Spread of Epidemic Disease on Edge-Weighted Graphs from a Database: A Case Study of COVID-19

Abstract

The understanding of infectious diseases is a priority in the field of public health. This has generated the inclusion of several disciplines and tools that allow for analyzing the dissemination of infectious diseases. The aim of this manuscript is to model the spreading of a disease in a population that is registered in a database. From this database, we obtain an edge-weighted graph. The spreading was modeled with the classic SIR model. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics. Moreover, a deterministic approximation is provided. With database COVID-19 from a city in Chile, we analyzed our model with relationship variables between people. We obtained a graph with 3866 vertices and 6,841,470 edges. We fitted the curve of the real data and we have done some simulations on the obtained graph. Our model is adjusted to the spread of the disease. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics, in this case with real data of COVID-19. This valuable information allows us to also include/understand the networks of dissemination of epidemics diseases as well as the implementation of preventive measures of public health. These findings are important in COVID-19’s pandemic context.

Protection Strategy against an Epidemic Disease on Edge-Weighted Graphs Applied to a COVID-19 Case

“…In this paper, we use a graph-based SIR model in the same way as in [13,28], namely, each individual is represented by a vertex in G E . At time t, each vertex v i is in a state v t i belonging to S = {0, 1, −1}, where 0, 1 and −1 represent the three discrete states: Susceptible (S), Infected (I) and Recovered or Removed (R).…”

“…The authors of [13] provide a way to obtain an edge-weighted graph from a database, which we briefly detail.…”

“…Regarding the COVID-19 pandemic, a series of models have been developed which allow the projection and establishment of the progress of this infectious disease based on the data available from different information sources (see, for instance, [12]). In this sense, Manríquez et al propose the use of weighted graphs at the edges, giving the network model, from a stochastic approach, the possibility of identifying the most important variables in the spread of COVID-19 with real data in a city in Chile [13]. The same authors, in order to classify the importance of the nodes, propose the generalization of the measure of importance of the line with the use of degree of centrality (DIL-W α ), improving the understanding of the network from a local perspective [14].…”

“…This study aims to analyze the protection effect against COVID-19 using the DIL-W α ranking with real data from a city in Chile (Olmué-City), obtained from the Epidemiological Surveillance System of the Ministry of Health of Chile, from which we obtain an edgeweighted graph, denoted by G E , according to the method proposed in [13]. We apply the protection to the G E network, according to the importance ranking list produced by DIL-W α , considering different protection budgets.…”

Protection Strategy for Edge-Weighted Graphs in Disease Spread

“…Modeling the spread of disease over networks has many applications in real life. For example, rumors or spam that spread on large social networks such as Facebook or Twitter [8], viruses that spread through computer systems [9], or diseases that spread over a population such as it does the actual SARS-CoV-2 (see for instance [10]). This leads to solve the problem of totally or partially controlling these spreads.…”