Finding patient zero in susceptible-infectious-susceptible epidemic processes
Robin Persoons1, Piet Van Mieghem1
1Faculty of Electrical Engineering, Mathematics and Computer Science, <a href="https://ror.org/02e2c7k09">Delft University of Technology</a>, P.O. Box 5031, 2600 GA Delft, The Netherlands.
Physical Review. E
|November 20, 2024
Summary
Tracing epidemic origins is crucial for control. Backward equations effectively identify sources in large susceptible-infectious-susceptible (SIS) networks, but not for realistic Markovian SIS models due to computational challenges.
Area of Science:
- Epidemiology
- Network Science
- Mathematical Modeling
Background:
- Identifying the source of an epidemic is vital for effective control and prevention strategies.
- Susceptible-infectious-susceptible (SIS) models are fundamental in understanding epidemic dynamics on networks.
Purpose of the Study:
- To investigate the feasibility of tracing epidemic origins using backward equations in network models.
- To compare the source identification capabilities between an N-intertwined mean-field approximation and a Markovian SIS model.
Main Methods:
- Utilizing backward equations derived from the N-intertwined mean-field approximation of the SIS process.
- Analyzing the analytical solution for the Markovian SIS model's initial condition s(0) = s(t)e^{-Qt}.
Main Results:
- Backward equations successfully traced epidemic sources in networks up to N=1500.
- Source identification for the Markovian SIS model proved infeasible even with known parameters due to numerical instability of the matrix exponential.
Conclusions:
- The N-intertwined mean-field approximation offers a computationally tractable method for identifying epidemic sources in large networks.
- Realistic Markovian SIS models present significant challenges for source identification, limiting practical application in real-world scenarios.
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