Eugenio Valdano

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.

Predicting Epidemic Risk from Past Temporal Contact Data

Understanding how epidemics spread in a system is a crucial step to prevent and control outbreaks, with broad implications on the system’s functioning, health, and associated costs. This can be achieved by identifying the elements at higher risk of infection and implementing targeted surveillance and control measures. One important ingredient to consider is the pattern of disease-transmission contacts among the elements, however lack of data or delays in providing updated records may hinder its use, especially for time-varying patterns. Here we explore to what extent it is possible to use past temporal data of a system’s pattern of contacts to predict the risk of infection of its elements during an emerging outbreak, in absence of updated data. We focus on two real-world temporal systems; a livestock displacements trade network among animal holdings, and a network of sexual encounters in high-end prostitution. We define the node’s loyalty as a local measure of its tendency to maintain contacts with the same elements over time, and uncover important non-trivial correlations with the node’s epidemic risk. We show that a risk assessment analysis incorporating this knowledge and based on past structural and temporal pattern properties provides accurate predictions for both systems. Its generalizability is tested by introducing a theoretical model for generating synthetic temporal networks. High accuracy of our predictions is recovered across different settings, while the amount of possible predictions is system-specific. The proposed method can provide crucial information for the setup of targeted intervention strategies.

Infection propagator approach to compute epidemic thresholds on temporal networks: impact of immunity and of limited temporal resolution

The epidemic threshold of a spreading process indicates the condition for the occurrence of the wide spreading regime, thus representing a predictor of the network vulnerability to the epidemic. Such threshold depends on the natural history of the disease and on the pattern of contacts of the network with its time variation. Based on the theoretical framework introduced in [E. Valdano, L. Ferreri, C. Poletto, V. Colizza, Phys. Rev. X 5, 21005 (2015)] for a susceptible-infectious-susceptible model, we formulate here an infection propagator approach to compute the epidemic threshold accounting for more realistic effects regarding a varying force of infection per contact, the presence of immunity, and a limited time resolution of the temporal network. We apply the approach to two temporal network models and an empirical dataset of school contacts. We find that permanent or temporary immunity do not affect the estimation of the epidemic threshold through the infection propagator approach. Comparisons with numerical results show the good agreement of the analytical predictions. Aggregating the temporal network rapidly deteriorates the predictions, except for slow diseases once the heterogeneity of the links is preserved. Weight-topology correlations are found to be the critical factor to be preserved to improve accuracy in the prediction.

Impact of spatially constrained sampling of temporal contact networks on the evaluation of the epidemic risk

The ability to directly record human face-to-face interactions increasingly enables the development of detailed data-driven models for the spread of directly transmitted infectious diseases at the scale of individuals. Complete coverage of the contacts occurring in a population is however generally unattainable, due for instance to limited participation rates or experimental constraints in spatial coverage. Here, we study the impact of spatially constrained sampling on our ability to estimate the epidemic risk in a population using such detailed data-driven models. The epidemic risk is quantified by the epidemic threshold of the susceptible-infectious-recovered-susceptible model for the propagation of communicable diseases, i.e. the critical value of disease transmissibility above which the disease turns endemic. We verify for both synthetic and empirical data of human interactions that the use of incomplete data sets due to spatial sampling leads to the underestimation of the epidemic risk. The bias is however smaller than the one obtained by uniformly sampling the same fraction of contacts: it depends nonlinearly on the fraction of contacts that are recorded and becomes negligible if this fraction is large enough. Moreover, it depends on the interplay between the timescales of population and spreading dynamics.

Disease persistence on temporal contact networks accounting for heterogeneous infectious periods

The infectious period of a transmissible disease is a key factor for disease spread and persistence. Epidemic models on networks typically assume an identical average infectious period for all individuals, thus allowing an analytical treatment. This simplifying assumption is however often unrealistic, as hosts may have different infectious periods, due, for instance, to individual host-pathogen interactions or inhomogeneous access to treatment. While previous work accounted for this heterogeneity in static networks, a full theoretical understanding of the interplay of varying infectious periods and time-evolving contacts is still missing. Here we consider an SIS epidemic on a temporal network with host-specific average infectious periods, and develop an analytical framework to estimate the epidemic threshold, i.e. the critical transmissibility for disease spread in the host population. Integrating contact data for transmission with outbreak data and epidemiological estimates, we apply our framework to three real-world case studies exploring different epidemic contexts – the persistence of bovine tuberculosis in southern Italy, the spread of nosocomial infections in a hospital, and the diffusion of pandemic influenza in a school. We find that the homogeneous parameterization may cause important biases in the assessment of the epidemic risk of the host population. Our approach is also able to identify groups of hosts mostly responsible for disease diffusion who may be targeted for prevention and control, aiding public health interventions.

Network-based assessment of the vulnerability of Italian regions to bovine brucellosis

The endemic circulation of bovine brucellosis in cattle herds has a markedly negative impact on economy, due to decreased fertility, increased abortion rates, reduced milk and meat production. It also poses a direct threat to human health. In Italy, despite the long lasting efforts and the considerable economic investment, complete eradication of this disease still eludes the southern regions, as opposed to the northern regions that are disease-free. Here we introduced a novel quantitative network-based approach able to fully exploit the highly resolved databases of cattle trade movements and outbreak reports to yield estimates of the vulnerability of a cattle market to brucellosis. Tested on the affected regions, the introduced vulnerability indicator was shown to be accurate in predicting the number of bovine brucellosis outbreaks (Spearman r= 0.82, p= 0.04), thus confirming the suitability of our tool for epidemic risk assessment. We evaluated the dependence of regional vulnerability to brucellosis on a set of factors including premises spatial distribution, trading patterns, farming practices, herd market value, compliance to outbreak regulations, and exploring different epidemiological conditions. Animal trade movements were identified as a major route for brucellosis spread between farms (r=0.85,p<10-5 between vulnerability and number of inbound movements), with an additional potential risk attributed to the use of shared pastures (r=0.4,p=0.04). By comparing the vulnerability of disease-free regions in the north to affected regions in the south, we found that more intense trade and higher market value of the cattle sector in the north (r=0.56,p=0.01) likely inducing more efficient biosafety measures, together with poor compliance to trade restrictions following outbreaks in the south were key factors explaining the diverse success in eradicating brucellosis. Our modeling scheme is both synthetic and effective in gauging regional vulnerability to brucellosis persistence. Its general formulation makes it adaptable to other diseases and host species, providing a useful tool for veterinary epidemiology and policy assessment.

Farm productive realities and the dynamics of bovine viral diarrhea (BVD) transmission

Bovine Viral Diarrhea (BVD) is a viral disease that affects cattle and that is endemic to many European countries. It has a markedly negative impact on the economy, through reduced milk production, abortions, and a shorter lifespan of the infected animals. Cows becoming infected during gestation may give birth to Persistently Infected (PI) calves, which remain highly infective throughout their life, due to the lack of immune response to the virus. As a result, they are the key driver of the persistence of the disease both at herd scale, and at the national level. In the latter case, the trade-driven movements of PIs, or gestating cows carrying PIs, are responsible for the spatial dispersion of BVD. Past modeling approaches to BVD transmission have either focused on within-herd or between-herd transmission. A comprehensive portrayal, however, targeting both the generation of PIs within a herd, and their displacement throughout the Country due to trade transactions, is still missing. We overcome this by designing a multiscale metapopulation model of the spatial transmission of BVD, accounting for both within-herd infection dynamics, and its spatial dispersion. We focus on Italy, a country where BVD is endemic and seroprevalence is very high. By integrating simple within-herd dynamics of PI generation, and the highly-resolved cattle movement dataset available, our model requires minimal arbitrary assumptions on its parameterization. Notwithstanding, it accurately captures the dynamics of the BVD epidemic, as demonstrated by the comparison with available prevalence data. We use our model to study the role of the different productive realities of the Italian market, and test possible intervention strategies aimed at prevalence reduction. We find that dairy farms are the main drivers of BVD persistence in Italy, and any control strategy targeting these farms would lead to significantly higher prevalence reduction, with respect to targeting other production compartments. Our multiscale metapopulation model is a simple yet effective tool for studying BVD dispersion and persistence at country level, and is a good instrument for testing targeted strategies aimed at the containment or elimination of this disease. Furthermore, it can readily be applied to any national market for which cattle movement data is available.