Mean-Field and Pairwise Approaches for the SIRI Model on Poisson Networks
Akshara Bhat, Abhishek Deshpande, Chittaranjan Hens, Subrata Ghosh
TLDR
This paper shows when complex SIRI epidemic dynamics on Poisson networks can be accurately approximated by simpler mean-field equations.
Key contributions
- Analyzes the SIRI epidemic model, including relapse, on Poisson random networks.
- Identifies parameter conditions where network SIRI dynamics align with mass-action ODEs.
- Shows alignment occurs when transmission per contact is low relative to recovery rate.
- Provides a framework to approximate complex network SIRI dynamics with simpler mean-field models.
Why it matters
Understanding epidemic spread on networks is crucial but often complex. This paper simplifies the analysis of the SIRI model, which includes relapse, by showing when its network dynamics can be approximated by more tractable mean-field equations. This has implications for modeling diseases with reactivation or behavioral contagions.
Original Abstract
Compartmental epidemic models, grounded in mass-action kinetics, often assume homogeneous mixing. Although this neglects network structure, recent results show that for Poisson random graphs, the classical SIR model, especially the susceptible decay curve, matches the susceptible decay dynamics of its network counterpart. Motivated by this, we investigate whether the extended SIRI model with relapse from the recovered class admits a similar correspondence. SIRI dynamics arise in sevaral scenarios like spread of diseases with reactivation and behavioral contagion with relapse. We derive parameter relationships under which the pairwise SIRI model on a Poisson network closely follows the mass-action ODE trajectories. When transmission per contact is small relative to recovery, the susceptible and infectious trajectories of both systems align. This establishes conditions under which nonlinear SIRI dynamics on networks can be effectively approximated by tractable mean-field equations.
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