Epidemiological Models for the analysis of corporate financial crises
In recent years, the interconnection between businesses and the growing complexity of financial markets have made the economic system particularly vulnerable to sudden and disruptive events, such as financial crises.
In this context, we observed an interesting analogy between the propagation of financial risk and the spread of an infectious disease within a population.
An innovative approach has been explored by applying epidemiological models – traditionally used in the medical field – to the analysis of corporate financial crises. In this way uncovering the unexpected capabilities of Epidemiological Models in Financial crises.
In particular, the transmission of bankruptcy risk among Italian companies has been studied using a graph. Here the nodes represent the companies and the edges indicate corporate relationships between them.
The aim is to explore how the structure of the network and its dynamics influence the propagation of risk, potentially identifying tools to anticipate or mitigate critical events in the national economic system.
Financial crises dataset and Epidemiological models
Financial crises dataset
The analysis is based on a directed graph (Financial crises dataset) centered on Italian companies, where each node represents a firm identified by various attributes.
The companies are connected to other nodes through relationships that describe geographical links, ownership ties, and signals of financial distress over the years.
The modeling was executed using the Neo4j graph database1, leveraging its ability to efficiently represent and query highly connected data.
Epidemiological models
To analyze the spread of financial risk, we adopted two classical epidemiological models:
- the SIR2 (Susceptible – Infected – Recovered) model;
- the SIRD (Susceptible – Infected – Recovered – Deceased) model.
These models, originally developed to simulate the dynamics of infectious disease transmission, were applied here in an economic context to study how financial distress can propagate across a population.
The models take as input a population, conceptually divided into compartments representing different states. We can describe the evolution of these states over time by a system of differential equations.
The transitions between compartments are governed by key parameters. The SIR model uses the infection rate β and recovery rate γ. On the other hand, the SIRD model includes an additional parameter: the mortality rate μ.
These parameters define the dynamics of the system throughout the simulation period.
Epidemiological models on graphs
Epidemiological models were not originally designed to operate on graph structures. For this reason it was necessary to adapt them to make them compatible with the data used in this analysis. Notably, we modify the differential equations that define the models, allowing them to process data represented as nodes and relationships. These adjustments primarily involved redefining the concept of population – the input of the models – represented, in this context, by each individual node in the graph. Additionally, we reformulated the transition parameters governing state changes to account for specific properties of nodes and their connecting links.
Models validation
To validate the models, we extracted three subgraphs from the dataset, corresponding to companies with registered offices in the provinces of Milan, Rome and Naples.
We adopted two different criteria for parameters assignment. The first one is based on arbitrary values. The other is based on specific properties of the graph’s nodes and relationships, such as company revenues and ownership shares. The results indicate that the second criterion leads to more realistic simulations, better aligned with the observed data.
SIR Model – Criteria 1 vs Criteria 2
Comparison of SIR model results with the first and second criteria for parameter allocation using the Rome subgraph as an example.
SIRD Model – Criteria 1 vs Criteria 2
In particular, the application of the SIRD model revealed a strong correlation between high simulated infection rates and companies that were no longer active in the actual dataset.
“stato” indicates whether the company is active (“Attiva”) or dissolved (“Estinto”).
“proceduraConcorsuale” refers to any ongoing or past insolvency procedures, such as:
“Fallimento” = Bankruptcy; “Liquidazione volontaria” = Voluntary liquidation; “Nessuna procedura concorsuale” = No insolvency procedure
Execution times remained low thanks to the limited size and low density of the selected graphs.
Analysis and Conclusions
After validating the model and selecting the most effective parameter configurations, the analysis focused on four major geographical areas of Italy: Northwest, Northeast, Center and South.
For each area we dedicated specific subgraphs, enabling a territorial comparison of business behavior under crisis scenarios. The results highlighted how the graph’s morphology and the distribution of relationships significantly influence the dynamics of risk propagation. Simulations confirmed that higher connection density facilitates faster and broader transmission of risk. On the other hand, more fragmented structures tend to limit its spread. For instance, in the analyzed cases, the Northwest and Central regions exhibited a more rapid and sustained propagation compared to other areas.
It is important to note, however, that the results are based on specific subgraphs selected for illustrative purposes. They do not constitute an exhaustive assessment of the national economic system.
In conclusion, the integration of epidemiological models with graph-based analysis offers a new perspectives for assessing economic stability and developing strategies to mitigate systemic financial risk.
SIR model results
Here below are the results if the SIR model with the second criteria is applied.
SIRD model results
Here below are the results if the SIRD model with the second criteria is applied.
Special thanks to our contributor:
Miriana Pompilio