# Topology of the World Tourism Web
## 3 Results and Discussion
### Network Diffusion Properties  
Network diffusion properties are of special interest due to the COVID-19 pandemic. However, some of the previously stated data and measures may also shed light on the situation, as we presume that noticed trends continue and we use the calculated parameters as orientation. First, as the outbreak started in China, it is important to note that China had the highest weighted out-degree (which showed a rise in China's importance in the tourism network since 2014 and can be an indication of a trend), with tourists visiting 152 distinct countries. Second, betweenness centrality shows critical places where otherwise unconnected tourists may interact or occupy the same location: the United States, Canada, Belgium, Australia, New Zealand, Japan, China, Italy, Finland, and Uganda. However, most of those countries do not have a peak season in that period. The first cases outside China were reported in the Republic of Korea, Japan, Thailand, Singapore, the United States, and Italy. While some of those countries share the same community with China, there are other ways and paths to travel (for example, many Chinese residents own shops or work in northern Italy). So, if betweenness centrality did not change by the end of 2019, most of the countries that are expected to behave as bridges, in this case, did not play a role (except for the United States, Japan, and Italy) in the initial days of the outbreak, probably because the outbreak occurred in an out-of-season period. Generally, assessment of the diffusion property is how one node's actions may have consequences for other nodes in a network. One of the prerequisites for diffusion is the existence of interconnected components, while the tourism network contains a giant component. In a contagion situation, usually applied models refer to susceptible-infected-recovered or susceptible-infected-susceptible models or their combination. In such models, it is assumed that some of the nodes have immunity (\(\pi\)). The basic presumption of these models is that if \(p\) (\(1-\pi\)) \(n\) is smaller than 1, the disease will die out, and if it is larger than 1, the disease will spread. So, a threshold for a giant component of infected nodes is \(p\) (\(1-\pi\)) \(n=1\), where \(p\) stands for the probability of the link creation, \(n\) is the number of nodes, and (\(1-\pi\)) is a share of susceptible nodes. Based on the presented network, we may assume that the probability of the node connection is \(p=0.29\), and we will be free to assume that periphery nodes have immunity, which leads to \(\pi=0.227\) (given that the countries cannot get vaccinated (only their citizens can); from the perspective of this network, the absence of connections is the only immunity that we can account for). As it can be intuitively deduced from the equations, in the case of a large \(p\), a fraction of susceptible population (\(q\)) can be quite high. The proportion of \(q\) can be approximated by solving \(q=1-e^{-q(1-\pi)np}\). The approximated share for stated measures is \(q=1\), leading to the possible infection of all the nodes in the interconnected part of the network. So basically, the change in that share can be achieved either by increasing the immunity (by any measure) or by reducing the probability of the connection. It was estimated that the international travel bans affected over 90% of the world population [42]. This reduced \(p\) to 0.1, which gives us \(q\sim 0.9\dot{\pi}\), and if further reduction takes \(p\) to 0.01, then the approximate share of susceptible countries is \(q\sim 0.75\). However, a glance at the initial expression shows that \(p\) (\(1-\pi\)) \(n\) should be reduced to less than 1 for a disease to die out, and this can be achieved by reducing the probability of creating a connection to \(p\)-0.0053. However, one must keep in mind that not only tourists but business and other travels and visits also create connections between countries.