Spreading of sexually transmitted diseases in heterosexual populations

Disease spreading has been the subject of intense research since long time ago [1,2,3]. On the one hand, epidemiologists have developed mathematical models that can be used as a guide to understanding how an epidemic spreads and to design immunization and vaccination policies [1,2,3]. On the other hand, data collections have provided information on the local patterns of relationships in a population. In particular, persons who may have come into contact with an infectious individual are identified and diagnosed, making it possible to contact-trace the way the epidemic spreads, and to validate the mathematical models. However, up to a few years ago, some of the assumptions at the basis of the theoretical models were difficult to test. This is the case, for instance, of the complete network of contacts -the backbone through which the diseases are transmitted. With the advent of modern society, fast transportation systems have changed human habits, and some diseases that just a few years ago would have produced local outbreaks, are nowadays a global threat for public health systems. A recent example is given by the severe acute respiratory syndrome (SARS), that spread very fast from Asia to North America a few years ago [4,5,6]. Therefore, it is of utmost importance to carefully take into account as much details as possible of the structural properties of the network on which the infection dynamics occurs.

Strikingly, a large number of statistical properties have been found to be common in the topology of real-world social, biological and technological networks [7,8,9]. Of particular relevance because of its ubiquity in nature, is the class of complex networks referred to as scale-free (SF) networks. In SF networks, the number of contacts or connections of a node with other nodes in the system, the degree (or connectivity) k, follows a power law distribution, P k ∼ k -γ . Recent studies have shown the importance of the SF topology on the dynamics and function of the system under study [7,8,9]. For instance, SF networks are very robust to random failures, but at the same time extremely fragile to targeted attacks of the highly connected nodes [10,11]. In the context of disease spreading, SF contact networks lead to a vanishing epidemic threshold in the limit of infinite population when γ ≤ 3 [12,13,14,15]. This is because the exponent γ is directly related to the first and second moment of the degree distribution, k and k 2 , and the ratio k / k 2 determines the epidemic threshold above which the outbreak occurs. When 2 < γ ≤ 3, k is finite while k 2 goes to infinity, that is, the transmission probability required for the infection to spread goes to zero. Conversely, when γ > 3, there is a finite threshold and the epidemic survives only when the spreading rate is above a certain critical value. The concept of a critical epidemic threshold is central in epidemiology. Its absence in SF networks with 2 < γ ≤ 3 has a number of important implications in terms of prevention policies: if diseases can spread and persist even in the case of vanishingly small transmission probabilities, then prevention campaigns where individuals are randomly chosen for vaccination are not much effective [12,13,14,15].

Our knowledge of the mechanisms involved in disease spreading as well as on the relation between the network structure and the dynamical patterns of the spreading process has improved in the last several years [16,17,18,19]. Current approaches are either individual-based simulations [18] or metapopulation models where network simulations are carried out through a detailed stratification of the population and infection dynamics [20]. In the particular case of sexually transmitted diseases (STDs), infections occur within the uniq

…(Full text truncated)…