Wusong Guo | Searcharxiv

arXiv2023

Epidemic extinction in a simplicial susceptible-infected-susceptible model

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 $β$ or by three-body interactions ($S+2I \to 3I$) with a rate $β(1+δ)$, and each infected individual spontaneously recovers ($I \to S$) with a rate $μ$. We focus on the case $δ>0$ 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 $β_b<β<β_c$ and for $β>β_c$, where $β_b=4 (1+δ)/(2+δ)^2$ and $β_c=1$ are two different bifurcation points. The action $\mathcal{S}$ shows different scaling laws with the distance of the infectious rate to the transition points $β_b$ and $β_c$, characterized by two different exponents: 3/2 and 1, respectively. Interestingly, the second-order derivative of $\mathcal{S}$ with respect to $β$ is discontinuous at $β=β_c$, 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.

cond-mat.stat-mech↗

arXiv2023

Extremal statistics for a resetting Brownian motion before its first-passage time

We study the extreme value statistics of a one-dimensional resetting Brownian motion (RBM) till its first passage through the origin starting from the position $x_0$ ($>0$). By deriving the exit probability of RBM in an interval $\left[0, M \right] $ from the origin, we obtain the distribution $P_r(M|x_0)$ of the maximum displacement $M$ and thus gives the expected value $\langle M \rangle$ of $M$ as functions of the resetting rate $r$ and $x_0$. We find that $\langle M \rangle$ decreases monotonically as $r$ increases, and tends to $2 x_0$ as $r \to \infty$. In the opposite limit, $\langle M \rangle$ diverges logarithmically as $r \to 0$. Moreover, we derive the propagator of RBM in the Laplace domain in the presence of both absorbing ends, and then leads to the joint distribution $P_r(M,t_m|x_0)$ of $M$ and the time $t_m$ at which this maximum is achieved in the Lapalce domain by using a path decomposition technique, from which the expected value $\langle t_m \rangle$ of $t_m$ is obtained explicitly. Interestingly, $\langle t_m \rangle$ shows a nonmonotonic dependence on $r$, and attains its minimum at an optimal $r^{*} \approx 2.71691 D/x_0^2$, where $D$ is the diffusion coefficient. Finally, we perform extensive simulations to validate our theoretical results.

cond-mat.stat-mech↗