macro and state-based models to be consistent (contradiction-free), a number of modelling issues must be understood and appropriate modelling procedures applied.
The paper  presents a uniform approach to micro, macro and state-based population modelling so that these different types of models produce consistent results and conclusions. In particular, we demonstrate the procedures (distributional, attributal and combinational expansions) necessary to keep these three types of models consistent.
We also show that the different time handling
methods usually used in micro, macro and state-based
models can be regarded as different integration methods
that can be applied to any of these modelling categories.
The result is free choice in selecting the modelling approach
and the time handling method most appropriate for the
study without distorting the results and conclusions.
Deterministic versus stochastic modelling of population systems
In the paper , Poisson simulation is used as a tool to
investigate the question to what extent the results from
deterministic models of population models will correspond to the averages of the experiment outcomes from the corresponding
stochastic simulation models.
The investigation covers many causes of bias and it indicate
that deterministic simulation will almost always generate some form of bias in the results.
Modellers should be very restrictive in their use of
deterministic modeling of populations. Disciplines dealing
with population models (ecology, epidemology etc.)
should not base theories and studies only on deterministic models.