dynamic systems
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2022 ◽  
Vol 156 ◽  
pp. 111781
Chao Wang ◽  
Ravi P. Agarwal ◽  
Donal O’Regan

2022 ◽  
Vol 32 (1) ◽  
pp. 1-27
Damian Vicino ◽  
Gabriel A. Wainer ◽  
Olivier Dalle

Uncertainty Propagation methods are well-established when used in modeling and simulation formalisms like differential equations. Nevertheless, until now there are no methods for Discrete-Dynamic Systems. Uncertainty-Aware Discrete-Event System Specification (UA-DEVS) is a formalism for modeling Discrete-Event Dynamic Systems that include uncertainty quantification in messages, states, and event times. UA-DEVS models provide a theoretical framework to describe the models’ uncertainty and their properties. As UA-DEVS models can include continuous variables and non-computable functions, their simulation could be non-computable. For this reason, we also introduce Interval-Approximated Discrete-Event System Specification (IA-DEVS), a formalism that approximates UA-DEVS models using a set of order and bounding functions to obtain a computable model. The computable model approximation produces a tree of all trajectories that can be traversed from the original model and some erroneous ones introduced by the approximation process. We also introduce abstract simulation algorithms for IA-DEVS, present a case study of UA-DEVS, its IA-DEVS approximation and, its simulation results using the algorithms defined.

PLoS ONE ◽  
2022 ◽  
Vol 17 (1) ◽  
pp. e0262244
Geon Lee ◽  
Se-eun Yoon ◽  
Kijung Shin

Given a sequence of epidemic events, can a single epidemic model capture its dynamics during the entire period? How should we divide the sequence into segments to better capture the dynamics? Throughout human history, infectious diseases (e.g., the Black Death and COVID-19) have been serious threats. Consequently, understanding and forecasting the evolving patterns of epidemic events are critical for prevention and decision making. To this end, epidemic models based on ordinary differential equations (ODEs), which effectively describe dynamic systems in many fields, have been employed. However, a single epidemic model is not enough to capture long-term dynamics of epidemic events especially when the dynamics heavily depend on external factors (e.g., lockdown and the capability to perform tests). In this work, we demonstrate that properly dividing the event sequence regarding COVID-19 (specifically, the numbers of active cases, recoveries, and deaths) into multiple segments and fitting a simple epidemic model to each segment leads to a better fit with fewer parameters than fitting a complex model to the entire sequence. Moreover, we propose a methodology for balancing the number of segments and the complexity of epidemic models, based on the Minimum Description Length principle. Our methodology is (a) Automatic: not requiring any user-defined parameters, (b) Model-agnostic: applicable to any ODE-based epidemic models, and (c) Effective: effectively describing and forecasting the spread of COVID-19 in 70 countries.

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