Inferring epidemic characteristics with networks

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Bayesian model comparison is naturally interpreted in a statistical physics context. We showed that taking this interpretation seriously leads to enormous reductions in computational effort. Given the complexity of translating the observed manifestations of the pandemic into an understanding of the virus's spread and the course of the infection, we opted for a simple data-driven approach, taking into account population age distributions and the age dependence of the death rate. While the conceptual basis of our approach is simple, there were computational difficulties we had to overcome to make the implementation amenable to computability with finite computational resources. Our results were checked to not depend on the size of the networks we simulated, on the number of stochastic runs we used for each model, nor on the number of days that we used for the linear regression. We can predict the posterior distribution of time of initial infection, TimeFirstDeath. The dynamic model can predict the number of people infected after the first infection and relative to the time of first death because we made no use of infection or recovery statistics in our analysis. Note the enormous variation in the number of infections for the same parameter set, only partly due to stochasticity of the networks themselves. With parameters intrinsic to the infection held fixed, we can predict the effect of various degrees of social distancing by varying network connectivity. We assumed that a certain fraction of nodes in the network would comply with social distancing and only these compliant nodes would reduce their connections at random by a certain fraction. Interestingly, while the fraction of compliant nodes that implement social distancing is relevant to the flattening of the cumulative number of deaths, the more important parameter appears to be the degree of social distancing by the compliant nodes, which in the present context means the fraction of edges in the network that are randomly deleted for compliant nodes only to simulate social distancing. The rate of exponential increase in the number of infected individuals is $0.18pm .03$ per day without social distancing. This rate falls to about $0.08$ per day with even the most pessimistic social-distancing effectuation. While the uncertainty of $0.03$ may not appear to be large, it appears in an exponent and leads to enormous ranges in the predicted number of infected individuals, a subject of great interest given possible asymptomatic transmission of the virus. With this caveat in mind, just focusing on the mean value $0.18$ per day implies that such a contact reduction corresponds to 65 million vs. 166000 infected individuals after a period of 100 days starting from one infected individual if social distancing is initiated two weeks after the first death on day 25.