Bio-PEPA for Epidemiological Models

AbstractMany 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

PEPA'd Oysters: Converting Dynamic Energy Budget Models to Bio-PEPA, illustrated by a Pacific oyster case study

We present a Bio-PEPA (Biochemical-Performance Evaluation Process Algebra) computational model for the Pacific oyster, derived from a DEB (Dynamic Energy Budget) mathematical model. Experience with this specific model allows us to propose a generic scheme for translation between the widely-used DEB theory and Bio-PEPA. The benefits of translation are that a range of novel analysis tools become available, therefore improving the potential to understand complex biological phenomena at a systems level. This work also provides a link between biology, mathematics and computer science: such interlinking of disciplines is the core of the systems approach to biology

A rigorous approach to investigating common assumptions about disease transmission: Process algebra as an emerging modelling methodology for epidemiology

Changing scale, for example the ability to move seamlessly from an individual-based model to a population-based model, is an important problem in many fields. In this paper we introduce process algebra as a novel solution to this problem in the context of models of infectious disease spread. Process algebra allows us to describe a system in terms of the stochastic behaviour of individuals, and is a technique from computer science. We review the use of process algebra in biological systems, and the variety of quantitative and qualitative analysis techniques available. The analysis illustrated here solves the changing scale problem: from the individual behaviour we can rigorously derive equations to describe the mean behaviour of the system at the level of the population. The biological problem investigated is the transmission of infection, and how this relates to individual interaction

Improving process algebra model structure and parameters in infectious disease epidemiology through data mining

Computational models are increasingly used to assist decision-making in public health epidemiology, but achieving the best model is a complex task due to the interaction of many components and variability of parameter values causing radically different dynamics. The modelling process can be enhanced through the use of data mining techniques. Here, we demonstrate this by applying association rules and clustering techniques to two stages of mod- elling: identifying pertinent structures in the initial model creation stage, and choosing optimal parameters to match that model to observed data. This is illustrated through application to the study of the circulating mumps virus in Scotland, 2004-2015

Decision Support Based on Bio-PEPA Modeling and Decision Tree Induction: A New Approach, Applied to a Tuberculosis Case Study

The problem of selecting determinant features generating appropriate model structure is a challenge in epidemiological modelling. Disease spread is highly complex, and experts develop their understanding of its dynamic over years. There is an increasing variety and volume of epidemiological data which adds to the potential confusion. We propose here to make use of that data to better understand disease systems. Decision tree techniques have been extensively used to extract pertinent information and improve decision making. In this paper, we propose an innovative structured approach combining decision tree induction with Bio-PEPA computational modelling, and illustrate the approach through application to tuberculosis. By using decision tree induction, the enhanced Bio-PEPA model shows considerable improvement over the initial model with regard to the simulated results matching observed data. The key finding is that the developer expresses a realistic predictive model using relevant features, thus considering this approach as decision support, empowers the epidemiologist in his policy decision making

Epidemic Analysis Using Traditional Model Checking and Stochastic Simulation

Stochastic model checking has been the mainstay for formal analysis of epidemic progression in recent years. However, such methods are sensitive to inaccuracies in estimating stochastic parameters like infection transmission and recovery rates. In this work, we revert to traditional model checking (specifically, for timed automata) to absorb inaccurately provided parameters into the non-determinism inherent in such traditional formalisms. Parameters obtained through stochastic simulation are used by the timed automata, with suficiently wide windows of non-determinism to account for error. A positive side effect of this approach is that separating the probabilistic component from actual epidemic timed automata model, helps us to focus on the progression logic while building the model

MELA: Modelling in Ecology with Location Attributes

Ecology studies the interactions between individuals, species and the environment. The ability to predict the dynamics of ecological systems would support the design and monitoring of control strategies and would help to address pressing global environmental issues. It is also important to plan for efficient use of natural resources and maintenance of critical ecosystem services. The mathematical modelling of ecological systems often includes nontrivial specifications of processes that influence the birth, death, development and movement of individuals in the environment, that take into account both biotic and abiotic interactions. To assist in the specification of such models, we introduce MELA, a process algebra for Modelling in Ecology with Location Attributes. Process algebras allow the modeller to describe concurrent systems in a high-level language. A key feature of concurrent systems is that they are composed of agents that can progress simultaneously but also interact - a good match to ecological systems. MELA aims to provide ecologists with a straightforward yet flexible tool for modelling ecological systems, with particular emphasis on the description of space and the environment. Here we present four example MELA models, illustrating the different spatial arrangements which can be accommodated and demonstrating the use of MELA in epidemiological and predator-prey scenarios.Comment: In Proceedings QAPL'16, arXiv:1610.0769

A review of modelling and verification approaches for computational biology

This paper reviews most frequently used computational modelling approaches and formal verification techniques in computational biology. The paper also compares a number of model checking tools and software suits used in analysing biological systems and biochemical networks and verifiying a wide range of biological properties