Deterministic Bounding Systems for Stochastic Compartmental Spreading\n Processes

2015/07/18 by Nicholas J. Watkins, Watkins, Nicholas J., Cameron Nowzari +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Cellular Automata and Applications #Diffusion and Search Dynamics #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1507.05208

openalex publication_date 2015/07/18 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28

Abstract

This paper studies a novel approach for approximating the behavior of\ncompartmental spreading processes. In contrast to prior work, the methods\ndeveloped describe a dynamics which bound the exact moment dynamics, without\nexplicitly requiring a priori knowledge of non-negative (or non-positive)\ncovariance between pairs of system variables. Moreover, we provide systems\nwhich provide both upper- and lower- bounds on the process moments. We then\nshow that when system variables are shown to be non-negatively (or\nnon-positively) correlated for all time in the system's evolution, we may\nleverage the knowledge to create better approximating systems. We then apply\nthe technique to several previously studied compartmental spreading processes,\nand compare the bounding systems' performance to the standard approximations\nstudied in prior literature.\n

Citations

• Moment Closure Approximations in a Genetic Negative Feedback Circuit
• Exact Markovian SIR and SIS epidemics on networks and an upper bound for\n the epidemic threshold

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