Epidemic extinction in a simplicial susceptible-infected-susceptible model

Abstract

We study the extinction of epidemics in a simplicial susceptible-infected-susceptible model, where each susceptible individual becomes infected either by two-body interactions ($S+I\to 2I$) with a rate $\beta$ or by three-body interactions ($S+2I\to 3I$) with a rate $\beta (1+\delta )$, and each infected individual spontaneously recovers ($I\to S$) with a rate $\mu$. We focus on the case $\delta >0$ that embodies a synergistic reinforcement effect in the group interactions. By using the theory of large fluctuations to solve approximately for the master equation, we reveal two different scenarios for optimal path to extinction, and derive the associated action $\mathcal{S}$ for ${\beta }_b<\beta <{\beta }_c$ and for $\beta >{\beta }_c$, where ${\beta }_b=4(1+\delta )/(2+\delta {)}^2$ and ${\beta }_c=1$ are two different bifurcation points. The action $\mathcal{S}$ shows different scaling laws with the distance of the infectious rate to the transition points ${\beta }_b$ and ${\beta }_c$, characterized by two different exponents: 3/2 and 1, respectively. Interestingly, the second-order derivative of $\mathcal{S}$ with respect to $\beta$ is discontinuous at $\beta ={\beta }_c$, while $\mathcal{S}$ and its first-order derivative are both continuous, reminiscent of the second-order phase transitions in equilibrium systems. Finally, a rare-event simulation method is used to compute the mean extinction time, which depends exponentially on $\mathcal{S}$ and the size $N$ of the population. The simulations results are in well agreement with the proposed theory.

arXiv comment7 doulbe-column pages, 5 figures. arXiv admin note: text overlap with arXiv:1608.08715

References in corpus (44)

• Epidemic processes in complex networks
• The large deviation approach to statistical mechanics
• The physics of higher-order interactions in complex systems
• Simplicial models of social contagion
• Sampling rare switching events in biochemical networks
• Forward Flux Sampling for rare event simulations
• Theory of Branching and Annihilating Random Walks
• Social contagion models on hypergraphs
• Rare Events Statistics in Reaction--Diffusion Systems
• Field Theory of Branching and Annihilating Random Walks
• Extinction of metastable stochastic populations
• The effect of heterogeneity on hypergraph contagion models
• Abrupt phase transition of epidemic spreading in simplicial complexes
• WKB theory of large deviations in stochastic populations
• Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
• Disease extinction in the presence of non-Gaussian noise
• Population extinction in a fluctuating environment
• Extinction of an infectious disease: a large fluctuation in a non-equilibrium system
• Universal nonlinear infection kernel from heterogeneous exposure on higher-order networks
• Simplicial SIS model in scale-free uniform hypergraph
• Spectral theory of metastability and extinction in birth-death systems
• Epidemic extinction and control in heterogeneous networks
• Population extinction in a time-modulated environment
• Spectral theory of metastability and extinction in a branching-annihilation reaction
• Extinction rates of established spatial populations
• Population Dynamics in a Changing Environment: Random versus Periodic Switching
• Effective epidemic containment strategy in hypergraphs
• On population extinction risk in the aftermath of a catastrophic event
• Minimizing the population extinction risk by migration
• Extinction of oscillating populations
• Multiple extinction routes in stochastic population models
• Speeding up disease extinction with a limited amount of vaccine
• Demographic stochasticity and extinction in populations with Allee effect
• Epidemic fronts in complex networks with metapopulation structure
• Epidemic Extinction Paths in Complex Networks
• Rare Event Extinction on Stochastic Networks
• Impact of Colored Environmental Noise on the Extinction of a Long-Lived Stochastic Population: Role of the Allee Effect
• Degree Dispersion Increases the Rate of Rare Events in Population Networks
• Enhancement of large fluctuations to extinction in adaptive networks
• Fast migration and emergent population dynamics
• Time-resolved extinction rates of stochastic populations
• Population switching under a time-varying environment
• Extinction risk of a Metapopulation under the Allee Effect
• Epidemic extinction in a generalized susceptible-infected-susceptible model