# Prediction of Spread Trend of Epidemic Based on Spatial-Temporal Sequence

^{*}

## Abstract

**:**

## 1. Introduction

- The distribution of weights is inaccurate due to the lack of consideration for the importance ranking of features and the lack of attention to important features. For example, a period of time with a larger migration index should have a greater impact on outcomes, and the epidemic transmission of infectious diseases in a region is more affected by its neighboring regions, which cannot be generalized.
- Lack of explanation for the results. End-to-end model processing and output results belong to black-box processing, which cannot be traced back to the source and lacks some confidence.

- The spatial map information is innovatively introduced into the data, that is, the intensity of association adjacency matrix between risk areas is constructed to represent the relationship between regions and neighborhood characteristics, and to improve the sensitivity of the model to the spatial information of the data.
- A prediction model STAGCN based on a space–time series is proposed. The model introduces the attention mechanism to adaptively assign the feature weights of epidemic data in different time periods, and adaptively extracts the spatial information of epidemic data using the attention network. We use the time series model LSTM to compare the effect with the model, and take STACN as the benchmark model to evaluate the generalization ability of the time series and time series models.
- The migration index in explainable data is analyzed and interpreted using explanatory methods, taking cities as units.

## 2. Materials and Methods

#### 2.1. Data Description

#### 2.2. Construction of Adjacency Matrix

#### 2.3. STAGCN

#### 2.3.1. STGCN

#### 2.3.2. STAGCN

#### 2.3.3. The TAGCN Layer of ST-Block

#### 2.3.4. The SGAT Layer of ST-Block

#### 2.3.5. The Output Layer of STAGCN

## 3. Experiments and Results

## 4. Interpretability Analysis

#### 4.1. Influence Weight of Each Migration Index of the Sample

#### 4.1.1. Impact Analysis of Each Migration Index of a Single Sample

#### 4.1.2. Impact Analysis of Each Migration Index of a Single Sample

#### 4.2. Analysis on the Dependence and Interaction of Migration Index

#### 4.2.1. The Dependence Analysis of Migration Index

#### 4.2.2. Interactive Analysis of Migration Index

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Geographic figure (each circle represents a city, each city is divided into $n$ area rectangles, and each area is divided into $n$ grids.

**Figure 2.**Spatial–temporal structure of the data (Each circular node represents an area, and the color of the node indicates the development of infectious diseases in the area. The darker the color, the more serious the infectious diseases in the area. The edges between nodes represent the strength of the association between the infectious disease areas, the redder the edges, the correlation is stronger; the greener the edges, the correlation is weaker).

**Figure 3.**(

**a**) Connectivity between different regions (Different squares represent different regions, and connectivity between regions is represented by color. The darker the color, the stronger the connectivity between the two, and the lighter the color, the weaker the connectivity between the two.); and (

**b**) adjacency matrix thermograms.

**Figure 11.**The number of new infectors in region 12, city C in the next 15 days (The black curve represents the truth data, the green curve represents the results predicted by the STAGCN model).

**Figure 12.**The influence of each migration index on the predicted value of the model (single sample) (base value) represents the average value of the model output after inputting the training set, Red indicates that positive push up. Blue indicates that reverse pull down.

**Figure 13.**Local SHAP value of each migration index (single sample) ($E[f(x)]$ on the horizontal axis represents the average value of model output after inputting the training set, and the left vertical axis represents the name and value of each input feature).

**Figure 14.**The distribution of input variables affecting the predicted value of the model output (each color point corresponds to the input migration index, the feature value of the vertical axis represents the value of the migration index, and the color represents its value). If the color is blue, it means its value is small, and if the color is red, it means its value is large. The horizontal axis represents the SHAP values of different input variables.

**Figure 15.**Dependence analysis of CtoA migration index (partial dependence graph method) (the horizontal axis represents the value of migration index, and the vertical axis represents the number of new infections).

**Figure 16.**Dependence analysis of migration index AtoE (individual conditional expectation method, the horizontal axis represents the value of migration index, and the vertical axis represents the number of new infections).

**Figure 17.**(

**a**) is the SHAP interaction value between AtoE, CtoA; (

**b**) is the SHAP interaction value between AtoE and DtoA.

Date | Region Name | Features (F) |
---|---|---|

20200501 | A_0 | temperature |

A_1 | Migration scale index | |

…… | …… | |

E_33 | Transfer intensity | |

20200502 | A_0 | temperature |

A_1 | Migration scale index | |

…… | …… | |

E_33 | Transfer intensity | |

…… | A_0 | temperature |

A_1 | Migration scale index | |

…… | …… | |

E_33 | Transfer intensity | |

20200629 | A_0 | temperature |

A_1 | Migration scale index | |

…… | …… | |

E_33 | Transfer intensity |

Area\Area | A_0 | A_1 | … | E_33 |
---|---|---|---|---|

A_0 | 0 | $0.076853/{e}_{\left({A}_{1},{A}_{0}\right)}$ | … | 0 |

A_1 | $0.230571/{e}_{\left({A}_{0},{A}_{1}\right)}$ | 0 | … | 0 |

… | … | … | … | … |

E_33 | 0 | 0 | … | 0 |

Period | Evaluate | Models | |||
---|---|---|---|---|---|

ARIMA | LSTM | STGCN | STAGCN | ||

5 days | RMSE | 20.62 | 18.94 | 17.07 | 16.67 |

RMSLE | 3.2137 | 2.1308 | 1.8613 | 1.7015 | |

10 days | RMSE | 20.78 | 19.44 | 18.99 | 18.71 |

RMSLE | 3.4992 | 2.2152 | 2.0870 | 1.9251 | |

15 days | RMSE | 22.68 | 20.52 | 19.28 | 18.93 |

RMSLE | 3.6209 | 2.4595 | 2.3393 | 2.0515 |

Period | Evaluate | Models | ||
---|---|---|---|---|

STAGCN without Attention | STAGCN without GAT | STAGCN | ||

5 days | RMSE | 17.87 | 18.31 | 16.67 |

RMSLE | 1.8366 | 1.9059 | 1.7015 | |

10 days | RMSE | 18.78 | 18.84 | 18.71 |

RMSLE | 1.9907 | 2.0192 | 1.9251 | |

15 days | RMSE | 19.38 | 19.57 | 18.93 |

RMSLE | 2.1290 | 2.2026 | 2.0515 |

Comparison Point | Benchmark#1 [27] | Benchmark#2 [28] | Benchmark#3 [30] | Proposed |
---|---|---|---|---|

Handling time series data | $\surd $ | $\surd $ | $\surd $ | $\surd $ |

Handling space series data | $\times $ | $\surd $ | $\surd $ | $\surd $ |

Considering the impacts of different features | $\times $ | $\times $ | $\times $ | $\surd $ |

Considering the complex data | $\times $ | $\times $ | $\times $ | $\surd $ |

Score | 25 | 50 | 50 | 100 |

Difference | 75 | 50 | 50 | / |

Parameters | Quantity |
---|---|

AtoB | Migration index from city A to city B |

AtoC | Migration index from city A to city C |

AtoD | Migration index from city A to city D |

AtoE | Migration index from city A to city E |

BtoA | Migration index from city B to city A |

CtoA | Migration index from city C to city A |

DtoA | Migration index from city D to city A |

EtoA | Migration index from city E to city A |

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**MDPI and ACS Style**

Li, Q.; Pan, Q.; Xie, L.
Prediction of Spread Trend of Epidemic Based on Spatial-Temporal Sequence. *Symmetry* **2022**, *14*, 1064.
https://doi.org/10.3390/sym14051064

**AMA Style**

Li Q, Pan Q, Xie L.
Prediction of Spread Trend of Epidemic Based on Spatial-Temporal Sequence. *Symmetry*. 2022; 14(5):1064.
https://doi.org/10.3390/sym14051064

**Chicago/Turabian Style**

Li, Qian, Qiao Pan, and Liying Xie.
2022. "Prediction of Spread Trend of Epidemic Based on Spatial-Temporal Sequence" *Symmetry* 14, no. 5: 1064.
https://doi.org/10.3390/sym14051064