Core Concepts
Open multi-agent systems can be effectively analyzed using replacements to approximate the dynamics of SIS epidemics.
Abstract
This paper analyzes continuous-time SIS epidemics in open networks, focusing on arrivals and departures of agents. By using an approximated process based on replacements, the study delves into the impact of changes in the set of agents on epidemic behavior. Stability results, Lyapunov functions, and upper bounds for expectations and variances are derived. The analysis extends to time-varying networks and considers mobility's role in disease spread. The study also introduces a numerical example to demonstrate the closeness between the original SIS process and its approximation with replacements.
I. Introduction
- Epidemic models like SIS are crucial for understanding contagion.
- Stability results often rely on network structures.
- Mobility plays a significant role in disease spread analysis.
II. SIS Model on Closed Networks
- Definition and features of classical SIS model.
- Stability conditions for disease-free equilibrium.
III. Open SIS Epidemics
- Formulation of SIS epidemic with arrivals and departures.
- Consideration of replacements as an approximation method.
IV. Replacements as an Approximation
- Analysis of aggregate function during replacement events.
- Proposition regarding aggregate function behavior under replacements.
V. First Moment
- Behavior analysis of aggregate function under pure replacement processes.
- Derivation of upper bounds for expectation values.
VI. Second Moment
- Analysis of variance in aggregate function due to agent replacements.
- Proposition establishing upper bounds for second moment expectations.
VII. Numerical and Simulation Results
- Illustrative computations showcasing moments evolution.
VIII. Conclusion
- Summary of findings regarding approximating open multi-agent systems with replacements.
Stats
この論文では、代替物を使用してSIS流行のダイナミクスを近似する方法に焦点を当てています。