Non-systemic transmission of tick-borne diseases: a network approach

Tick-Borne diseases can be transmitted via non-systemic (NS) transmission. This occurs when tick gets the infection by co-feeding with infected ticks on the same host resulting in a direct pathogen transmission between the vectors, without infecting the host. This transmission is peculiar, as it does not require any systemic infection of the host. The NS transmission is the main efficient transmission for the persistence of the Tick-Borne Encephalitis virus in nature. By describing the heterogeneous ticks aggregation on hosts through a \hyphenation{dynamical} bipartite graphs representation, we are able to mathematically define the NS transmission and to depict the epidemiological conditions for the pathogen persistence. Despite the fact that the underlying network is largely fragmented, analytical and computational results show that the larger is the variability of the aggregation, and the easier is for the pathogen to persist in the population.Comment: 15 pages, 4 figures, to be published in Communications in Nonlinear Science and Numerical Simulatio

Analytical computation of the epidemic threshold on temporal networks

The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes and affect the condition for large-scale propagation, as encoded in the epidemic threshold. Despite the great interest in the problem for the physics, applied mathematics, computer science and epidemiology communities, a full theoretical understanding is still missing and currently limited to the cases where the time-scale separation holds between spreading and network dynamics or to specific temporal network models. We consider a Markov chain description of the Susceptible-Infectious-Susceptible process on an arbitrary temporal network. By adopting a multilayer perspective, we develop a general analytical derivation of the epidemic threshold in terms of the spectral radius of a matrix that encodes both network structure and disease dynamics. The accuracy of the approach is confirmed on a set of temporal models and empirical networks and against numerical results. In addition, we explore how the threshold changes when varying the overall time of observation of the temporal network, so as to provide insights on the optimal time window for data collection of empirical temporal networked systems. Our framework is both of fundamental and practical interest, as it offers novel understanding of the interplay between temporal networks and spreading dynamics.Comment: 22 pages, 6 figure

Interplay of network dynamics and ties heterogeneity on spreading dynamics

The structure of a network dramatically affects the spreading phenomena unfolding upon it. The contact distribution of the nodes has long been recognized as the key ingredient in influencing the outbreak events. However, limited knowledge is currently available on the role of the weight of the edges on the persistence of a pathogen. At the same time, recent works showed a strong influence of temporal network dynamics on disease spreading. In this work we provide an analytical understanding, corroborated by numerical simulations, about the conditions for infected stable state in weighted networks. In particular, we reveal the role of heterogeneity of edge weights and of the dynamic assignment of weights on the ties in the network in driving the spread of the epidemic. In this context we show that when weights are dynamically assigned to ties in the network an heterogeneous distribution is able to hamper the diffusion of the disease, contrary to what happens when weights are fixed in time.Comment: 10 pages, 10 figure

Modeling the effects of variable feeding patterns of larval ticks on the transmission of Borrelia lusitaniae and Borrelia afzelii

Spirochetes belonging to the Borrelia burgdoferi sensu lato (sl) group cause Lyme Borreliosis (LB), which is the most commonly reported vector-borne zoonosis in Europe. B. burgdorferi sl is maintained in nature in a complex cycle involving Ixodes ricinus ticks and several species of vertebrate hosts. The transmission dynamics of B. burgdorferi sl is complicated by the varying competence of animals for different genospecies of spirochetes that, in turn, vary in their capability of causing disease. In this study, a set of difference equations simplifying the complex interaction between vectors and their hosts (competent and not for Borrelia) is built to gain insights into conditions underlying the dominance of B. lusitaniae (transmitted by lizards to susceptible ticks) and the maintenance of B. afzelii (transmitted by wild rodents) observed in a study area in Tuscany, Italy. Findings, in agreement with field observations, highlight the existence of a threshold for the fraction of larvae feeding on rodents below which the persistence of B. afzelii is not possible. Furthermore, thresholds change as nonlinear functions of the expected number of nymph bites on mice, and the transmission and recovery probabilities. In conclusion, our model provided an insight into mechanisms underlying the relative frequency of different Borrelia genospecies, as observed in field studies.Comment: 14 pages, 3 figures, to be published in Theoretical Population Biolog