Μελέτη δύο ανταγωνιστικών ιών σε έναν πληθυσμό με βάση το επιδημιολογικό μοντέλο SIS
SubjectΕπιδημίες -- Στατιστική
The epidemiology was developed as a branch of mathematics in the twentieth century with the parallel development of technology and mathematics concepts. The abstract approach and modeling in a rigorous mathematical framework led epidemiology in many important results. The mathematical tools used are many, from the study of dynamical systems, solving differential equations, the study of continuous functions of several variables and their transformations to the graphs and theoretical computer science. Continuous study of possible models of a virus attack in a population with different properties led to further study of epidemics. But the introduction of the theoretical information from the mid-20th century gave another direction in epidemiology for the internet. A trend can be treated like a virus and the Internet as the population to study with pandemic conditions. This also applies and vice versa, studying viruses spread phenomena in homogeneous populations using modeling resulting from an advertising model on the internet and the spread of a trend or a product. But all the existing tools cover a small range of this specific research sector, which due to the increasing use of social media is now growing rapidly. The object of this project is the theoretical and practical study of the spread two competing viruses in a homogeneous population. The aim of this thesis is to clarify the possible outcomes in a competition two viruses for the capture of a population. To achieve this objective a study of the concepts of Epidemiology will be conducted and we will investigate the models used and the basic mathematical tools that are necessary to model the key relationships. Based on the above we will initially present the basic theories of Epidemiology, some of the most important models used in epidemiology and the particular model we have chosen to study. There will be an explanation on how this model was chosen to cover the questions that arise in case study of 2 viruses spreading in a population. Moreover through the study of epidemiological models we can understand the variables that must be defined when we model our problem. After this we will proceed to the exposition of the mathematical tools and basic mathematical concepts used to model the problem. Generally we will need dynamic systems because the spread of a virus is identified within a dynamic environment. The mechanisms of the populations and the spread of a virus are based on many variables. To study these variables and rules we need dynamic systems. Additionally we will refer to graphs as a population in computing can be modeled as a graph. Finally we indicate the points of stability because they are used to finding the limits for the outbreak of an epidemic. For the modeling of the problem the basic mathematics and epidemiological SIS model will be used in order to build the frame which will to be used for calculating the results of the outcome for the competing two viruses in a population. Based on these, we are led to assumptions that must be in place to implement the algorithm which will calculate the outcome of these two competing viruses. Finally place the implementation of the algorithm is based on the above assumptions. Various scenarios will be run to lead to conclusions. Ultimately we want to show how a powerful virus (or rumor), will spread more successfully in the population and over time will occupy if not all, the majority of the population.