Statistical and Mathematical Modeling in Biological Applications
Abstract: We consider a stochastic model of infection spread, with a general probability distribution of infectious epochs (i.e., not necessarily exponential) and constant, per capita transmission rate and detection rate (medical examination, symptom appearance,...). We have developed a new technique for the analysis of such non-Markovian processes, that allows us to give simple formulae for the (probability of) the state of the infection (number of infectives, time since infection,...) at the first time when an infective is detected. These results have applications for characterizing outbreaks of antibiotic resistant bacteria in the hospital. In particular, we disprove the formerly believed uniformativeness of this kind of data. (Joint work with P. Trapman from Stockholm University).