Starting from the well-known field theory for directed percolation (DP), we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (Model A)...

We investigate an epidemic spreading process by means of a computational simulation on the Apollonian network, which is simultaneously small-world, scale-free, Euclidean, space-filling and matching graphs. An analysis of the critical behavior of the Contact Process (CP) is presented using a...

We introduce a model for the Contact Process with relaxing immunization CPRI. In this model, local memory is introduced by a time and space dependence of the contamination probability. The model has two parameters: a typical immunization time τ and a maximum contamination probability a. The...

We investigate possible extensions of the susceptible–infective-removed (SIR) epidemic model. We show that there exists a large class of functions representing interaction between the susceptible and infective populations for which the model has a realistic behaviour and preserves the...

We study a model of an epidemic where the individuals which are cured from the infection are not permanently immunised but have a finite probability of becoming reinfected. We show that the epidemic does not follow the usual pattern of growth and decay but rather oscillates towards an...