Evolution towards criticality in an epidemiological model for meningococcal disease

• Published in: Physics letters. A 2003-10, Vol.317 (1), p.87-96
• Main Authors: Stollenwerk, Nico, Jansen, Vincent A.A.
• Format: Article
• Language: English
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2003.08.017

In a model for bacterial infections with various mutants we find the epidemiological system evolving towards criticality without outer tuning of a control parameter. This is an indication for self-organized criticality. The epidemic model is a susceptible–infected–recovered hosts system (SIR) for the harmless agent infecting hosts  I, acting as a background to a mutant strain Y which occasionally creates severely affected hosts  X. The full system of SIRYX is described in the master equation framework, confirming limiting assumptions about a reduced YX-system with the SIR-system in stationarity. In this limiting case we can analytically show convergence to power law scaling typical of critical states. Furthermore, in this approximation we can show analytically that the control parameter, the pathogenicity in this model, evolves to be predominantly in its critical value zero. These findings are then confirmed by simulations of the full SIRYX-system.