Epidemic variability in complex networks

We study numerically the variability of the outbreak of diseases on complex networks. We use a SI model to simulate the disease spreading at short times, in homogeneous and in scale-free networks. In both cases, we study the effect of initial conditions on the epidemic's dynamics and its variability. The results display a time regime during which the prevalence exhibits a large sensitivity to noise. We also investigate the dependence of the infection time on nodes' degree and distance to the seed. In particular, we show that the infection time of hubs have large fluctuations which limit their reliability as early-detection stations. Finally, we discuss the effect of the multiplicity of shortest paths between two nodes on the infection time. Furthermore, we demonstrate that the existence of even longer paths reduces the average infection time. These different results could be of use for the design of time-dependent containment strategies

The Cost of Simplifying Air Travel When Modeling Disease Spread

BACKGROUND: Air travel plays a key role in the spread of many pathogens. Modeling the long distance spread of infectious disease in these cases requires an air travel model. Highly detailed air transportation models can be over determined and computationally problematic. We compared the predictions of a simplified air transport model with those of a model of all routes and assessed the impact of differences on models of infectious disease. METHODOLOGY/PRINCIPAL FINDINGS: Using U.S. ticket data from 2007, we compared a simplified "pipe" model, in which individuals flow in and out of the air transport system based on the number of arrivals and departures from a given airport, to a fully saturated model where all routes are modeled individually. We also compared the pipe model to a "gravity" model where the probability of travel is scaled by physical distance; the gravity model did not differ significantly from the pipe model. The pipe model roughly approximated actual air travel, but tended to overestimate the number of trips between small airports and underestimate travel between major east and west coast airports. For most routes, the maximum number of false (or missed) introductions of disease is small (<1 per day) but for a few routes this rate is greatly underestimated by the pipe model. CONCLUSIONS/SIGNIFICANCE: If our interest is in large scale regional and national effects of disease, the simplified pipe model may be adequate. If we are interested in specific effects of interventions on particular air routes or the time for the disease to reach a particular location, a more complex point-to-point model will be more accurate. For many problems a hybrid model that independently models some frequently traveled routes may be the best choice. Regardless of the model used, the effect of simplifications and sensitivity to errors in parameter estimation should be analyzed

Retrospective public health impact of a quadrivalent influenza vaccine in the United States over the period 2000-2014

Objectives: Vaccination has proven to be an efficient preventive strategy against influenza infection. Each year, two genetically distinct influenza B lineages cocirculate. Current trivalent influenza vaccines (TIVs) contain only one influenza B and two influenza A strains, but vaccine mismatch are frequent due to the difficulty to predict which B lineage will predominate during the next epidemic. Recently licensed quadrivalent influenza vaccines (QIVs) containing a strain from each B lineage should address these issues, but their impact still needs to be estimated. Our study assesses retrospectively what would have been the public health benefit of routinely vaccinating the US population with QIV instead of TIV. Methods: We developed a dynamic compartmental model able to account for interactions between influenza B lineages (natural or vaccine-induced). The model simulates influenza dynamics for the period 2000-2014, to account for the long-term impact of infection and vaccination. Age-structured population dynamics, vaccine efficacy (VE) per strain, and weekly ramp-up of vaccination coverage are modelled. Sensitivity analyses were performed on VE, duration of immunity, levels of vaccine-induced cross-protection between B strains. Results: Assuming a cross-protection of 70% of the matched VE, the model predicts that QIV would have prevented on average 15% more B-lineages cases. Elderly people (65+yo) and young seniors (50-64yo) benefit the most from QIV with 21% and 18% reduction of B cases respectively in those age groups. Reducing the cross-protection estimate of the matched VE to 50%, 30%, and 0% improves the relative benefit of QIV to 25%, 30%, and 34% fewer B cases in the US. Conclusions: Using a realistic retrospective framework, with real-life vaccine mismatch, our analysis shows that routine vaccination with QIV has the potential to substantially reduce the number of influenza infections, even with relatively conservative estimates of TIV induced cross-protection

Nonlinearity Valuation Adjustment

We develop a consistent, arbitrage-free framework for valuing derivative trades with collateral, counterparty credit risk, and funding costs. Credit, debit, liquidity, and funding valuation adjustments (CVA, DVA, LVA, and FVA) are simply introduced as modifications to the payout cash-flows of the trade position. The framework is flexible enough to accommodate actual trading complexities such as asymmetric collateral and funding rates, replacement close-out, and rehypothecation of posted collateral – all aspects which are often neglected. The generalized valuation equation takes the form of a forward-backward SDE or semilinear PDE. Nevertheless, it may be recast as a set of iterative equations which can be efficiently solved by our proposed least-squares Monte Carlo algorithm. We implement numerically the case of an equity option and show how its valuation changes when including the above effects. In the paper we also discuss the financial impact of the proposed valuation framework and of nonlinearity more generally. This is fourfold: Firstly, the valuation equation is only based on observable market rates, leaving the value of a derivatives transaction invariant to any theoretical risk-free rate. Secondly, the presence of funding costs makes the valuation problem a highly recursive and nonlinear one. Thus, credit and funding risks are non-separable in general, and despite common practice in banks, CVA, DVA, and FVA cannot be treated as purely additive adjustments without running the risk of double counting. To quantify the valuation error that can be attributed to double counting, we introduce a ’nonlinearity valuation adjustment’ (NVA) and show that its magnitude can be significant under asymmetric funding rates and replacement close-out at default. Thirdly, as trading parties cannot observe each others’ liquidity policies nor their respective funding costs, the bilateral nature of a derivative price breaks down. The value of a trade to a counterparty will not be just the opposite of the value seen by the bank. Finally, valuation becomes aggregation-dependent and portfolio values cannot simply be added up. This has operational consequences for banks, calling for a holistic, consistent approach across trading desks and asset classes

Preparing for the upcoming 2022/23 influenza season: a modelling study of the susceptible population in Australia, France, Germany, Italy, Spain and the United Kingdom.

Objective and method We analysed the influenza epidemic that occurred in Australia during the 2022 winter using an age-structured dynamic transmission model, which accounts for past epidemics to estimate the population susceptibility to an influenza infection. We applied the same model to five European countries. Conclusion Our analysis suggests Europe might experience an early and moderately large influenza epidemic. Also, differences may arise between countries, with Germany and Spain experiencing larger epidemics, than France, Italy and the United Kingdom, especially in children

Cost-effectiveness of quadrivalent versus trivalent influenza vaccine in the United States

BACKGROUND: Currently used trivalent influenza vaccines (TIVs) contain two strains of influenza A and one strain of influenza B. However, co-circulation of two distinct B lineages and difficulties in predicting which lineage will predominate in the next season have led to frequent B-strain mismatches. Newly registered quadrivalent influenza vaccines (QIVs) include two B strains and might therefore provide wider protection. Objectives: To evaluate the cost-effectiveness of using QIV versus TIV for routine influenza vaccination in the United States (US) during the next 20 years. Methods: A dynamic transmission model was used to estimate the additional protection offered by QIV over TIV against symptomatic influenza B disease. Subsequently, we used a decision tree model to determine the costeffectiveness of replacing TIV with QIV from a societal perspective. US data on influenza-related disease outcomes and corresponding costs were derived from published sources (e. g. Molinari et al. 2007). Results: Over 20 years, replacing TIV with QIV is predicted to prevent 13.3 million influenza B cases. According to our model this resulted in a reduction of 113,000 hospitalizations and 13,200 deaths. Moreover, 200,000 quality- adjusted life-years (QALYs), US$3.1 billion in medical costs and US$0.6 billion in indirect costs were saved. The base case estimate of the incremental cost-effectiveness ratio (ICER) was US$29,000 per QALY gained. Economic parameters with highest impact on the ICER were vaccine price, QALY loss due to influenza and probability of hospitalization or death given symptomatic infection. Conclusions: Introducing QIV into the immunization program of the United States would prevent a substantial number of hospitalizations and deaths. Moreover, cost-effectiveness was shown to be favorable when a cost-effectiveness threshold of US$50,000 is applied