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A hybrid framework for compartmental models enabling simulation-based inference
Domenic P J Germano1,2, Alexander E Zarebski1,3, Sophie Hautphenne1
1The School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, Australia.
Journal of Mathematical Biology
|May 27, 2026
Summary
This study introduces Jump-Switch-Flow (JSF), a novel framework for simulating complex biological systems. JSF efficiently models both continuous and discrete dynamics, overcoming limitations of existing methods for population dynamics and disease spread.
Area of Science:
- Computational Biology
- Mathematical Modeling
- Systems Biology
Background:
- Multi-scale systems integrate stochastic and deterministic dynamics.
- Low occupancy compartments show stochasticity, high occupancy show deterministic dynamics.
- Existing methods struggle to represent both, leading to issues like 'atto-foxes' in small populations.
Purpose of the Study:
- To develop a mathematical framework coupling continuous ordinary differential equations (ODEs) and discrete continuous-time Markov chains (CTMCs).
- To address limitations in simulating systems with both high and low occupancy compartments.
- To overcome computational challenges in simulating CTMCs for high-frequency events.
Main Methods:
- Introduced the "Jump-Switch-Flow" (JSF) mathematical framework.
- Coupled continuous ODEs with discrete CTMCs.
- Enabled compartments to reach absorbing (extinct) states.
Main Results:
- JSF resolves 'atto-fox' problems by allowing compartment extinction.
- Achieved computational speeds at least one order of magnitude faster than alternatives.
- Demonstrated constant scaling irrespective of compartment occupancy.
- Enabled nuanced analysis of public health interventions and viral clearance in SARS-CoV-2 infections.
Conclusions:
- JSF offers a computationally efficient and accurate method for simulating multi-scale compartmental models.
- The framework overcomes limitations of existing simulation techniques.
- JSF is valuable for simulation-based inference in complex biological systems and public health.
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