We present a model of the non-immune disease spread, as well as an algorithmic approach and the corresponding results of its study by computer simulations. The model is a generalization of the SIS model with the uniform two-dimensional spatial distribution of individuals undergoing a Markov-type evolution with discrete time. In this work, we describe our approach and present a number of the preliminary results obtained for the case of the quenched distribution of individuals on the sites of a simple square lattice and the one-parameter stochastic dynamics (synchronous SIS model on a square lattice with varying number of neighbors). The dynamical properties of the model are studied in terms of the behavior of the fraction of the infected individuals as well as of the maximum size and dimension of the largest cluster formed by them. These properties are found to be affected by the effective range of the local infectivity, which demonstrates the role of the underlying graph of the individual communications on the global disease spread. The presented approach allows for numerous extensions, including the possibility to consider non-homogeneous spatial distributions and various forms of the stochastic dynamics.
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