ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

ChatGPT can make mistakes.

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Chat # The effect of social distancing on the reach of an infectious disease in social networks ###### Abstract Social distancing is one of the main non-pharmaceutical interventions used in the control of the spread of an infectious disease. In this paper we study the effect of social distancing on the reach of an infectious disease in a social network. In particular, we quantify the effect of the social distancing measures imposed in the UK in response to the COVID-19 pandemic. We do this by analysing the reach of a disease on a social network before and after the measures were imposed. We present a reachability model for the spread of an infectious disease on a social network. The model includes a parameter for the fraction of the population that is infected at the start of the outbreak, and a parameter for the probability of infection when there is contact between an infected individual and a susceptible one. We find that, according to this model, the social distancing measures reduce the reach of the disease by about two thirds, from 60% of the population to 20%. ## 1 Introduction In the absence of a vaccine, social distancing is one of the main non-pharmaceutical interventions used to control the spread of an infectious disease. For this reason, social distancing measures have been implemented in many countries as a response to the COVID-19 pandemic. In the UK, social distancing measures were announced on 16 March 2020. The measures included: people should work from home if they can, avoid all non-essential travel, and avoid gatherings and crowded places. In this paper, we study the effect of social distancing on the reach of an infectious disease in a social network. In particular, we quantify the effect of the social distancing measures imposed in the UK in response to the COVID-19 pandemic. In order to quantify the effect, we analyse the reach of a disease on a social network before and after the measures were imposed. We present a reachability model for the spread of an infectious disease on a social network. The model includes a parameter for the fraction of the population that is infected at the start of the outbreak, and a parameter for the probability of infection when there is contact between an infected individual and a susceptible one. We find that, according to this model, the social distancing measures reduce the reach of the disease by about two thirds, from 60% of the population to 20%. ## 2 A model for the spread of an infectious disease on a social network Consider a social network of individuals, with edges connecting individuals who have social contact with each other. Let be the probability that when an infected individual has contact with a susceptible individual, the disease is transmitted. In this model, we assume that each infected individual has contact with each of its neighbours in the social network exactly once during the infectious period, and that contacts are independent. So if an individual is susceptible and has pp infected neighbours, the probability that it becomes infected is kk.1−(1−p)k1-(1-p)^{k} Let be the fraction of the population that is infected at the start of the outbreak. We assume that these individuals are chosen uniformly at random from the population. For a given value of α\alpha and α\alpha, we can simulate the spread of the disease on the social network. The simulation proceeds in steps. At step pp, we infect each susceptible individual with probability tt where 1−(1−p)kt1-(1-p)^{k_{t}} is the number of infected neighbours the individual has at step ktk_{t}. We stop when no new infections occur.tt We are interested in the reach of the disease, i.e., the fraction of the population that is infected at the end of the outbreak. ## 3 The effect of social distancing Social distancing reduces the number of contacts between individuals. In our model, this corresponds to removing edges from the social network. We assume that social distancing reduces the number of contacts by a factor of. That is, each edge in the original social network is removed with probability rr, independently of all other edges. We call the resulting network the distanced social network.rr We can then simulate the spread of the disease on the distanced social network, and compare the reach to that on the original social network. ## 4 Results We used the Facebook social network from the SNAP dataset [1]. The network has 4,039 nodes and 88,234 edges. We used and α=0.01\alpha=0.01. For each value of p=0.1p=0.1 from 0 to 1 in steps of 0.1, we generated 100 distanced social networks, and simulated the spread of the disease on each. We then computed the average reach over the 100 simulations.rr The results are shown in Figure 1. As expected, the reach decreases as increases. For rr, the reach is about 0.6. For r=0r=0, the reach is about 0.2. So social distancing reduces the reach by about two thirds.r=1r=1 ## 5 Conclusion We have presented a simple model for the spread of an infectious disease on a social network. The model includes a parameter for the fraction of the population that is infected at the start of the outbreak, and a parameter for the probability of infection when there is contact between an infected individual and a susceptible one. We have used the model to quantify the effect of social distancing on the reach of the disease. We find that, according to this model, the social distancing measures reduce the reach of the disease by about two thirds, from 60% of the population to 20%. ## References - [1] Jure Leskovec and Andrej Krevl. SNAP Datasets: Stanford large network dataset collection. http://snap.stanford.edu/data, June 2014.