Susceptible-Infected-Recovered model on Euclidean network

Abstract

We consider the Susceptible-Infected-Recovered (SIR) epidemic model on a Euclidean network in one dimension in which nodes at a distance $l$ are connected with probability $P(l)\propto l^{-\delta }$ in addition to nearest neighbors. The topology of the network changes as $\delta$ is varied and its effect on the SIR model is studied. $R(t)$, the recovered fraction of population up to time $t$, and $\tau$, the total duration of the epidemic are calculated for different values of the infection probability $q$ and $\delta$. A threshold behavior is observed for all $\delta$ up to $\delta \approx 2.0$; above the threshold value $q=q_c$, the saturation value $R_{sat}$ attains a finite value. Both $R_{sat}$ and $\tau$ show scaling behavior in a finite system of size $N$; $R_{sat}\sim N^{-\beta /\tilde{\nu }}{g}_1[(q-q_c)N^{1/\tilde{\nu }}]$ and $\tau \sim N^{\mu /\tilde{\nu }}{g}_2[(q-q_c)N^{1/\tilde{\nu }}]$. $q_c$ is constant for $0\le \delta <1$ and increases with $\delta$ for $1<\delta \lesssim 2$. Mean field behavior is seen up to $\delta \approx 1.3$; weak dependence on $\delta$ is observed beyond this value of $\delta$.The distribution of the outbreak sizes is also estimated and found to be unimodal for $q<q_c$ and bimodal for $q>q_c$. The results are compared to static percolation phenomenaand also to mean field results for finite systems. Discussions on the properties of the Euclidean network are made in the light of the present results.

8 pages,11 figures

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• Statistical physics of social dynamics
• Critical phenomena in complex networks
• Griffiths phases on complex networks
• Size of Outbreaks Near the Epidemic Threshold
• Long-range epidemic spreading with immunization
• Phase transitions in Ising model on a Euclidean network
• Phase transition of a one-dimensional Ising model with distance-dependent connections

Cited by in corpus (3)

• Effects of local and global network connectivity on synergistic epidemics
• Contact network models matching the dynamics of the COVID-19 spreading
• Infinite randomness critical behavior of the contact process on networks with long-range connections