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All Journal Statistika Journal of the Indonesian Mathematical Society Jurnal Matematika & Sains Journal of Mathematical and Fundamental Sciences Indonesian Journal of Science and Technology JOURNAL OF EARTH ENERGY ENGINEERING Journal of Fundamental Mathematics and Applications (JFMA) International Journal of Computing Science and Applied Mathematics-IJCSAM
Agus Yodi Gunawan
Industrial And Financial Mathematics Research Group, Institut Teknologi Bandung (ITB)
Astronomy Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Energy Engineering Environmental Science Industrial & Manufacturing Engineering Materials Science & Nanotechnology Mathematics Physics

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A Probability Flux Approach for Binary Dynamics on Networks Mohamad Riyadi; Agus Yodi Gunawan; Dewi Handayani
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 11 No. 2 (2025)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.ijcsam.v11i2.8848

Abstract

Binary-state dynamics on networks provide a powerfulframework for modeling epidemics and related spreading processes.Two main approaches are commonly used, namely exactcontinuous-time Markov chain (CTMC) formulations and meanfieldapproximations. The CTMC approach ensures stochastic accuracybut suffers from exponential state-space growth, whereasmean-field approximations lose reliability in heterogeneous orsmall networks. In this study, we formulate the master equationfor binary dynamics using a probability flux approach, yieldingan exact formulation for arbitrary networks. By integrating localtransition rules, network topology, and state-space partitioning,the framework captures microscopic dynamics while enablingmacroscopic analysis. Numerical simulations reveal that bothstate probabilities and expected infection levels are influencednot only by mean degree but also by structural heterogeneity.For instance, star and line topologies exhibit distinct behaviorsdespite having identical connectivity. Spectral analysis confirmsthe asymptotic stability of the disease-free equilibrium, whileinvariance under node relabeling emphasizes the role of graphsymmetries in reducing state-space complexity. This work extendsflux-based theory to network epidemics and provides a foundationfor future studies on adaptive or time-varying networks.Index Terms - Binary dynamics, probability flux, master equation,CTMC, ep
Co-Authors Aang Nuryaman Aceng Komarudin Mutaqin Anggita Septiani Dewi Handayani Edward L. Tobing Edy Soewono Edy Soewono Fachry Abda El Rahman Iskandar Fahmi Kartika Yulianti Kasbawati Kasbawati Kuntjoro Adji Sidarto Kuntjoro Adji Sidarto Kurni Permadi Mohamad Riyadi Nina Fitriyati NURTITI SUNUSI Pratama, Muchamad Harry Yudha Pudjo Sukarno Ray Novita Yasa Rini Marwati S. Sutawanir Septoratno Siregar Silvya Dewi Rahmawati Sri Wahyuningsih Sutawanir Darwis Tasmi Tasmi, Tasmi Yogi Wibisono Budhi ZAI, FIDELIS NOFERTINUS