Basic reproduction number of epidemic models on sparse networks,Physical Review E

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Basic reproduction number of epidemic models on sparse networks
Physical Review E ( IF 2.2 ) Pub Date : 2022-09-22 , DOI: 10.1103/physreve.106.034318
Satoru Morita ₁

Affiliation

The basic reproduction number

R_{0}

is a standard indicator of infection control in epidemiology. Although

R_{0}

has been studied extensively for deterministic epidemic models, it has not been formulated accurately for models adopting network structures. Here, we extend a four-compartment model that includes commonly used epidemic models to a Markov process on networks. By examining the Markov process in detail, we derive a canonical formula for

R_{0}

involving two probability values. Numerical calculations show that the derived formula is a better approximation than the conventional formula when the network is very sparse. We propose this as a standard formula for controlling infections that can only be transmitted through intimate contact, where contacts between individuals can be described as a sparse network.

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