Computational Modelling in Epidemiological Dispersion Using Diffusion and Epidemiological Equations

Abstract

Although a considerable amount of knowledge is gathered concerning diseases and their transmission, still more is to learn on their mathematical modelling. The present work reviews the existent knowledge on models of epidemiological dispersion, the creation of a new form of an epidemiological diffusion equation, and the subsequent application of this equation to the investigation of epidemiological phenomena. Towards that scope, the authors have used mathematical models which have been previously reported, as well as algorithmic approaches of stochastic nature for the solution of complex functions. In particular, they have used dynamic programming algorithms, Robbins-Monro and Kiefer-Wolfowitz stochastic optimization algorithms, Markov chains and cellular automata. The modified diffusion equation could potentially provide a useful tool to the investigation of epidemiological phenomena. More research is required in order to explore the extent of its possibilities and uses.