As opposed to most sociological fields, data are available in good quality for human epidemiology, describing the interaction between individuals being susceptible to or infected by a disease. Mathematically, the modelling of such systems is done on the level of stochastic master equations, giving likelihood functions for real live data. We show in a case study of meningococcal disease, that the observed large fluctuations of outbreaks of disease among the human population can be explained by the theory of accidental pathogens, leading the system towards a critical state, characterized by power laws in outbreak distributions. In order to make the extremely difficult parameter estimation close to a critical state with absorbing boundary possible, we investigate new algorithms for simulation of the disease dynamics on the basis of winner takes all strategies, and combine them with previously developed parameter estimation schemes.

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