By: Zhuohan Zhang, RIG Inc Intern Researcher

Since 2020, Covid_19 has negatively impacted our daily life. The coronavirus disease pandemic took many people’s lives and seriously affected various countries’ economic and social development. To prevent such a disease, we can construct complex networks, which can reveal necessary information about disease transmission across countries. By definition, a complex network is a graph with non-trivial topological features that do not occur in simple networks such as lattices or random graphs, but often occur in networks representing real systems (Wikipedia). Scholars have found that “a complex network with a community structure can promote or effectively inhibit the spread of diseases” (Stegehuis C, Van Der Hofstad R).

In a complex system features such as nodes and connections, need to be defined. Complex networks are a set of many-connected nodes that interact in different ways. For example, it can be used to describe friendship relationships where two people are connected if they are friends. Complex networks can be defined in a family relationship where two people are connected if they belong to the same close family. Network is defined as two computers that are connected if they are in the same domain, a Covid network is characterized as two people infected with Coronavirus if they have been in close contact. The following graphs intuitively explained the structure of complex networks where the nodes below represent people and lines represent the connection. One infected person, initial node in the network, did not wear a face mask and stayed in a closed room with another person. The second person is highly likely to test positive for Covid, and therefore a line is connected between these two people. As more and more people interact with the two people, more nodes are added, and more lines begin to connect. This forms a complex network.

Detailed principles underlying complex network is topology. To understand the structure of a network, we need first to have the degree of distribution, which is the probability that a randomly chosen node has connections. We also need to identify the aggregation coefficient, which is defined as the probability that two nodes directly connected to a third node are connected to each other. Also required is the minimum length between two nodes, which is the minimum number of steps to reach one node Vi from a node Vj and the average length in the network (MIT edu). As more and more research is completed scholars, we can come to the conclusion that the global COVID-19 pandemic has some prominent complex network properties (Zhu, Kou, Lai, Feng, Du). Since it varies over time, here, a time-varying dynamical network is more appropriate to describe the synchronization phenomena. It is determined by the inner-coupling matrix, and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network. (Lu Chen)

In addition, RIG’s Dynamic Trust models can be applied to complex networks as well. It is a useful model for trust evaluation, and dynamically predicts trust levels based on given data. As we gain more information about the agent, device, or service, we develop a trust level. RIG’s Dynamic Trust models have extensive applications, such as healthcare fraud evaluation, connected car evaluation, service rating and so on. We can apply RIG’s Dynamic Trust models combined with machine learning techniques, to predict Covid_19 disease transmission across countries. On each node of a complex network, we can identify symptoms for infected people, ranging from mild symptoms to severe illness. Mild symptoms include fever, cough and shortness of breath; moderate symptoms include headache, new loss of taste or smell, and sore throat. Severe symptoms include congestion, nausea, and diarrhea. After assigning these levels, supervised machine learning models, such as SVM or random forest, are able to classify the data. The outputs determine the probability of infection. The higher the level, the higher the possibility of being a high–degree node in a complex network. Due to the connectivity of high-degree nodes, link removal strategies suggest that complete isolation of susceptible nodes from infected nodes is an effective method for reducing the average number of new infections, and it is a way to prevent the spread of COVID-19 (M. Bellingeri). Thus, the combination of Dynamic Trust models and machine learning techniques can help predict the transmission of the Covid_19 virus and provides a effective and efficient method to prevent the spread of the virus.

Reference

https://ieeexplore.ieee.org/document/1440569/authors#authors

http://web.mit.edu/8.334/www/grades/projects/projects10/Hernandez-Lopez-Rogelio/structure_1.html

M.Bellingeri, M. Turchetto, Modeling the Consequences of Social Distancing Over Epidemics Spreading in Complex Social Networks: From Link Removal Analysis to SARS-CoV-2 Prevention, 28 May 2021

Stegehuis C, Van Der Hofstad R, Van Leeuwaarden JS. Epidemic spreading on complex networks with community structures. Sci Rep (2016) 6(1):29748–7. doi:10.1038/srep29748