Replicating disease spread in empirical cattle networks by adjusting the probability of infection in random networks

Comparisons between mass-action or "random" network models and empirical networks have produced mixed results. Here we seek to discover whether a simulated disease spread through randomly constructed networks can be coerced to model the spread in empirical networks by altering a single disease parameter - the probability of infection. A stochastic model for disease spread through herds of cattle is utilised to model the passage of an SEIR (susceptible-latent-infected-resistant) through five networks. The first network is an empirical network of recorded contacts, from four datasets available, and the other four networks are constructed from randomly distributed contacts based on increasing amounts of information from the recorded network. A numerical study on adjusting the value of the probability of infection was conducted for the four random network models. We found that relative percentage reductions in the probability of infection, between 5.6% and 39.4% in the random network models, produced results that most closely mirrored the results from the empirical contact networks. In all cases tested, to reduce the differences between the two models, required a reduction in the probability of infection in the random network.