Spot Patterns in Gray Scott Model with Application to Epidemic Control

In this work, we analyse a pair of two-dimensional coupled reaction-diffusion equations known as the Gray-Scott model, in which spot patterns have been observed. We focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. A complete numerical study of the system is presented. We use backward Euler and Crank-Nicolson methods to study the model 1. We compute the error in L2 and L∞ norms and also the EOCS are calculated for each method. The errors and the EOCs show that the methods converge with the correct order. The main mathematical techniques employed in this analysis of the stationary patterns is the Turing instability theory. This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the Gray-Scott model by Turing mechanisms. In particular, we present a theoretical analysis of results of the numerical simulations in two dimensions. We have observed the formation of spatial patterns during the evolution, which are sparsely isolated ordered spot patterns that emerge in space. In this research we focuse on three areas: first, the analytical analysis; second, the numerical analysis and third, the application. We use these spatial patterns to understand the nature of population distribution and to understand the mechanism of interaction of the populations.