We present and analyse numerical methods with operator splitting procedures, applied to an epidemic model which takes into account the space-dependence of infection. derive conditions on time step, under preserve non-negativity monotonicity properties exact solution. Our results are illustrated by experiments.

Disease and information spread over social networks. Understanding the phenomena in networks requires paying attention not only to degree distribution but also correlation. However, it is considered difficult analytically deal with effect of correlation on phenomena. Here, we introduce using a simple method present theoretical formulas outbreak threshold basic reproduction number. We theoretica...