### Abstract

through plantsthe shape of the plots and fields where the host of the disease is located may play a fundamental role on the propagation dynamics. Here we consider a generalization of the RGG to account for the variation of the shape of the plots/fields where the hosts of a disease are allocated. We consider a disease propagation taking place on the nodes of a random rectangular graph (RRG) and we consider a lower bound for the epidemic threshold of a Susceptible-Infected-

Susceptible (SIS) or Susceptible-Infected-Recovered (SIR) model on these networks. Using extensive numerical simulations and based on our analytical results we conclude that (ceteris paribus) the elongation of the plot/field in which the nodes are distributed makes the network more resilient to the propagation of a disease due to the fact that the epidemic threshold increases with the elongation of the rectangle. These results agree with accumulated empirical evidence and simulation results about the propagation of diseases on plants in plots/fields of the same area and different shapes.

Language | English |
---|---|

Article number | 052316 |

Number of pages | 9 |

Journal | Physical Review E |

Volume | 94 |

Issue number | 5 |

DOIs | |

Publication status | Published - 28 Nov 2016 |

### Fingerprint

### Keywords

- network theory
- disease propagation
- random geometric graphs
- RGGs

### Cite this

*Physical Review E*,

*94*(5), [052316]. https://doi.org/10.1103/PhysRevE.94.052316

}

*Physical Review E*, vol. 94, no. 5, 052316. https://doi.org/10.1103/PhysRevE.94.052316

**Epidemic spreading in random rectangular networks.** / Estrada, Ernesto; Meloni, Sandro; Sheerin, Matthew; Moreno, Yamir.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Epidemic spreading in random rectangular networks

AU - Estrada, Ernesto

AU - Meloni, Sandro

AU - Sheerin, Matthew

AU - Moreno, Yamir

PY - 2016/11/28

Y1 - 2016/11/28

N2 - The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGG) is one of such network models that allows for the consideration of spatial properties on disease propagation. In certain real-world scenarioslike in the analysis of a disease propagatingthrough plantsthe shape of the plots and fields where the host of the disease is located may play a fundamental role on the propagation dynamics. Here we consider a generalization of the RGG to account for the variation of the shape of the plots/fields where the hosts of a disease are allocated. We consider a disease propagation taking place on the nodes of a random rectangular graph (RRG) and we consider a lower bound for the epidemic threshold of a Susceptible-Infected-Susceptible (SIS) or Susceptible-Infected-Recovered (SIR) model on these networks. Using extensive numerical simulations and based on our analytical results we conclude that (ceteris paribus) the elongation of the plot/field in which the nodes are distributed makes the network more resilient to the propagation of a disease due to the fact that the epidemic threshold increases with the elongation of the rectangle. These results agree with accumulated empirical evidence and simulation results about the propagation of diseases on plants in plots/fields of the same area and different shapes.

AB - The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGG) is one of such network models that allows for the consideration of spatial properties on disease propagation. In certain real-world scenarioslike in the analysis of a disease propagatingthrough plantsthe shape of the plots and fields where the host of the disease is located may play a fundamental role on the propagation dynamics. Here we consider a generalization of the RGG to account for the variation of the shape of the plots/fields where the hosts of a disease are allocated. We consider a disease propagation taking place on the nodes of a random rectangular graph (RRG) and we consider a lower bound for the epidemic threshold of a Susceptible-Infected-Susceptible (SIS) or Susceptible-Infected-Recovered (SIR) model on these networks. Using extensive numerical simulations and based on our analytical results we conclude that (ceteris paribus) the elongation of the plot/field in which the nodes are distributed makes the network more resilient to the propagation of a disease due to the fact that the epidemic threshold increases with the elongation of the rectangle. These results agree with accumulated empirical evidence and simulation results about the propagation of diseases on plants in plots/fields of the same area and different shapes.

KW - network theory

KW - disease propagation

KW - random geometric graphs

KW - RGGs

U2 - 10.1103/PhysRevE.94.052316

DO - 10.1103/PhysRevE.94.052316

M3 - Article

VL - 94

JO - Physical Review E

T2 - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 5

M1 - 052316

ER -