The SIS and SIR stochastic epidemic models revisited
Jesus Artalejo, Complutense University of Madrid
Many stochastic biological systems use Markov chains in which there is a set of
absorbing states. In particular, this is the case of the SIS and SIR stochastic epidemic
models. The aim of this talk is to revise these two basic models and provide some new
insight. More concretely, we will focus on three aspects:
i) to view the quasi-stationarity and ratio of expectations as two different approaches for
understanding the dynamics of the system before absorption. We also investigate the
possibility of using the ratio of expectations distribution as an approximation to the
quasi-stationary distribution.
ii) to extend the classical study of the length of an outbreak by investigating the whole
probability distribution of the extinction time via Laplace transforms.
iii) to study a new descriptor namely the time until a non-infected individual becomes
infected.
The talk is based in the two following recent papers:
1. Artalejo J.R. and López-Herrero M.J. (2010). Quasi-stationary and ratio of
expectations distributions: A comparative study. Journal of Theoretical Biology
266, 264-274.
2. Artalejo J.R., Economou A. and López-Herrero M.J. (2011). Stochastic
epidemic models revisited: Analysis of some continuous performance measures.
Journal of Biological Dynamics (forthcoming).