Dynamic modeling of an epidemic disease with the ising model built on voronoi tessellation

The effects of interactions and displacement rates among individuals in a randomly distributed population on disease spread have been examined. Based on the Voronoi tessellation, a modified Ising model has been developed to simulate how individuals' health statuses change with neighborhood interactions and displacement rates. The dynamics of the system were analyzed using Monte Carlo simulations and the Metropolis algorithm. The hypothesis posits that individuals' health statuses can significantly change with neighborhood interactions and displacement rates. In the Ising model, the spin states expressed as +1 or -1 were interpreted as "Sick" or "Not Sick" and it was assumed that individuals' health statuses were influenced by their neighbors. The analyses evaluated the effect of the coupling constant 𝐽, representing the transmissibility coefficient, on individuals' health statuses. The findings indicate that as the J value increases, there is a significant change in the number of infected regions. Positive 𝐽 values were found to increase the spread of the disease, while negative 𝐽 values were found to decrease it. This thesis provides important data for understanding the effects of interactions and displacement rates among individuals on disease spread and offers critical findings for optimizing epidemiological models.