Endemicity and prevalence of multipartite viruses under heterogeneous between-host transmission

Multipartite viruses replicate through a puzzling evolutionary strategy. Their genome is segmented into two or more parts, and encapsidated in separate particles that appear to propagate independently. Completing the replication cycle, however, requires the full genome, so that a systemic infection of a host requires the concurrent presence of several particles. This represents an apparent evolutionary drawback of multipartitism, while its advantages remain unclear. A transition from monopartite to multipartite viral forms has been described in vitro under conditions of high multiplicity of infection, suggesting that cooperation between defective mutants is a plausible evolutionary pathway towards multipartitism. However, it is unknown how the putative advantages that multipartitism might enjoy at the microscopic level affect its epidemiology, or if an explicit advantange is needed to explain its ecological persistence. To disentangle which mechanisms might contribute to the rise and fixation of multipartitism, we investigate the interaction between viral spreading dynamics and host population structure. We set up a compartmental model of the spread of a virus in its different forms and explore its epidemiology using both analytical and numerical techniques. We uncover that the impact of host contact structure on spreading dynamics entails a rich phenomenology of ecological relationships that includes cooperation, competition, and commensality. We find that multipartitism might rise to fixation even in the absence of explicit microscopic advantages. Multipartitism allows the virus to colonize environments that could not be invaded by the monopartite form, facilitated by homogeneous contacts among hosts. We conjecture that these features might have led to an increase in the diversity and prevalence of multipartite viral forms concomitantly with the expansion of agricultural practices.Comment: 27 pages, 4 figures, 1 tabl

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

Epidemic Threshold in Continuous-Time Evolving Networks

Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We introduce the {\em weak commutation} condition allowing the interpretation of annealed networks, activity-driven networks, and time scale separation into one formalism. Our work provides a coherent connection between discrete and continuous time representations applicable to realistic scenarios.Comment: 13 pages, 2 figure

Analyse quantitative de la vulnérabilité des réseaux temporels aux maladies infectieuses

Infectious disease modeling represents a powerful tool for assessing the vulnerability of a population to the introduction of a new infectious pathogen. The increased availability of highly resolved data tracking host interactions is making epidemic models potentially increasingly accurate. Integrating into them all the features emerging from these data, however, still represents a challenge. In particular, the interaction between disease dynamics and the time evolution of contact structures has been shown to impact the way pathogens spread, changing the conditions that lead to the wide-spreading regime, as encoded in epidemic threshold. Up to now researchers have characterized the epidemic threshold on time evolving contact structures only in specific settings. Using a multilayer formalism, we analytically compute the epidemic threshold on a generic temporal network, accounting for several different disease features. We use this methodology to assess the impact of time resolution and network duration on the estimation of the threshold. Then, thanks to it, we assess the global vulnerability of different systems to pathogen introduction, and in particular we analyze the networks of cattle trade movements Data collection strategies often inform us only about past network configurations, and that limits our prediction capabilities. We face this by developing a data-driven methodology for predicting targeted epidemic that relies only past contact data. Our work provides new methodologies for assessing and predicting the risk associated to an emerging pathogen, both at the population scale and targeting specific hosts.La modélisation des maladies infectieuses représente un outil important pour évaluer la vulnérabilité d'une population à l'introduction d'un nouveau agent pathogène. La possibilité d’enregistrer les contacts responsables de la propagation des maladies représente à la fois une ressource et un défi pour les modèles épidémiques. En particulier, l'interaction entre la dynamique des maladies et l'évolution dans le temps des structures de contact influence la façon dont les agents pathogènes se propagent, en changeant les conditions qui mènent à une flambée épidémique (seuil épidémique). Jusqu'à maintenant, les chercheurs n'ont caractérisé le seuil épidémique sur des structures de contact qui évoluent dans le temps que dans des contextes spécifiques. En utilisant un formalisme multi-couches, nous calculons analytiquement le seuil épidémique sur un réseau temporel générique. Nous utilisons cette méthode pour évaluer l'impact de la résolution temporelle et la durée du réseau sur l'estimation du seuil. De plus, grâce à cette méthode, nous évaluons la vulnérabilité globale de différents systèmes à l'introduction d'agents pathogènes, et en particulier nous analysons les réseaux de mouvements des bovins. Les données de contact souvent ne sont pas disponible en temps réel, et cela limite notre capacité de prévision. Pour répondre à ça, nous développons une méthodologie numérique pour prédire le risque épidémique ciblé, qui repose uniquement sur les données de contact passées. Notre travail fournit de nouvelles méthodologies pour évaluer et prédire le risque associé à un agent pathogène émergent, à la fois à l'échelle de la population et en ciblant des hôtes spécifiques

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.Comment: 24 pages, 5 figures + SI (18 pages, 15 figures

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.Comment: 21 pages, 7 figure

Estimates of the reproduction ratio from epidemic surveillance may be biased in spatially structured populations

An accurate and timely estimate of the reproduction ratio R of an infectious disease epidemic is crucial to make projections on its evolution and set up the appropriate public health response. Estimates of R routinely come from statistical inference on timelines of cases or their proxies like symptomatic cases, hospitalizatons, deaths. Here, however, we prove that these estimates of R may not be accurate if the population is made up of spatially distinct communities, as the interplay between space and mobility may hide the true epidemic evolution from surveillance data. This means that surveillance may underestimate R over long periods, to the point of mistaking a growing epidemic for a subsiding one, misinforming public health response. To overcome this, we propose a correction to be applied to surveillance data that removes this bias and ensures an accurate estimate of R across all epidemic phases. We use COVID-19 as case study; our results, however, apply to any epidemic where mobility is a driver of circulation, including major challenges of the next decades: respiratory infections (influenza, SARS-CoV-2, emerging pathogens), vector-borne diseases (arboviruses). Our findings will help set up public health response to these threats, by improving epidemic monitoring and surveillance.Comment: 11 pages, 4 figures, plus Supplementary Informatio

Dynamics of new strain emergence on a temporal network

Multi-strain competition on networks is observed in many contexts, including infectious disease ecology, information dissemination or behavioral adaptation to epidemics. Despite a substantial body of research has been developed considering static, time-aggregated networks, it remains a challenge to understand the transmission of concurrent strains when links of the network are created and destroyed over time. Here we analyze how network dynamics shapes the outcome of the competition between an initially endemic strain and an emerging one, when both strains follow a susceptible-infected-susceptible dynamics, and spread at time scales comparable with the network evolution one. Using time-resolved data of close-proximity interactions between patients admitted to a hospital and medical health care workers, we analyze the impact of temporal patterns and initial conditions on the dominance diagram and coexistence time. We find that strong variations in activity volume cause the probability that the emerging strain replaces the endemic one to be highly sensitive to the time of emergence. The temporal structure of the network shapes the dominance diagram, with significant variations in the replacement probability (for a given set of epidemiological parameters) observed from the empirical network and a randomized version of it. Our work contributes towards the description of the complex interplay between competing pathogens on temporal networks.Comment: 9 pages, 4 figure