By means of the asynchronous cellular automata algorithm we study stationary states and spatial patterning in an SIS model, in which the individuals' are attached to the vertices of a graph and their mobility is mimicked by varying the neighbourhood size q. The versions with fixed q and those taken at random at each step and for each individual are studied. Numerical data on the local behaviour of the model are mapped onto the solution of its zero dimensional version, corresponding to the limit q → +∞ and equivalent to the logistic growth model. This allows for deducing an explicit form of the dependence of the fraction of infected individuals on the curing rate γ. A detailed analysis of the appearance of spatial patterns of infected individuals in the stationary state is performed.
We consider the compartmental model for the non-immune disease with both ordinary and resistant carriers. The same infecting rate β is assumed for both types of carriers, whereas the curing rates γ and γ ′ for the ordinary and resistant carriers, respectively, are different. The conversion from an ordinary into resistant carrier takes place with the rate δ. The stationary states for the model are evaluated and rewritten in a compact form using two reduced parameters that are combinations of initial four rates. The lower and upper bounds are given for both these parameters and the 3D plot for the fixed points is presented.
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