The impact of contact-network structure on important epidemiological quantities of infectious disease transmission and the identification of the extremes.

An individual-based stochastic model was developed to simulate the spread of an infectious disease in an SEIR-type system on all possible contact-networks of size between six and nine nodes. We assessed systematically the impact of the change in the population contact structure on four important epidemiological quantities: i) the epidemic duration, ii) the maximum number of infected individuals at a time point during the epidemic, iii) the time at which the maximum number of infected individuals is reached, and iv) the total number of individuals that have been infected during the epidemic. We considered the potential relationship of these quantities as the network changes and identified the networks that maximise and minimise each of these in the case of an epidemic outbreak. Chain-like networks minimise the peak and final epidemic size, but the disease spread is slow on such contact structures which leads to the maximisation of the epidemic duration. Star-like networks maximise the time to the peak whereas highly connected networks lead to faster disease transmission, and higher peak and final epidemic size. While the pairwise relationship of most of the quantities becomes almost linear, or inverse linear, as the network connectivity increases and approaches the complete network, the relationships are non-linear towards networks of low connectivity. In particular, the pairwise relationship between the final epidemic size and other quantities is changed in a 'bow-shaped' manner. There is a strong inverse linear relationship between epidemic duration and peak epidemic size with increasing network connectivity. The (inverse) linear relationships between quantities are more pronounced in cases of high disease transmissibility. All the values of the quantities change in a non-linear way with the increase of network connectivity and are characterised by high variability between networks of the same degree. The variability decreases as network connectivity increases.