# Effects of Community Connectivity on the Spreading Process of Epidemics

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## Abstract

**:**

## 1. Introduction

## 2. Community Network Model

## 3. Infectious Disease Dynamics Model and Analysis

#### 3.1. Model Description

#### 3.2. The Basic Reproduction Number

**Theorem**

**1:**

## 4. The Impact of Community Structure on the Spreading of Infectious Diseases

#### 4.1. The Influence of the Connection Rate on the Basic Reproduction Number

#### 4.2. The Influence of the Connection Rate and Connected Edges on Infection Density

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**The flow chart of the infectious disease transmission in two community structure networks.

**Figure 7.**The variation curves of infection density with time for different ${p}_{in}$, ${p}_{out}=0.2$.

**Figure 9.**The variation curves of infection density with time for different ${m}_{3}$ and ${R}_{0}<1$.

**Figure 10.**The variation curves of infection density with time for different ${m}_{4}$ and ${R}_{0}>1$.

Parameter | Explanation |
---|---|

${\beta}_{i}$ | Infection rate in the $i-\mathrm{th}$ community |

$\alpha $ | Probability of nodes being connected in the inner community at the initial moment |

${p}_{in}$ | Probability of nodes being connected in the inner community at each time step |

${p}_{out}$ | Probability of nodes being connected in the outer community at each time step |

${\delta}_{i}$ | Recovery rate of infected in the $i-\mathrm{th}$ community |

${\mu}_{i}$ | Probability of recovered reverting to susceptible |

${\gamma}_{ij}$ | Coefficient factor affecting the infection rate in the outer community |

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**MDPI and ACS Style**

Gao, Z.; Gu, Z.; Yang, L. Effects of Community Connectivity on the Spreading Process of Epidemics. *Entropy* **2023**, *25*, 849.
https://doi.org/10.3390/e25060849

**AMA Style**

Gao Z, Gu Z, Yang L. Effects of Community Connectivity on the Spreading Process of Epidemics. *Entropy*. 2023; 25(6):849.
https://doi.org/10.3390/e25060849

**Chicago/Turabian Style**

Gao, Zhongshe, Ziyu Gu, and Lixin Yang. 2023. "Effects of Community Connectivity on the Spreading Process of Epidemics" *Entropy* 25, no. 6: 849.
https://doi.org/10.3390/e25060849