Computational Modelling in Epidemiological Dispersion Using Diffusion and Epidemiological Equations: Epidemiological Dispersion Modelling

Computational Modelling in Epidemiological Dispersion Using Diffusion and Epidemiological Equations: Epidemiological Dispersion Modelling

George I. Lambrou (National and Kapodistiran University of Athens, Athens, Greece), Kyriaki Hatziagapiou (National and Kapodistrian University of Athens, Athens, Greece), Petros Toumpaniaris (Biomedical Engineering Lab, National Technical University of Athens, Athens, Greece), Penelope Ioannidou (National Technical University of Athens, Athens, Greece) and Dimitrios Koutsouris (Biomedical Engineering Lab, National Technical University of Athens, Athens, Greece)
Copyright: © 2019 |Pages: 37
DOI: 10.4018/IJRQEH.2019100101

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.
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Introduction

In the recent years, the globalization, and environmentally destructive phenomena have led to changes in the spreading and dispersion of biological agents, altering their epidemiological properties (Pimentel, 1991; Schiermeier, 2005). At the same time, socio-political changes, migration, global climate change and warming constitute an explosive mixture for epidemic dispersions (Randolph, 2004). Under these conditions, new challenges emerged as the volume of data to be processed exceeds all expectations and will increase geometrically over the next few years. To this end, new tools are needed to process and understand these data. Epidemiological dispersion is a multifactorial phenomenon, which is the cornerstone of exploring and understanding the dispersion of a biological or chemical agent. Several tools and methodologies have been proposed towards that end and many are already being used successfully.

Resolving issues related to human life and in particular public health, has changed immensely in recent years, due to the extensive increase of information (Salerno, Knoppers, Lee, Hlaing, & Goodman, 2017). For example, genome analytical methodologies and tools have created incredibly large amounts of data, which provide a new framework for understanding biological phenomena. Noteworthy, genome analysis follows Moore's law, moving progressively from the so called the “thousand dollar genome” to the “hundred dollar genome”. Thus, it is immediately understood that from biological perspective the information available is almost limitless. At the same time, the usage of mass social media has completely changed the landscape of information management, consisting an important source of information both for the individual and social behavior, thus for the sociobiology of public health. All the aforementioned information sources form the so called “Big Data”, which consist of data volumes that go beyond previous data sizes, and now reach the peta- and exabytes (1 petabyte=106 gigabytes, 1 exabyte=109 gigabytes).

From that point of view, it is evident that developments in technology, the volume of information and sociopolitical changes require a whole new approach, both methodologically and analytically. This involves data management, from the level of data simulation, via usage of Geographic Information Systems (GIS) to the usage of new methods, known as “Big Data analytics” (Luke, 2005; Musa et al., 2013; Scholte et al., 2012).

In the present work we attempted to review some of the existing knowledge on the subject of epidemiological dispersion models, as well as explored the use of additional dispersion models, using population, epidemiological and diffusion dynamics.

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