TY - JOUR

T1 - Effects of void nodes on epidemic spreads in networks

AU - Kuga, Kazuki

AU - Tanimoto, Jun

N1 - Funding Information:
This study was partially supported by the Grant-in-Aid for Scientific Research (KAKENHI) from JSPS (Grant Nos. JP 19KK0262, JP 20H02314, JP 20K21062) awarded to Professor Tanimoto. We appreciate Mr. Md. Rajib Arefin’s substantial inputs to deepen the discussion.
Publisher Copyright:
© 2022, The Author(s).

PY - 2022/12

Y1 - 2022/12

N2 - We present the pair approximation models for susceptible–infected–recovered (SIR) epidemic dynamics in a sparse network based on a regular network. Two processes are considered, namely, a Markovian process with a constant recovery rate and a non-Markovian process with a fixed recovery time. We derive the implicit analytical expression for the final epidemic size and explicitly show the epidemic threshold in both Markovian and non-Markovian processes. As the connection rate decreases from the original network connection, the epidemic threshold in which epidemic phase transits from disease-free to endemic increases, and the final epidemic size decreases. Additionally, for comparison with sparse and heterogeneous networks, the pair approximation models were applied to a heterogeneous network with a degree distribution. The obtained phase diagram reveals that, upon increasing the degree of the original random regular networks and decreasing the effective connections by introducing void nodes accordingly, the final epidemic size of the sparse network is close to that of the random network with average degree of 4. Thus, introducing the void nodes in the network leads to more heterogeneous network and reduces the final epidemic size.

AB - We present the pair approximation models for susceptible–infected–recovered (SIR) epidemic dynamics in a sparse network based on a regular network. Two processes are considered, namely, a Markovian process with a constant recovery rate and a non-Markovian process with a fixed recovery time. We derive the implicit analytical expression for the final epidemic size and explicitly show the epidemic threshold in both Markovian and non-Markovian processes. As the connection rate decreases from the original network connection, the epidemic threshold in which epidemic phase transits from disease-free to endemic increases, and the final epidemic size decreases. Additionally, for comparison with sparse and heterogeneous networks, the pair approximation models were applied to a heterogeneous network with a degree distribution. The obtained phase diagram reveals that, upon increasing the degree of the original random regular networks and decreasing the effective connections by introducing void nodes accordingly, the final epidemic size of the sparse network is close to that of the random network with average degree of 4. Thus, introducing the void nodes in the network leads to more heterogeneous network and reduces the final epidemic size.

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U2 - 10.1038/s41598-022-07985-9

DO - 10.1038/s41598-022-07985-9

M3 - Article

C2 - 35273312

AN - SCOPUS:85126179012

SN - 2045-2322

VL - 12

JO - Scientific reports

JF - Scientific reports

IS - 1

M1 - 3957

ER -