Influence of Network Heterogeneity on Chaotic Dynamics of Infectious Diseases

It is well known that the topology of contacts among individuals can sharply influence the persistence of a disease. Much less is known on how the network structure influences the dynamical properties in the important case of seasonal diseases. Aim of this work is to study a periodically forced SIR contact process with demography in host populations modeled through complex networks (of either Erdős-Rényi or scale-free type). We systematically perform one-parameter bifurcation analyses with respect to the strength of seasonality, and find that the epidemiological regime is largely independent of the network class. However, the structure of the host networks does matter. In fact, the heterogeneity of the network degree distribution emerges as a key element in determining the epidemic temporal patterns. In particular, we find that the dynamical complexity is maximal (i.e., chaotic) at intermediate values of the heterogeneity.