Bio-PEPA for Epidemiological Models

Many models have been defined in order to describe the evolution of a disease in a population. The modelling of diseases is helpful to understand the mechanisms for their spread and to predict their future evolution. Most of the models in the literature are defined in terms of systems of differential equations and only a few of them propose stochastic simulation for the analysis.

The main aim of this work is to apply the process algebra Bio-PEPA for the modelling and analysis of epidemiological models. As Bio-PEPA has been originally defined for biochemical networks, we define a variant of it suitable for representing epidemiological models. Some features of Bio-PEPA are useful in the context of epidemiology as well: location can abstract spatial structure and event can describe the introduction of prophylaxis in a population infected by a disease at a given day. Concerning the analysis, we can take advantage of the various kinds of analysis supported by Bio-PEPA, such as, for instance, stochastic simulation, model checking and ODE-based analyses. In particular, the modeller can select the most appropriate approach for the study of the model and analysis techniques can be used together for a better understanding of the behaviour of the system.

In this paper we apply Bio-PEPA to the study of epidemiological models of avian influenza, based on different assumptions about the spatial structure and the possible kind of treatment. These models demonstrate that Bio-PEPA has several features that facilitate epidemiological modelling.