Effect of clustering to the dynamics of epidemic spread in a square lattice
Abstract
We analyze contact epidemic spread over automatons on a square lattice using Moore and von Neumann neighborhood types, for varying values of agent density, Ï. The total fraction of infected individuals after very long iterations, Ω∞, is calculated to see the effect of the neighborhood and them spatial constraints. It is found out Ω∞ depends on the fraction of agents that belongs to the largest cluster in the system, <S>. Also, we found that consistent with percolation theory, there exists a critical density Ïc wherein the whole population will be infected. At Ï âˆ¼ Ïc, it takes the longest time for the infection to spread and is explained to be due to the configuration of the formed connected clusters. As Ï approaches unity (maximum density), the rate of infection approaches a constant rate for the von Neumann neighborhood and linearly increases for Moore neighborhood implying a dependence of the spread to the average connection <k>each agent has.
