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Disease modelers have been modeling progression of diseases for several decades using tools such as Markov Models or microsimulation. However, they need to address a serious challenge; many models they create are not reproducible. Moreover, there is no proper practice that ensures reproducible models, since modelers rely on loose guidelines that change periodically, rather than well-defined machine-readable standards. The Systems Biology Markup Language (SBML) is one such standard that allows exchange of models amongst different software tools. Recently, the SBML Arrays package has been developed, which extends the standard to allow handling simulation of populations. This paper demonstrates through several abstract examples how microsimulation disease models can be encoded using the SBML Arrays package enabling reproducible disease modeling. 

Motivation: Systems biology models are typically simulated using a single formalism such as ordinary differential equations (ODE) or stochastic methods. However, more complex models require the coupling of multiple formalisms since different biological concepts are better described using different methods, e.g., stationary metabolism is often modeled using flux-balance analysis (FBA) whereas dynamic changes of model components are better described via ODEs. The coupling of FBA and ODE frameworks results in dynamic FBA models. A major challenge is how to describe such hybrid models coupling multiple frameworks in a standardized way, so that they can be exchanged between tools and simulated consistently and in a reproducible manner. Results: This paper presents a scheme and implementation for encoding dynamic FBA models in the Systems Biology Markup Language (SBML), thereby allowing to exchange multi-framework computational models between software tools. The paper shows the feasibility of the approach using various example models and demonstrates that different tools are able to simulate the hybrid models and agree on the results. As part of this work, two independent implementations of a multi-framework simulation method for dynamic FBA have been developed supporting such models: iBioSim and sbmlutils. Availability: All materials and models are available from https://github.com/matthiaskoenig/dfba. The tools used in this project are freely available: iBioSim at http://www.async.ece.utah.edu/ibiosim and sbmlutils at https://github.com/matthiaskoenig/sbmlutils/.