Dynamic resource allocation for controlling pathogen spread on a large metapopulation network.

To control the spread of an infectious disease over a large network, the optimal allocation by a social planner of a limited resource is a fundamental and difficult problem. We address this problem for a livestock disease that propagates on an animal trade network according to an epidemiological-demographic model based on animal demographics and trade data. We assume that the resource is dynamically allocated following a certain score, up to the limit of resource availability. We adapt a greedy approach to the metapopulation framework, obtaining new scores that minimize approximations of two different objective functions, for two control measures: vaccination and treatment. Through intensive simulations, we compare the greedy scores with several heuristics. Although topology-based scores can limit the spread of the disease, information on herd health status seems crucial to eradicating the disease. In particular, greedy scores are among the most effective in reducing disease prevalence, even though they do not always perform the best. However, some scores may be preferred in real life because they are easier to calculate or because they use a smaller amount of resources. The developed approach could be adapted to other epidemiological models or to other control measures in the metapopulation setting.

A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic.

The effective reproduction number Reff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate Reff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted by Bayesian inference (particle Markov Chain Monte Carlo method) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its Reff(t). Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We can thus estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).

Controlling bovine paratuberculosis at a regional scale: Towards a decision modelling tool.

Johne's disease (paratuberculosis), a worldwide enzootic disease of cattle caused by Mycobacterium avium subsp. paratuberculosis (Map), mainly introduced into farms by purchasing infected animals, has a large economic impact for dairy producers. Since diagnostic tests used in routine are poorly sensitive, observing Map spread in the field is hardly possible, whereas there is a need for evaluating control strategies. Our objective was to provide a modelling framework to compare the efficacy of regional control strategies combining internal biosecurity measures and testing of traded animals, against Map spread in a metapopulation of dairy cattle herds. We represented 12,857 dairy herds located in Brittany (France), based on data from 2005 to 2013, used to calibrate herd sizes and demographic rates and to define trade events in a multiscale model of Map infection dynamics. By clustering and categorical descriptive analysis of intensive simulations of this model, based on a numerical experimental design, a large panel of control measures was explored. Their efficacy was assessed on model outputs such as the prevalence and probability of extinction at the metapopulation level. In addition, we proposed a scoring for the effort required to implement control measures and prioritized control strategies based on their theoretical epidemiological efficacy. Our results clearly indicate that eradication cannot be achieved on the mid term using available control measures. However, we identified relevant combinations of measures that lead to the control of Map spread with realistic level of implementation and coverage. The study highlights the challenge of controlling paratuberculosis in an endemically infected region as related to the poor test characteristics and frequent trade movements. Our model lays the foundations for a flexible and efficient tool to help collective animal health managers in defining relevant control strategies at a regional scale, accounting for local specificities in terms of contact network and farms' characteristics.

Market analyses of livestock trade networks to inform the prevention of joint economic and epidemiological risks.

Conventional epidemiological studies of infections spreading through trade networks, e.g., via livestock movements, generally show that central large-size holdings (hubs) should be preferentially surveyed and controlled in order to reduce epidemic spread. However, epidemiological strategies alone may not be economically optimal when costs of control are factored in together with risks of market disruption from targeting core holdings in a supply chain. Using extensive data on animal movements in supply chains for cattle and swine in France, we introduce a method to identify effective strategies for preventing outbreaks with limited budgets while minimizing the risk of market disruptions. Our method involves the categorization of holdings based on position along the supply chain and degree of market share. Our analyses suggest that trade has a higher risk of propagating epidemics through cattle networks, which are dominated by exchanges involving wholesalers, than for swine. We assess the effectiveness of contrasting interventions from the perspectives of regulators and the market, using percolation analysis. We show that preferentially targeting minor, non-central agents can outperform targeting of hubs when the costs to stakeholders and the risks of market disturbance are considered. Our study highlights the importance of assessing joint economic-epidemiological risks in networks underlying pathogen propagation and trade.

Epidemics in markets with trade friction and imperfect transactions.

Market trade-routes can support infectious-disease transmission, impacting biological populations and even disrupting trade that conduces the disease. Epidemiological models increasingly account for reductions in infectious contact, such as risk-aversion behaviour in response to pathogen outbreaks. However, responses in market dynamics clearly differ from simple risk aversion, as are driven by other motivation and conditioned by "friction" constraints (a term we borrow from labour economics). Consequently, the propagation of epidemics in markets of, for example livestock, is frictional due to time and cost limitations in the production and exchange of potentially infectious goods. Here we develop a coupled economic-epidemiological model where transient and long-term market dynamics are determined by trade friction and agent adaptation, and can influence disease transmission. The market model is parameterised from datasets on French cattle and pig exchange networks. We show that, when trade is the dominant route of transmission, market friction can be a significantly stronger determinant of epidemics than risk-aversion behaviour. In particular, there is a critical level of friction above which epidemics do not occur, which suggests some epidemics may not be sustained in highly frictional markets. In addition, friction may allow for greater delay in removal of infected agents that still mitigates the epidemic and its impacts. We suggest that policy for minimising contagion in markets could be adjusted to the level of market friction, by adjusting the urgency of intervention or by increasing friction through incentivisation of larger-volume less-frequent transactions that would have limited effect on overall trade flow. Our results are robust to model specificities and can hold in the presence of non-trade disease-transmission routes.

Approximation of epidemic models by diffusion processes and their statistical inference.

Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.

Spread of Q fever within dairy cattle herds: key parameters inferred using a Bayesian approach.

Q fever is a worldwide zoonosis caused by Coxiella burnetii. Although ruminants are recognized as the most important source of human infection, no previous studies have focused on assessing the characteristics of the bacterial spread within a cattle herd and no epidemic model has been proposed in this context. We assess the key epidemiological parameters from field data in a Bayesian framework that takes into account the available knowledge, missing data and the uncertainty of the observation process owing to the imperfection of diagnostic tests. We propose an original individual-based Markovian model in discrete time describing the evolution of the infection for each animal. Markov chain Monte Carlo methodology is used to estimate parameters of interest from data consisting of individual health states of 217 cows of five chronically infected dairy herds sampled every week for a four-week period. Outputs are the posterior distributions of the probabilities of transition between health states and of the environmental bacterial load. Our findings show that some herds are characterized by a very low infection risk while others have a mild infection risk and a non-negligible intermittent shedding probability. Moreover, the antibody status seems to be a key point in the bacterial spread (shedders with antibodies shed for a longer period of time than shedders without antibodies). In addition to the biological insights, these estimates also provide information for calibrating simulation models to assess control strategies for C. burnetii infection.

Does the effectiveness of control measures depend on the influenza pandemic profile?

BACKGROUND: Although strategies to contain influenza pandemics are well studied, the characterization and the implications of different geographical and temporal diffusion patterns of the pandemic have been given less attention. METHODOLOGY/MAIN FINDINGS: Using a well-documented metapopulation model incorporating air travel between 52 major world cities, we identified potential influenza pandemic diffusion profiles and examined how the impact of interventions might be affected by this heterogeneity. Clustering methods applied to a set of pandemic simulations, characterized by seven parameters related to the conditions of emergence that were varied following Latin hypercube sampling, were used to identify six pandemic profiles exhibiting different characteristics notably in terms of global burden (from 415 to >160 million of cases) and duration (from 26 to 360 days). A multivariate sensitivity analysis showed that the transmission rate and proportion of susceptibles have a strong impact on the pandemic diffusion. The correlation between interventions and pandemic outcomes were analyzed for two specific profiles: a fast, massive pandemic and a slow building, long-lasting one. In both cases, the date of introduction for five control measures (masks, isolation, prophylactic or therapeutic use of antivirals, vaccination) correlated strongly with pandemic outcomes. Conversely, the coverage and efficacy of these interventions only moderately correlated with pandemic outcomes in the case of a massive pandemic. Pre-pandemic vaccination influenced pandemic outcomes in both profiles, while travel restriction was the only measure without any measurable effect in either. CONCLUSIONS: our study highlights: (i) the great heterogeneity in possible profiles of a future influenza pandemic; (ii) the value of being well prepared in every country since a pandemic may have heavy consequences wherever and whenever it starts; (iii) the need to quickly implement control measures and even to anticipate pandemic emergence through pre-pandemic vaccination; and (iv) the value of combining all available control measures except perhaps travel restrictions.

Medication sales and syndromic surveillance, France.

Although syndromic surveillance systems using nonclinical data have been implemented in the United States, the approach has yet to be tested in France. We present the results of the first model based on drug sales that detects the onset of influenza season and forecasts its trend. Using weekly lagged sales of a selected set of medications, we forecast influenzalike illness (ILI) incidence at the national and regional level for 3 epidemic seasons (2000-01, 2001-02, and 2002-03) and validate the model with real-time updating on the fourth (2003-04). For national forecasts 1-3 weeks ahead, the correlation between observed ILI incidence and forecast was 0.85-0.96, an improvement over the current surveillance method in France. Our findings indicate that drug sales are a useful additional tool to syndromic surveillance, a complementary and independent source of information, and a potential improvement for early warning systems for both epidemic and pandemic planning.