Stochastic Population Models: A Compartmental Perspective

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Rerun the simulation. In a perspective to reduce antibiotic use, metaphylaxis collective treatment triggered after first cases are detected was compared to early detection methods, based on sensors measuring hyperthermia durations. Think of each compartment as a room in a house. Oecologia , 83— Modeling targeted layered containment of an influenza pandemic in the United States. What happens to the trajectory in phase space?

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About This Item We aim to show you accurate product information. Manufacturers, suppliers and others provide what you see here, and we have not verified it. See our disclaimer. However, developing realistic models which involve multi-disciplinary knowledge integration faces three major challenges in predictive epidemiology: lack of readability once translated into simulation code, low reproducibility and reusability, and long development time compared to outbreak time scale.

Stochastic population models: A compartmental perspective. (Book Reviews)

We introduce here EMULSION, an artificial intelligence-based software intended to address those issues and help modellers focus on model design rather than programming. EMULSION defines a domain-specific language to make all components of an epidemiological model structure, processes, parameters… explicit as a structured text file. This file is readable by scientists from other fields epidemiologists, biologists, economists , who can contribute to validate or revise assumptions at any stage of model development. The modelling language and simulation architecture both rely on the combination of advanced artificial intelligence methods knowledge representation and multi-level agent-based simulation , allowing several modelling paradigms from compartment- to individual-based models at several scales up to metapopulation.

The flexibility of EMULSION and its capability to support iterative modelling are illustrated here through examples of progressive complexity, including late revisions of core model assumptions. It is released under Apache PLoS Comput Biol 15 9 : e This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: All relevant data are within the manuscript and its Supporting Information files.

The funders did not play any role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. Understanding and predicting the spread of pathogens at several scales from individuals to territories under various scenarios control measures, climate, etc.

Yet, predictive epidemiology is currently facing key methodological challenges which could be faced mobilizing Artificial Intelligence AI technologies. Second, epidemiological models highly depend on implementation details, which affects reusability in even slightly different contexts. Third, developing mechanistic models for complex systems is an iterative process, rendering it difficult to get reliable forecasts in a duration relevant with regards to on-field needs e.

Fourth, the complexity of realistic models often leads to misinterpretations coming from programming biases [ 6 ], thus it is difficult to ensure that model assumptions are correctly implemented in the simulation code. Fifth, model granularity is likely to change throughout the model development process, either to account for increased detail level, or conversely to keep only relevant features at a broader scale.

Changes in core model assumptions can also occur late in the modelling process, for instance because a feature first considered negligible must finally be accounted for. This requires a capability to move back and forth between modelling paradigms stochastic vs. To address such challenges, the implementation of epidemiological models must first gain transparency, in order to make all assumptions as explicit as possible.

Models are a deliberately simplified representation of reality, thus it is crucial to present the underlying assumptions and their implications, to help understand their benefits and limitations and assess their relevance. Once models are translated into simulation code which is the usual process , scientists without programming skills, involved either in the co-design of the model or in a peer-reviewing process, cannot develop a thorough understanding of the models nor make an informed judgment.

Instead, models should be described in a readable form. On the other hand, enhancing reusability requires reproducibility the capability for others to recode a model and flexibility the possibility to adapt it. Though necessary, best practices in software engineering [ 9 ] cannot settle those issues alone: ad hoc codes can be documented, tested, reproducible, and yet wrong [ 10 ]. A first step to reduce development time and errors is to use simulation platforms, which provide high-level built-in features.

In general-purpose platforms such as GAMA [ 11 ], NetLogo [ 12 ] or Repast [ 13 ], a substantial programming effort is still required as algorithms involved in epidemiological models are not provided as platform features. Simulation libraries and platforms dedicated to epidemiological issues are rising, e.

SimInf [ 14 ], a R library for data-driven compartment-based models; MicroSim [ 15 ], an agent-based platform for several kinds of diseases; or GLEaMviz [ 16 ], a metapopulation-oriented platform. To our knowledge, the most advanced approach in terms of diversity of modelling paradigms is Broadwick [ 17 ], a Java framework for compartment- and individual-based models with interaction networks, which nevertheless still requires writing large portions of code to derive specific classes and carry out simulations on practical cases.

Artificial intelligence AI can help going further, as demonstrated in a promising approach, KENDRICK [ 18 ], which defines a domain-specific language DSL, [ 19 ] , which allows to describe models as text files rather than executable code, enforces a clear separation of concerns infection, demography, etc. To the best of our knowledge, none of existing solutions address those methodological challenges simultaneously, the most advanced approaches providing either a flexibility in modelling paradigms at the expense of software development efforts, or an enhanced readability through a DSL limited to a specific modelling paradigm.

  • Stochastic Population Models: A Compartmental Perspective by J.H. Matis, T.R. Kiffe -
  • Original Research ARTICLE?
  • Inclusions in Prokaryotes: 1 (Microbiology Monographs).
  • 1. Introduction.

EMULSION intends to help modellers develop mechanistic stochastic models of complex systems in epidemiology at several scales using multiple paradigms, and to facilitate the co-construction and assessment of model components biological assumptions, model structure, parameters, scenarios, etc. This makes our software an outstanding contribution towards reliable, reactive and transparent predictive epidemiology. The first one is a DSL designed for the description of all components of an epidemiological model, to make them explicit in a human-readable form as a structured text file, so that scientists from different fields can better interact with modellers throughout the modelling process, and discuss, assess or revise model structure, assumptions, parameters at any moment without having to read or write any line of simulation code. The second one is the use of a generic simulation engine, whose core architecture relies upon a multi-level agent-based system [ 21 ]. This allows several scales individuals, groups, populations, metapopulations and modelling paradigms compartment- or individual-based models to be encompassed within a homogeneous software interface, as agents act as wrappers which can be dynamically combined regardless of what they have to compute and the scale at which they operate. To run an experiment, the simulation engine reads the DSL file containing the model description, assembles the agents required for a particular type of model and a specific scale, initializes parameters, functions, processes specified in the DSL file, and make them interact to produce simulation outputs Fig 1.

A generic simulation engine is coupled to a domain-specific modelling language DSL , reinforcing interactions between modellers and scientists from other fields. Knowledge involved in epidemiological models is kept explicit, understandable and revisable as a structured text file. A few specific software add-ons can be written to complement the simulation engine if needed.

Processes occurring in the pathosystem infection, demography, migrations… are a core component of epidemiological models, often described by flow diagrams [ 22 , 23 ] with nodes denoting state variables amount of individuals in each state , and transitions labelled with rates. Though flow diagrams can be easily derived into ordinary differential equations or into stochastic difference equations, they often mix several concerns in a unique, monolithic representation, involve implicit computational assumptions e.

EMULSION relies upon a formalism close to flow diagrams but more accurate: finite state machines [ 24 ], classically used in computer science. Compared to flow diagrams, state machines describe the evolution of one individual instead of a population, and one state machine represents one single process, so that a complex flow diagram may be split into several simpler state machines. Besides, states can be endowed with additional properties, such as a duration distribution specifying how long an individual is expected to stay in the current state, and actions performed by individuals when entering, being in, or leaving the state.

Transitions are labelled with either a rate, a probability or an absolute amount rates are automatically converted into probabilities. They can also specify: 1 calendar conditions to indicate time periods when transitions are available; 2 escape conditions allowing to free from state duration constraints; 3 individual conditions to filter which agents are allowed to cross the transition; 4 actions performed by individuals crossing the transition, i. Individuals can be given a duration and actions when entering, staying in, or leaving the state. Transitions feature a rate, probability, or amount, and can be associated with actions performed on crossing, time-dependent "calendar" conditions, or individual conditions restricting the capability to cross the transition, and escape conditions allowing individuals to leave their state before the nominal duration.

SEIR Model - Differential Equations in Action

Multi-agent systems are composed of autonomous entities agents endowed with a behaviour and interacting in a shared environment. In the last decade, multi-level agent-based systems emerged using agents to explicitly represent intermediary abstraction levels groups, sub-populations, organizations… with behaviours of their own, between individuals and the whole system [ 25 — 28 ]. Recent advances in this field [ 21 ] led to design patterns, i.

Those patterns were used in EMULSION to build the architecture of the generic simulation engine, in which nested agents are in charge of implementing a specific modelling paradigm at a given scale. Agents currently defined in EMULSION allow to implement the main paradigms used in epidemiological models: 1 compartment-based models [ 29 ], where state variables represent aggregate amounts of individuals which only differ by few key variables, such as health state or age group; and 2 individual-based models [ 30 ] necessary for finer grained representations.

Besides, EMULSION provides a hybrid approach which combines the capability of representing detailed information through individuals, with an adaptive grouping of individuals based on their state, to optimize computation Fig 3 , and Table A in S1 Appendix. The same approach allows to wrap different scales within agents to build either groups, populations, or metapopulations [ 31 , 32 ] which can handle region-wide models at a moderate computational cost focusing only on relevant populations endowed with a contact structure.

Scales and paradigms can be chosen independently: hence, a metapopulation at regional scale can rely at the local scale upon compartment-based, individual-based or hybrid models, depending on the required detail level. In this modular architecture, simulations are run in discrete time to better cope with the potential complexity of interactions between agents from all scales.

EMULSION allows to represent within a same formalism nested agents several modelling paradigms, from the finest grained individuals to aggregations compartments , including intermediary representations as a trade-off between computation time and preservation of individual details.

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This monograph has been heavily influenced by two books. One is Ren shaw's [ 82] work on modeling biological populations in space and time. It was published . Request PDF on ResearchGate | On Jan 1, , James H. Matis and others published Stochastic population models. A compartmental perspective.

The chosen modelling paradigm is associated with the appropriate combinations of agents. The main benefits of the DSL defined in EMULSION are a modular decomposition of the model, which reduces dependencies between model components and facilitates further extensions, and a high readability by non-modeller scientists.

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When EMULSION simulation engine reads the DSL, it selects the agent classes corresponding to the chosen paradigm and scales, instantiate agents depending on initial conditions, transforms expressions into Python functions using SymPy, a library for symbolic computation , builds the state machines, and runs the simulations. Hence, the execution of simulations based on an EMULSION model is univocal, all required information being directly usable yet human-readable by the simulation engine.

In very specific cases, processes or actions may require the definition of small code add-ons, as demonstrated below for data-driven events in a metapopulation.

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But in the majority of situations, no additional code is required. Section and subsection names are chosen to be as self-evident as possible, and a substantial part of the documentation is dedicated to explaining the syntax of the DSL in detail, with comprehensive examples and tutorials. Almost all items have to be accompanied by a textual description of their meaning and role.

Also, in S1 Appendix , the three modelling paradigms provided by EMULSION compartment, hybrid and individual-based are compared on two SIR models one with constant population, one with birth and death processes : differences in model files are presented side-by-side to highlight how to transform one paradigm into the other; simulation outcomes are shown for the three paradigms in each model implemented with EMULSION and for the equivalent compartment-based model implemented with the R library SimInf [ 14 ]. We illustrate this below with an example from within-population to between-population scales, and demonstrate how easy it is to operate late changes in core model assumptions.

First, a classical SIR model is developed S: susceptible, I: infectious, R: resistant , assuming a frequency-dependent force of infection.

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In this example, we use the hybrid modelling paradigm, where individuals are grouped according to similar health states. Infectious Diseases of Humans. Oxford Univ.