Spatial heterogeneity, sediment-water exchange, and diffusion mechanisms of organophosphate esters from river to coastal aquatic system in a typical economic circle of northern China.

Organophosphate esters (OPEs) have proven to be pervasive in aquatic environments globally. However, understanding their partitioning behavior and mechanisms at the sediment-water interface remains limited. This study elucidated the spatial heterogeneity, interfacial exchange, and diffusion mechanisms of 14 OPEs (∑14OPEs) from river to coastal aquatic system. The transport tendencies of OPEs at the sediment-water interface were quantitatively assessed using fugacity methods. The total ∑14OPEs concentrations in water and sediments ranged from 154 ng/L to 528 ng/L and 2.41 ng/g dry weight (dw) to 230 ng/g dw, respectively. This result indicated a descending spatial tendency with moderate variability. OPE distribution was primarily influenced by temperature, pH, and dissolved oxygen levels. As the carbon atom number increased, alkyl and chlorinated OPEs transitioned from diffusion towards the aqueous phase to equilibrium. In contrast, aryl OPEs and triphenylphosphine oxide, which had equivalent carbon atom counts, maintained equilibrium throughout. Diffusion trends of individual OPE congener at the sediment-water interface varied at the same total organic carbon contents (foc). As the foc increased, the fugacity fraction values for all OPE homologs showed a declining trend. The distinct molecular structure of each OPE monomer might lead to unique diffusive behaviors at the sediment-water interface. Higher soot carbon content had a more pronounced effect on the distribution patterns of OPEs. The sediment-water distribution of OPEs was primarily influenced by total organic carbon, sediment particle size, dry density, and moisture content. OPEs displayed the highest sensitivity to fluctuations in ammonium and dissolved organic carbon. This study holds significant scientific and theoretical implications for elucidating the interfacial transport and driving forces of OPEs and comprehending their fate and endogenous release in aquatic ecosystems.

[Analysis of Ozone and VOCs Pollution Characteristics, Sources, and Abatement Control Strategies in Hebi].

In order to control the increasing ozone （O3） pollution in Hebi, Henan Province, clarifying the pollution characteristics of ozone and its precursors is vital. Therefore, we conducted a comprehensive analysis of O3 pollution utilizing the OFP-PMF-EKMA method combined with online hourly resolution monitoring data of conventional pollutants and volatile organic compounds （VOCs） in the summer of 2022 （June-September）. Ozone formation potential （OFP） was used to identify the key VOCs species, and the PMF model was used to identify the VOCs emission sources, whereas EKMA curves and scenario analysis were used to identify the main ozone control area in Hebi and to determine the reduction ratio of VOCs and NOx in a scientifically refined way. In 2022, Hebi had persistent O3 pollution, with the highest concentration in June. Conditions of high temperature, low humidity, and low atmospheric pressure contributed to the O3 accumulation. Aromatic and oxygenated volatile organic compounds （OVOCs） contributed significantly to the OFP and VOCs fraction, which were the dominant active substance and concentration dominant species. The results of the VOCs source analysis indicated that vehicle exhaust sources （25.3%） were the main source of atmospheric VOCs, followed by process sources （17.7%） and biomass combustion sources （17.6%）. Thus, emission sources associated with the combustion of fossil fuels and industrial production emissions were the most urgent sources of atmospheric VOCs to be controlled in Hebi. The O3 generation in Hebi occurred in the VOCs-sensitive zones, and the emission reduction results showed that a synergistic emission reduction of VOCs and nitrogen oxide （NOx） could effectively control O3 pollution with a 75% reduction in VOCs and a 10% reduction in NOx.

Evolutionary game analysis between regional governments and shipping companies: Considering the impact of government subsidy on shipping companies.

Maritime agencies are imposing stricter limits on fuel sulfur content, and regional governments are encouraging the reduction of various emissions through subsidies. In this study, an evolutionary game model is constructed to analyze the interaction between regional governments and shipping companies under the fixed and dynamic subsidies. The sensitivity analysis reveals the effect of parameters on stabilization strategies. The results show that the bilateral stakeholders can adopt stabilization strategies under dynamic subsidies. The fines, maximum subsidies and extra cost paid by regional governments have a significant impact on these strategies. To reduce the dependence of shipping companies on subsidy policies, it is recommended to improve the LSFO refining technology in the future. Expanding the implementation scope of LSFO subsidy policies will increase the utilization of LSFO by shipping companies. This study offers insights for governments to optimize the LSFO subsidy policy and shipping companies to choose sulfur oxides reduction approaches.

NITIRSOIL: A model that balances complexity with prediction uncertainty for improving nitrogen fertilization in agriculture.

Mismanagement of the nitrogen (N) fertilization in agriculture leads to low N use efficiency (NUE) and therefore pollution of waters and atmosphere due to NO3- leaching, and N2O and NH3 emissions. The use of N simulation models of the soil-plant system can help improve the N fertilizer management increasing NUE and decreasing N pollution issues. However, many N simulation models lack balance between complexity and uncertainty with the result that they are not applied in actual practice. The NITIRSOIL is a one-dimensional transient-state model with a monthly time step that aims at addressing this lack in the estimation of, mainly, dry matter yield (DMY), crop N uptake (Nupt), soil mineral N (Nmin), and NO3- leaching in agricultural fields. According to its global sensitivity analysis for horticulture, the NITIRSOIL simulations of the aforementioned outputs mostly depend on the critical N dilution curve, harvest index, dry matter fraction, potential fresh yield and nitrification coefficients. According to its validation for 35 nitrogen fertilization trials with 11 vegetables under semi-arid Mediterranean climate in Eastern Spain, the NITIRSOIL presents indices of agreement between 0.87 and 0.97 for the prediction of total dry matter, DMY, Nupt, NO3- leaching and soil Nmin at crop season end. Therefore, the NITIRSOIL model can be used in actual practice to improve the sustainability of the N management in, particularly horticulture, due to the balance it features between complexity and prediction uncertainty. For this aim, the NITRISOIL can be used either on its own, or in combination with "Nmin" on-site N fertilization recommendation methods, or even could be implemented as the calculation core of decision support systems.

Improving groundwater vulnerability assessment in structurally controlled hard rock aquifer: insight from lineament density and land use/land cover pattern.

A comprehensive seasonal assessment of groundwater vulnerability was conducted in the weathered hard rock aquifer of the upper Swarnrekha watershed in Ranchi district, India. Lineament density (Ld) and land use/land cover (LULC) were integrated into the conventional DRASTIC and Pesticide DRASTIC (P-DRASTIC) models and were extensively compared with six modified models, viz. DRASTIC-Ld, DRASTIC-Lu, DRASTIC-LdLu, P-DRASTIC-Ld, P-DRASTIC-Lu, and P-DRASTIC-LdLu, to identify the most optimal model for vulnerability mapping in hard rock terrain of the region. Findings were geochemically validated using NO3- concentrations of 68 wells during pre-monsoon (Pre-M) and post-monsoon (Post-M) 2022. Irrespective of the applied model, groundwater vulnerability shows significant seasonal variation, with > 45% of the region classified as high to very high vulnerability in the pre-M, increasing to Ì´67% in post-M season, highlighting the importance of seasonal vulnerability assessments. Agriculture and industries' dominant southern region showed higher vulnerability, followed by regions with high Ld and thin weathered zone. Incorporating Ld and LULC parameters into DRASTIC-LdLu and P-DRASTIC-LdLu models increases the 'Very High' vulnerability zones to 17.4% and 17.6% for pre-M and 29.4% and 27.9% for post-M, respectively. Similarly, 'High' vulnerable zones increase from 32.5% and 25% in pre-M to 33.8% and 35.3% in post-M for respective models. Model output comparisons suggest that modified DRASTIC-LdLu and P-DRASTIC-LdLu perform better, with accurate estimations of 83.8% and 89.7% for pre-M and post-M, respectively. However, results of geochemical validation suggest that among all the applied modified models, DRASTIC-LdLu performs best, with accurate estimations of 34.4% and 20.6% for pre-M and post-M, respectively.

Physics-informed machine learning algorithms for forecasting sediment yield: an analysis of physical consistency, sensitivity, and interpretability.

The sediment transport, involving the movement of the bedload and suspended sediment in the basins, is a critical environmental concern that worsens water scarcity and leads to degradation of land and its ecosystems. Machine learning (ML) algorithms have emerged as powerful tools for predicting sediment yield. However, their use by decision-makers can be attributed to concerns regarding their consistency with the involved physical processes. In light of this issue, this study aims to develop a physics-informed ML approach for predicting sediment yield. To achieve this objective, Gaussian, Center, Regular, and Direct Copulas were employed to generate virtual combinations of physical of the sub-basins and hydrological datasets. These datasets were then utilized to train deep neural network (DNN), conventional neural network (CNN), Extra Tree, and XGBoost (XGB) models. The performance of these models was compared with the modified universal soil loss equation (MUSLE), which serves as a process-based model. The results demonstrated that the ML models outperformed the MUSLE model, exhibiting improvements in Nash-Sutcliffe efficiency (NSE) of approximately 10%, 18%, 32%, and 41% for the DNN, CNN, Extra Tree, and XGB models, respectively. Furthermore, through Sobol sensitivity and Shapley additive explanation-based interpretability analyses, it was revealed that the Extra Tree model displayed greater consistency with the physical processes underlying sediment transport as modeled by MUSLE. The proposed framework provides new insights into enhancing the accuracy and applicability of ML models in forecasting sediment yield while maintaining consistency with natural processes. Consequently, it can prove valuable in simulating process-related strategies aimed at mitigating sediment transport at watershed scales, such as the implementation of best management practices.

Model simplification and sensitivity analysis of chemical species for oxidation behavior in multi route complex chemical mechanism.

This study employs a Model Reduction Technique (MRT) to simplify the four-step catalytic carbon monoxide (CO) oxidation reaction. The C-matrix method identifies key elements, key/non key components, and key reactions, while the Intrinsic Low-Dimensional Manifold (ILDM) pinpoints a Slow-Invariant Manifold (SIM) important for understanding key species behavior. Sensitivity analysis can be considered for measuring the efficiency of the chemical species in detailed mechanism. This systematic approach contributes to optimizing and controlling complex reactions offering broad application potential. In addition to the mathematical proof, the validation of the given chemical model is rectified. The comparison between the slow invariant manifold of both reaction routes is reported and the computational based results performed in this study are obtained through MATLAB.

Mathematical and sensitivity analysis for chemical species in multistep dynamical system: A computational study.

This study presents a significant contribution to the field of chemical kinetics by providing a detailed analysis of a multi-step chemical kinetic process using ordinary differential equations (ODEs). The aim is to describe complex chemical processes' kinetics and the steady-state behavior of chemical species. The research employs reduction techniques to simplify the model by separating fast and slow processes based on their time scales, with a focus on a two-step reversible reaction mechanism. Special consideration is given to the phase flow of solution trajectories near equilibrium points, providing a clear depiction of system behavior. MATLAB simulations demonstrate the physical properties of observed data, while sensitivity analysis reveals parameters' impact on species behavior. Overall, this study enhances our understanding of chemical kinetics and offers insights into modeling complex reaction processes, with implications for various applications in chemistry and related fields.

Impact of variable economic conditions on the cost of energy and the economic viability of floating photovoltaics.

This work evaluates the effects of economic conditions' variations on the costs and viability of floating photovoltaics, a novel solution where modules are installed on or above water. A sensitivity analysis of key economic criteria is conducted across multiple European countries, first generating country-specific baseline scenarios and then introducing systematic variations into the input parameters. The results show that capital expenditure and electricity prices, which have both experienced significant variations in recent years, have the largest influence on the net present value and the internal rate of return. Similarly, capital expenditure and discount rate are found to be the most influencing factors for the levelized cost of electricity. Overall, this study contributes to the literature by identifying the correlations between the economic variables and the viability of floating photovoltaics. The findings can be used to assess the effectiveness of potential government policies and support mechanisms and to evaluate the viability of this technology under varying national and international economic conditions.

Parsimonious Random-Forest-Based Land-Use Regression Model Using Particulate Matter Sensors in Berlin, Germany.

Machine learning (ML) methods are widely used in particulate matter prediction modelling, especially through use of air quality sensor data. Despite their advantages, these methods' black-box nature obscures the understanding of how a prediction has been made. Major issues with these types of models include the data quality and computational intensity. In this study, we employed feature selection methods using recursive feature elimination and global sensitivity analysis for a random-forest (RF)-based land-use regression model developed for the city of Berlin, Germany. Land-use-based predictors, including local climate zones, leaf area index, daily traffic volume, population density, building types, building heights, and street types were used to create a baseline RF model. Five additional models, three using recursive feature elimination method and two using a Sobol-based global sensitivity analysis (GSA), were implemented, and their performance was compared against that of the baseline RF model. The predictors that had a large effect on the prediction as determined using both the methods are discussed. Through feature elimination, the number of predictors were reduced from 220 in the baseline model to eight in the parsimonious models without sacrificing model performance. The model metrics were compared, which showed that the parsimonious_GSA-based model performs better than does the baseline model and reduces the mean absolute error (MAE) from 8.69 µg/m3 to 3.6 µg/m3 and the root mean squared error (RMSE) from 9.86 µg/m3 to 4.23 µg/m3 when applying the trained model to reference station data. The better performance of the GSA_parsimonious model is made possible by the curtailment of the uncertainties propagated through the model via the reduction of multicollinear and redundant predictors. The parsimonious model validated against reference stations was able to predict the PM2.5 concentrations with an MAE of less than 5 µg/m3 for 10 out of 12 locations. The GSA_parsimonious performed best in all model metrics and improved the R2 from 3% in the baseline model to 17%. However, the predictions exhibited a degree of uncertainty, making it unreliable for regional scale modelling. The GSA_parsimonious model can nevertheless be adapted to local scales to highlight the land-use parameters that are indicative of PM2.5 concentrations in Berlin. Overall, population density, leaf area index, and traffic volume are the major predictors of PM2.5, while building type and local climate zones are the less significant predictors. Feature selection based on sensitivity analysis has a large impact on the model performance. Optimising models through sensitivity analysis can enhance the interpretability of the model dynamics and potentially reduce computational costs and time when modelling is performed for larger areas.

Evaluation of fluoride exposure using disability-adjusted life years and health risk assessment in south-western Iran: A novel Monte Carlo simulation.

Consumption of fluoride-contaminated water is a worldwide concern, especially in developing countries, including Iran. However, there are restricted studies of non-single-value health risk assessment and the disease burden regarding fluoride intake nationwide. Prolonged exposure to excessive fluoride has been linked to adverse health effects such as dental and skeletal fluorosis. This can lead to under-mineralization of hard tissues, causing aesthetic concerns for teeth and changes in bone structure, increasing the risk of fractures. As such, we aimed to implement probability-based frameworks using Monte Carlo methods to explore the potential adverse effects of fluoride via the ingestion route. This platform consists of two sectors: 1) health risk assessment of various age categories coupled with a variance decomposition technique to measure the contributions of predictor variables in the outcome of the health risk model, and 2) implementing Monte Carlo methods in dose-response curves to explore the fluoride-induced burden of diseases of dental fluorosis and skeletal fractures in terms of disability-adjusted life years (DALYs). For this purpose, total water samples of 8053 (N=8053) from 57 sites were analyzed in Fars and Bushehr Provinces. The mean fluoride concentrations were 0.75 mg/L and 1.09 mg/L, with maximum fluoride contents of 6.5 mg/L and 3.22 mg/L for the Fars and Bushehr provinces, respectively. The hazard quotient of the 95th percentile (HQ>1) revealed that all infants and children in the study area were potentially vulnerable to over-receiving fluoride. Sobol' sensitivity analysis indices, including first-order, second-order, and total order, disclosed that fluoride concentration (Cw), ingestion rate (IRw), and their mutual interactions were the most influential factors in the health risk model. DALYs rate of dental fluorosis was as high as 981.45 (uncertainty interval: UI 95 % 353.23-1618.40) in Lamerd, and maximum DALYs of skeletal fractures occurred in Mohr 71.61(49.75-92.71), in Fars Province, indicated severe dental fluorosis but mild hazard regarding fractures. Residents of the Tang-e Eram in Bushehr Province with a DALYs rate of 3609.40 (1296.68-5993.73) for dental fluorosis and a DALYs rate of 284.67 (199.11-367.99) for skeletal fractures were the most potentially endangered population. By evaluating the outputs of the DALYs model, the gap in scenarios of central tendency exposure and reasonable maximum exposure highlights the role of food source intake in over-receiving fluoride. This research insists on implementing defluoridation programs in fluoride-endemic zones to combat the undesirable effects of fluoride. The global measures presented in this research aim to address the root causes of contamination and help policymakers and authorities mitigate fluoride's harmful impacts on the environment and public health.

ANN Prediction of Laser Power, Cutting Speed, and Number of Cut Annual Rings and Their Influence on Selected Cutting Characteristics of Spruce Wood for CO2 Laser Processing.

In this work, we focus on the prediction of the influence of CO2 laser parameters on the kerf properties of cut spruce wood. Laser kerf cutting is mainly characterized by the width of kerf and the width of the heat-affected zone, which depend on the laser power, cutting speed, and structure of the cut wood, represented by the number of cut annual rings. According to the measurement results and ANN prediction results, for lower values of the laser power (P) and cutting speed (v), the effect of annual rings (ARs) is non-negligible. The results of the sensitivity analysis show that the effect of v increases at higher energy density (E) values. With P in the range between 100 and 500 W, v values between 3 and 50 mm·s-1, and AR numbers between 3 and 11, the combination of P = 200 W and v = 50 mm·s-1, regardless of the AR value, leads to the best cut quality for spruce wood. In this paper, the main goal is to show how changes in the input parameters affect the characteristics of the cutting kerf and heat-affected zones for all possible input parameter values.

A Mathematical Model for Fibrous Dysplasia: The Role of the Flow of Mutant Cells.

Fibrous dysplasia (FD) is a mosaic non-inheritable genetic disorder of the skeleton in which normal bone is replaced by structurally unsound fibro-osseous tissue. There is no curative treatment for FD, partly because its pathophysiology is not yet fully known. We present a simple mathematical model of the disease incorporating its basic known biology, to gain insight on the dynamics of the involved bone-cell populations, and shed light on its pathophysiology. We develop an analytical study of the model and study its basic properties. The existence and stability of steady states are studied, an analysis of sensitivity on the model parameters is done, and different numerical simulations provide findings in agreement with the analytical results. We discuss the model dynamics match with known facts on the disease, and how some open questions could be addressed using the model.

Mathematical analysis of simple behavioral epidemic models.

COVID-19 highlighted the importance of considering human behavior change when modeling disease dynamics. This led to developing various models that incorporate human behavior. Our objective is to contribute to an in-depth, mathematical examination of such models. Here, we consider a simple deterministic compartmental model with endogenous incorporation of human behavior (i.e., behavioral feedback) through transmission in a classic Susceptible-Exposed-Infectious-Recovered (SEIR) structure. Despite its simplicity, the SEIR structure with behavior (SEIRb) was shown to perform well in forecasting, especially compared to more complicated models. We contrast this model with an SEIR model that excludes endogenous incorporation of behavior. Both models assume permanent immunity to COVID-19, so we also consider a modification of the models which include waning immunity (SEIRS and SEIRSb). We perform equilibria, sensitivity, and identifiability analyses on all models and examine the fidelity of the models to replicate COVID-19 data across the United States. Endogenous incorporation of behavior significantly improves a model's ability to produce realistic outbreaks. While the two endogenous models are similar with respect to identifiability and sensitivity, the SEIRSb model, with the more accurate assumption of the waning immunity, strengthens the initial SEIRb model by allowing for the existence of an endemic equilibrium, a realistic feature of COVID-19 dynamics. When fitting the model to data, we further consider the addition of simple seasonality affecting disease transmission to highlight the explanatory power of the models.

A compartmental model for smoking dynamics in Italy: a pipeline for inference, validation, and forecasting under hypothetical scenarios.

We propose a compartmental model for investigating smoking dynamics in an Italian region (Tuscany). Calibrating the model on local data from 1993 to 2019, we estimate the probabilities of starting and quitting smoking and the probability of smoking relapse. Then, we forecast the evolution of smoking prevalence until 2043 and assess the impact on mortality in terms of attributable deaths. We introduce elements of novelty with respect to previous studies in this field, including a formal definition of the equations governing the model dynamics and a flexible modelling of smoking probabilities based on cubic regression splines. We estimate model parameters by defining a two-step procedure and quantify the sampling variability via a parametric bootstrap. We propose the implementation of cross-validation on a rolling basis and variance-based Global Sensitivity Analysis to check the robustness of the results and support our findings. Our results suggest a decrease in smoking prevalence among males and stability among females, over the next two decades. We estimate that, in 2023, 18% of deaths among males and 8% among females are due to smoking. We test the use of the model in assessing the impact on smoking prevalence and mortality of different tobacco control policies, including the tobacco-free generation ban recently introduced in New Zealand.

Modeling and investigating malaria P. Falciparum and P. Vivax infections: Application to Djibouti data.

Malaria is an infectious and communicable disease, caused by one or more species of Plasmodium parasites. There are five species of parasites responsible for malaria in humans, of which two, Plasmodium Falciparum and Plasmodium Vivax, are the most dangerous. In Djibouti, the two species of Plasmodium are present in different proportions in the infected population: 77% of P. Falciparum and 33% of P. Vivax. In this study we present a new mathematical model describing the temporal dynamics of Plasmodium Falciparum and Plasmodium Vivax co-infection. We focus briefly on the well posedness of this model and on the calculation of the basic reproductive numbers for the infections with each Plasmodium species that help us understand the long-term dynamics of this model (i.e., existence and stability of various eqiuilibria). Then we use computational approaches to: (a) identify model parameters using real data on malaria infections in Djibouti; (b) illustrate the influence of different estimated parameters on the basic reproduction numbers; (c) perform global sensitivity and uncertainty analysis for the impact of various model parameters on the transient dynamics of infectious mosquitoes and infected humans, for infections with each of the Plasmodium species. The originality of this research stems from employing the FAST method and the LHS method to identify the key factors influencing the progression of the disease within the population of Djibouti. In addition, sensitivity analysis identified the most influential parameter for Falciparium and Vivax reproduction rates. Finally, the uncertainty analysis enabled us to understand the variability of certain parameters on the infected compartments.

Improved Efficiency and Sensitivity Analysis of 3-D Agent-based Model for Pain-related Neural Activity in the Amygdala.

Neuropathic pain is caused by nerve injury and involves brain areas such as the central nucleus of the amygdala (CeA). We developed the first 3-D agent-based model (ABM) of neuropathic pain-related neurons in the CeA using NetLogo3D. The execution time of a single ABM simulation using realistic parameters (e.g., 13,000 neurons and 22,000+ neural connections) is an important factor in the model's usability. In this paper, we describe our efforts to improve the computational efficiency of our 3-D ABM, which resulted in a 28% reduction in execution time on average for a typical simulation. With this upgraded model, we performed one- and two-parameter sensitivity analyses to study the sensitivity of model output to variability in several key parameters along the anterior to posterior axis of the CeA. These results highlight the importance of computational modeling in exploring spatial and cell-type specific properties of brain regions to inform future wet lab experiments.

Machine learning prediction of methane, nitrogen, and natural gas mixture viscosities under normal and harsh conditions.

The accurate estimation of gas viscosity remains a pivotal concern for petroleum engineers, exerting substantial influence on the modeling efficacy of natural gas operations. Due to their time-consuming and costly nature, experimental measurements of gas viscosity are challenging. Data-based machine learning (ML) techniques afford a resourceful and less exhausting substitution, aiding research and industry at gas modeling that is incredible to reach in the laboratory. Statistical approaches were used to analyze the experimental data before applying machine learning. Seven machine learning techniques specifically Linear Regression, random forest (RF), decision trees, gradient boosting, K-nearest neighbors, Nu support vector regression (NuSVR), and artificial neural network (ANN) were applied for the prediction of methane (CH4), nitrogen (N2), and natural gas mixture viscosities. More than 4304 datasets from real experimental data utilizing pressure, temperature, and gas density were employed for developing ML models. Furthermore, three novel correlations have developed for the viscosity of CH4, N2, and composite gas using ANN. Results revealed that models and anticipated correlations predicted methane, nitrogen, and natural gas mixture viscosities with high precision. Results designated that the ANN, RF, and gradient Boosting models have performed better with a coefficient of determination (R2) of 0.99 for testing data sets of methane, nitrogen, and natural gas mixture viscosities. However, linear regression and NuSVR have performed poorly with a coefficient of determination (R2) of 0.07 and - 0.01 respectively for testing data sets of nitrogen viscosity. Such machine learning models offer the industry and research a cost-effective and fast tool for accurately approximating the viscosities of methane, nitrogen, and gas mixture under normal and harsh conditions.

Modeling and analysis of a human papilloma virus transmission model with impact of media.

The human papillomavirus (HPV) is threatening human health as it spreads globally in varying degrees. On the other hand, the speed and scope of information transmission continues to increase, as well as the significant increase in the number of HPV-related news reports, it has never been more important to explore the role of media news coverage in the spread and control of the virus. Using a decreasing factor that captures the impact of media on the actions of people, this paper develops a model that characterizes the dynamics of HPV transmission with media impact, vaccination and recovery. We obtain global stability of equilibrium points employing geometric method, and further yield effective methods to contain the HPV pandemic by sensitivity analysis. With the center manifold theory, we show that there is a forward bifurcation when R0=1. Our study suggested that, besides controlling contact between infected and susceptible populations and improving effective vaccine coverage, a better intervention would be to strengthen media coverage. In addition, we demonstrated that contact rate and the effect of media coverage result in multiple epidemics of infection when certain conditions are met, implying that interventions need to be tailored to specific situations.

How many Monte Carlo samples are needed for probabilistic cost-effectiveness analyses?

OBJECTIVE: Probabilistic sensitivity analysis (PSA) is conducted to account for the uncertainty in cost and effect of decision options under consideration. PSA involves obtaining a large sample of input parameter values (N) to estimate the expected cost and effect of each alternative in the presence of parameter uncertainty. When the analysis involves using stochastic models (e.g., individual-level models), the model is further replicated P times for each sampled parameter set. We study how N and P should be determined. METHODS: We show that PSA could be structured such that P can be an arbitrary number (say, P=1). To determine N, we derive a formula based on Chebyshev's inequality such that the error in estimating the incremental cost-effectiveness ratio (ICER) of alternatives (or equivalently, the willingness-to-pay value at which the optimal decision option changes) is within a desired level of accuracy. We described two methods to confirmed, visually and quantitatively, that the N informed by this method results in ICER estimates within the specified level of accuracy. RESULTS: When N is arbitrarily selected, the estimated ICERs could be substantially different from the true ICER (even as P increases), which could lead misleading conclusions. Using a simple resource allocation model, we demonstrate that the proposed approach can minimize the potential for this error. CONCLUSIONS: The number of parameter samples in probabilistic CEAs should not be arbitrarily selected. We describe three methods to ensure that enough parameter samples are used in probabilistic CEAs.