Optimal Control and Sensitivity Analysis of an Influenza Model with Treatment and Vaccination

We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin’s maximum principle, and it is observed that full treatment effort should be given while increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive parameters for the endemic equilibrium point.     

A Simulation Model for Assessing Soybean Rust Epidemics

A soybean rust (causal agent Phakopsora pachyrhizt) simulation model was developed for assessing disease epidemics as a part of pest risk analysis. Equations describing environmental effects on disease components were developed by re-analyzing previous data with a view toward a systems approach. The infection rate was predicted well using dew period and temperature after inoculation as independent variables (R²=0.88, P < 0.0001). The exponential models which used physiological day as an independent variable explained 98% of the variations of latent period and senescence of disease lesions. The simulation model was validated with data from 72 sequential planting experiments during 1980 and 1981 in Taiwan. Time of onset for these epidemics varied from 25—60 days and 50—80 days after planting soybean cultivars TK 5 and G 8587, respectively. The epidemic periods were 75—95 for TK 5 and 100—120 days for G 8587. Variation of epidemics was accurately predicted by the simulator. Predicted disease curves fit well the observed disease curves for the recognized cropping seasons, spring- and autumn-seeded crops. For G 8587, which is very sensitive to photoperiod, the data from spring and autumn gave a better fit compared with data from pre-summer planting. The model underestimated disease epidemics during the winter, probably because the plant growth model failed to reflect the photoperiod rection of soybean. The simulation model was validated with data from other experiments conducted in three cropping seasons in 1979 and 1980. Determination coefficients of the regression between observed and predicted disease severity were significant.     

A Small Community Model for the Transmission of Infectious Diseases: Comparison of School Closure as an Intervention in Individual-Based Models of an Influenza Pandemic

Background

In the absence of other evidence, modelling has been used extensively to help policy makers plan for a potential future influenza pandemic.

Method

We have constructed an individual based model of a small community in the developed world with detail down to exact household structure obtained from census collection datasets and precise simulation of household demographics, movement within the community and individual contact patterns. We modelled the spread of pandemic influenza in this community and the effect on daily and final attack rates of four social distancing measures: school closure, increased case isolation, workplace non-attendance and community contact reduction. We compared the modelled results of final attack rates in the absence of any interventions and the effect of school closure as a single intervention with other published individual based models of pandemic influenza in the developed world.

Results

We showed that published individual based models estimate similar final attack rates over a range of values for R₀ in a pandemic where no interventions have been implemented; that multiple social distancing measures applied early and continuously can be very effective in interrupting transmission of the pandemic virus for R₀ values up to 2.5; and that different conclusions reached on the simulated benefit of school closure in published models appear to result from differences in assumptions about the timing and duration of school closure and flow-on effects on other social contacts resulting from school closure.

Conclusion

Models of the spread and control of pandemic influenza have the potential to assist policy makers with decisions about which control strategies to adopt. However, attention needs to be given by policy makers to the assumptions underpinning both the models and the control strategies examined.     

Individual-Based Model for Quorum Sensing with Background Flow

Quorum sensing is a wide-spread mode of cell–cell communication among bacteria in which cells release a signalling substance at a low rate. The concentration of this substance allows the bacteria to gain information about population size or spatial confinement. We consider a model for \(N\) cells which communicate with each other via a signalling substance in a diffusive medium with a background flow. The model consists of an initial boundary value problem for a parabolic PDE describing the exterior concentration \(u\) of the signalling substance, coupled with \(N\) ODEs for the masses \(a_i\) of the substance within each cell. The cells are balls of radius \(R\) in \(\mathbb {R} ^3\) , and under some scaling assumptions we formally derive an effective system of \(N\) ODEs describing the behaviour of the cells. The reduced system is then used to study the effect of flow on communication in general, and in particular for a number of geometric configurations.     

Spatial Prediction of Invasion Success Across Heterogeneous Landscapes using an Individual-Based Model

The limited resources available for managing invasive plant species in native ecosystems and the magnitude of the problem make it essential that we develop methods to prioritize sites for management efforts. We used the individual-based simulation model ECOTONE in conjunction with climate and soil texture data to identify grassland site types where the invasive perennial forb Acroptilon repens is likely to be successful, and to create a threat map indicating the most vulnerable regions of Colorado. Acroptilon repens has the potential to become most abundant in dry areas with fine-textured soils. This information can be used to direct management efforts towards the areas at greatest risk, allowing the most effective use of limited resources. The most common approach for identifying invasible regions has been to extrapolate from the locations of existing invasions to find similar sites. Two major drawbacks to this method are the lack of consideration of the role of the existing plant community in inhibiting or facilitating invasion, and the assumption that the invading species is at equilibrium with the environment. The combination of an individual-based simulation model and a geographic information system provides a flexible tool to investigate the community and regional dynamics of invasive plant species.     

Towards an Explainable Model for Sepsis Detection Based on Sensitivity Analysis

ObjectivesSepsis is a life-threatening condition which is responsible for a high proportion of intra-hospital deaths and related healthcare costs each year. Early detection and treatment of sepsis episodes is critical, since an early treatment may highly improve prognosis. This study proposed an original method to increase the interpretability of a set of machine learning models for the early detection of sepsis onset.Material and methodsOpen data from the electronic medical records of 40,336 patients monitored in intensive care units (ICU), provided by the PhysioNet/Computing in Cardiology Challenge 2019 is used in this paper. We proposed a method including data preprocessing, feature engineering, model construction and tuning, as well as an original interpretability analysis method for the final stage.ResultsA total of 24 models were developed and analyzed. The best model, based on 142 features achieved a 0.4274 utility score. The best compact model integrates only 20 selected features, and provided a utility score of 0.3862. Meanwhile, the proposed sensitivity analysis method allows for the identification of the most relevant markers to early detect the onset of sepsis, as well as their interdependence and relative importance on the final decision.ConclusionA set of optimized machine-learning models were proposed for predicting sepsis early in a real-time way with high performance, and interpretable information including the most significant biomarkers were analyzed through novel interpretability method.     

Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine

The identification of mechanisms responsible for recurrent epidemic outbreaks, such as age structure, cross-immunity and variable delays in the infective classes, has challenged and fascinated epidemiologists and mathematicians alike. This paper addresses, motivated by mathematical work on influenza models, the impact of imperfect quarantine on the dynamics of SIR-type models. A susceptible-infectious-quarantine-recovered (SIQR) model is formulated with quarantined individuals altering the transmission dynamics process through their possibly reduced ability to generate secondary cases of infection. Mathematical and numerical analyses of the model of the equilibria and their stability have been carried out. Uniform persistence of the model has been established. Numerical simulations show that the model supports Hopf bifurcation as a function of the values of the quarantine effectiveness and other parameters. The upshot of this work is somewhat surprising since it is shown that SIQR model oscillatory behavior, as shown by multiple researchers, is in fact not robust to perturbations in the quarantine regime.     

Incidence of Neoplasms in Children Born after Influenza Epidemics

Following a recent report that neoplasia of the lymphatic and haematopoietic tissues is commoner than average in children whose mothers have had influenza in pregnancy, the incidence of neoplasms in 1954-68 in children of the Manchester Hospital Region was examined in relation to date of birth. There were no significant differences between cohorts born in different quinquennia. Incidence among children born after six influenza epidemics in 1951-68 was no higher than among other children born in these years. It is concluded that if there is an association between maternal influenza and childhood neoplasia it is probably due to factors such as immunological deficiencies which may predispose independently to both conditions.     

An Individual-Based Model of Zebrafish Population Dynamics Accounting for Energy Dynamics

Developing population dynamics models for zebrafish is crucial in order to extrapolate from toxicity data measured at the organism level to biological levels relevant to support and enhance ecological risk assessment. To achieve this, a dynamic energy budget for individual zebrafish (DEB model) was coupled to an individual based model of zebrafish population dynamics (IBM model). Next, we fitted the DEB model to new experimental data on zebrafish growth and reproduction thus improving existing models. We further analysed the DEB-model and DEB-IBM using a sensitivity analysis. Finally, the predictions of the DEB-IBM were compared to existing observations on natural zebrafish populations and the predicted population dynamics are realistic. While our zebrafish DEB-IBM model can still be improved by acquiring new experimental data on the most uncertain processes (e.g. survival or feeding), it can already serve to predict the impact of compounds at the population level.     

Simulating Carbon Stocks and Fluxes of an African Tropical Montane Forest with an Individual-Based Forest Model

Tropical forests are carbon-dense and highly productive ecosystems. Consequently, they play an important role in the global carbon cycle. In the present study we used an individual-based forest model (FORMIND) to analyze the carbon balances of a tropical forest. The main processes of this model are tree growth, mortality, regeneration, and competition. Model parameters were calibrated using forest inventory data from a tropical forest at Mt. Kilimanjaro. The simulation results showed that the model successfully reproduces important characteristics of tropical forests (aboveground biomass, stem size distribution and leaf area index). The estimated aboveground biomass (385 t/ha) is comparable to biomass values in the Amazon and other tropical forests in Africa. The simulated forest reveals a gross primary production of 24 t_cha^-1yr^-1. Modeling above- and belowground carbon stocks, we analyzed the carbon balance of the investigated tropical forest. The simulated carbon balance of this old-growth forest is zero on average. This study provides an example of how forest models can be used in combination with forest inventory data to investigate forest structure and local carbon balances.     

Explaining Bacterial Dispersion on Leaf Surfaces with an Individual-Based Model (PHYLLOSIM)

We developed the individual-based model PHYLLOSIM to explain observed variation in the size of bacterial clusters on plant leaf surfaces (the phyllosphere). Specifically, we tested how different ‘waterscapes’ impacted the diffusion of nutrients from the leaf interior to the surface and the growth of individual bacteria on these nutrients. In the ‘null’ model or more complex ‘patchy’ models, the surface was covered with a continuous water film or with water drops of equal or different volumes, respectively. While these models predicted the growth of individual bacterial immigrants into clusters of variable sizes, they were unable to reproduce experimentally derived, previously published patterns of dispersion which were characterized by a much larger variation in cluster sizes and a disproportionate occurrence of clusters consisting of only one or two bacteria. The fit of model predictions to experimental data was about equally poor (<5%) regardless of whether the water films were continuous or patchy. Only by allowing individual bacteria to detach from developing clusters and re-attach elsewhere to start a new cluster, did PHYLLOSIM come much closer to reproducing experimental observations. The goodness of fit including detachment increased to about 70–80% for all waterscapes. Predictions of this ‘detachment’ model were further supported by the visualization and quantification of bacterial detachment and attachment events at an agarose-water interface. Thus, both model and experiment suggest that detachment of bacterial cells from clusters is an important mechanism underlying bacterial exploration of the phyllosphere.     

The Role of Environmental Transmission in Recurrent Avian Influenza Epidemics

Avian influenza virus (AIV) persists in North American wild waterfowl, exhibiting major outbreaks every 2–4 years. Attempts to explain the patterns of periodicity and persistence using simple direct transmission models are unsuccessful. Motivated by empirical evidence, we examine the contribution of an overlooked AIV transmission mode: environmental transmission. It is known that infectious birds shed large concentrations of virions in the environment, where virions may persist for a long time. We thus propose that, in addition to direct fecal/oral transmission, birds may become infected by ingesting virions that have long persisted in the environment. We design a new host–pathogen model that combines within-season transmission dynamics, between-season migration and reproduction, and environmental variation. Analysis of the model yields three major results. First, environmental transmission provides a persistence mechanism within small communities where epidemics cannot be sustained by direct transmission only (i.e., communities smaller than the critical community size). Second, environmental transmission offers a parsimonious explanation of the 2–4 year periodicity of avian influenza epidemics. Third, very low levels of environmental transmission (i.e., few cases per year) are sufficient for avian influenza to persist in populations where it would otherwise vanish.     

Comparison of Filtering Methods for the Modeling and Retrospective Forecasting of Influenza Epidemics

A variety of filtering methods enable the recursive estimation of system state variables and inference of model parameters. These methods have found application in a range of disciplines and settings, including engineering design and forecasting, and, over the last two decades, have been applied to infectious disease epidemiology. For any system of interest, the ideal filter depends on the nonlinearity and complexity of the model to which it is applied, the quality and abundance of observations being entrained, and the ultimate application (e.g. forecast, parameter estimation, etc.). Here, we compare the performance of six state-of-the-art filter methods when used to model and forecast influenza activity. Three particle filters—a basic particle filter (PF) with resampling and regularization, maximum likelihood estimation via iterated filtering (MIF), and particle Markov chain Monte Carlo (pMCMC)—and three ensemble filters—the ensemble Kalman filter (EnKF), the ensemble adjustment Kalman filter (EAKF), and the rank histogram filter (RHF)—were used in conjunction with a humidity-forced susceptible-infectious-recovered-susceptible (SIRS) model and weekly estimates of influenza incidence. The modeling frameworks, first validated with synthetic influenza epidemic data, were then applied to fit and retrospectively forecast the historical incidence time series of seven influenza epidemics during 2003–2012, for 115 cities in the United States. Results suggest that when using the SIRS model the ensemble filters and the basic PF are more capable of faithfully recreating historical influenza incidence time series, while the MIF and pMCMC do not perform as well for multimodal outbreaks. For forecast of the week with the highest influenza activity, the accuracies of the six model-filter frameworks are comparable; the three particle filters perform slightly better predicting peaks 1–5 weeks in the future; the ensemble filters are more accurate predicting peaks in the past.     

Leading Indicators and the Evaluation of the Performance of Alerts for Influenza Epidemics

Background

Most evaluations of epidemic thresholds for influenza have been limited to internal criteria of the indicator variable. We aimed to initiate discussion on appropriate methods for evaluation and the value of cross-validation in assessing the performance of a candidate indicator for influenza activity.

Methods

Hospital records of in-patients with a diagnosis of confirmed influenza were extracted from the Canadian Discharge Abstract Database from 2003 to 2011 and aggregated to weekly and regional levels, yielding 7 seasons and 4 regions for evaluation (excluding the 2009 pandemic period). An alert created from the weekly time-series of influenza positive laboratory tests (FluWatch, Public Health Agency of Canada) was evaluated against influenza-confirmed hospitalizations on 5 criteria: lead/lag timing; proportion of influenza hospitalizations covered by the alert period; average length of the influenza alert period; continuity of the alert period and length of the pre-peak alert period.

Results

Influenza hospitalizations led laboratory positive tests an average of only 1.6 (95% CI: -1.5, 4.7) days. However, the difference in timing exceeded 1 week and was statistically significant at the significance level of 0.01 in 5 out of 28 regional seasons. An alert based primarily on 5% positivity and 15 positive tests produced an average alert period of 16.6 weeks. After allowing for a reporting delay of 2 weeks, the alert period included 80% of all influenza-confirmed hospitalizations. For 20 out of the 28 (71%) seasons, the first alert would have been signalled at least 3 weeks (in real time) prior to the week with maximum number of influenza hospitalizations.

Conclusions

Virological data collected from laboratories was a good indicator of influenza activity with the resulting alert covering most influenza hospitalizations and providing a reasonable pre-peak warning at the regional level. Though differences in timing were statistically significant, neither time-series consistently led the other.     

研究SIR传染病数学模型的Lagrange-Noether方法

应用分析力学的方法讨论了SIR传染病数学模型方程,得到了与其对应的Lagrange函数和Noether守恒量,并根据Noether守恒量具体探讨了对感染病者和易感染病者人群的隔离率与患病者人数最大值的关系.     

Predictive Validation of an Influenza Spread Model

Background

Modeling plays a critical role in mitigating impacts of seasonal influenza epidemics. Complex simulation models are currently at the forefront of evaluating optimal mitigation strategies at multiple scales and levels of organization. Given their evaluative role, these models remain limited in their ability to predict and forecast future epidemics leading some researchers and public-health practitioners to question their usefulness. The objective of this study is to evaluate the predictive ability of an existing complex simulation model of influenza spread.

Methods and Findings

We used extensive data on past epidemics to demonstrate the process of predictive validation. This involved generalizing an individual-based model for influenza spread and fitting it to laboratory-confirmed influenza infection data from a single observed epidemic (1998–1999). Next, we used the fitted model and modified two of its parameters based on data on real-world perturbations (vaccination coverage by age group and strain type). Simulating epidemics under these changes allowed us to estimate the deviation/error between the expected epidemic curve under perturbation and observed epidemics taking place from 1999 to 2006. Our model was able to forecast absolute intensity and epidemic peak week several weeks earlier with reasonable reliability and depended on the method of forecasting-static or dynamic.

Conclusions

Good predictive ability of influenza epidemics is critical for implementing mitigation strategies in an effective and timely manner. Through the process of predictive validation applied to a current complex simulation model of influenza spread, we provided users of the model (e.g. public-health officials and policy-makers) with quantitative metrics and practical recommendations on mitigating impacts of seasonal influenza epidemics. This methodology may be applied to other models of communicable infectious diseases to test and potentially improve their predictive ability.     

SIR传染病数学模型的隔离控制

本文研究的SIR传染病隔离控制,不仅对染病者进行隔离,而且隔离易感者．对该模型闽值进行分析,探讨隔离率与患病人数最大值之间的关系,旨在消除该传染病．仿真表明此法行之有效．     

Investigating the Effect of Recruitment Variability on Length-Based Recruitment Indices for Antarctic Krill Using an Individual-Based Population Dynamics Model

Antarctic krill (Euphausia superba; herein krill) is monitored as part of an on-going fisheries observer program that collects length-frequency data. A krill feedback management programme is currently being developed, and as part of this development, the utility of data-derived indices describing population level processes is being assessed. To date, however, little work has been carried out on the selection of optimum recruitment indices and it has not been possible to assess the performance of length-based recruitment indices across a range of recruitment variability. Neither has there been an assessment of uncertainty in the relationship between an index and the actual level of recruitment. Thus, until now, it has not been possible to take into account recruitment index uncertainty in krill stock management or when investigating relationships between recruitment and environmental drivers. Using length-frequency samples from a simulated population – where recruitment is known – the performance of six potential length-based recruitment indices is assessed, by exploring the index-to-recruitment relationship under increasing levels of recruitment variability (from ±10% to ±100% around a mean annual recruitment). The annual minimum of the proportion of individuals smaller than 40 mm (F40 min, %) was selected because it had the most robust index-to-recruitment relationship across differing levels of recruitment variability. The relationship was curvilinear and best described by a power law. Model uncertainty was described using the 95% prediction intervals, which were used to calculate coverage probabilities and assess model performance. Despite being the optimum recruitment index, the performance of F40 min degraded under high (>50%) recruitment variability. Due to the persistence of cohorts in the population over several years, the inclusion of F40 min values from preceding years in the relationship used to estimate recruitment in a given year improved its accuracy (mean bias reduction of 8.3% when including three F40 min values under a recruitment variability of 60%).     

A Mechanistic Individual-Based Model of the Feeding Processes for Oikopleura dioica

A mechanistic physiological model of the appendicularian Oikopleura dioica has been built to represent its three feeding processes (filtration, ingestion and assimilation). The mathematical formulation of these processes is based on laboratory observations from the literature, and tests different hypotheses. This model accounts for house formation dynamics, the food storage capacity of the house and the gut throughput dynamics. The half-saturation coefficient for ingestion resulting from model simulations is approximately 28 and is independent of the weight of the organism. The maximum food intake for ingestion is also a property of the model and depends on the weight of the organism. Both are in accordance with data from the literature. The model also provides a realistic representation of carbon accumulation within the house. The modelled half-saturation coefficient for assimilation is approximately 15 and is also independent of the weight of the organism. Modelled gut throughput dynamics are based on faecal pellet formation by gut compaction. Model outputs showed that below a food concentration of 30 , the faecal pellet weight should represent a lower proportion of the body weight of the organism, meaning that the faecal pellet formation is not driven by gut filling. Simulations using fluctuating environmental food availability show that food depletion is not immediately experienced by the organism but that it occurs after a lag time because of house and gut buffering abilities. This lag time duration lasts at least 30 minutes and can reach more than 2 hours, depending on when the food depletion occurs during the house lifespan.     

Model Analysis of Fomite Mediated Influenza Transmission

Fomites involved in influenza transmission are either hand- or droplet-contaminated. We evaluated the interactions of fomite characteristics and human behaviors affecting these routes using an Environmental Infection Transmission System (EITS) model by comparing the basic reproduction numbers (R ₀) for different fomite mediated transmission pathways. Fomites classified as large versus small surface sizes (reflecting high versus low droplet contamination levels) and high versus low touching frequency have important differences. For example, 1) the highly touched large surface fomite (public tables) has the highest transmission potential and generally strongest control measure effects; 2) transmission from droplet-contaminated routes exceed those from hand-contaminated routes except for highly touched small surface fomites such as door knob handles; and 3) covering a cough using the upper arm or using tissues effectively removes virus from the system and thus decreases total fomite transmission. Because covering a cough by hands diverts pathogens from the droplet-fomite route to the hand-fomite route, this has the potential to increase total fomite transmission for highly touched small surface fomites. An improved understanding and more refined data related to fomite mediated transmission routes will help inform intervention strategies for influenza and other pathogens that are mediated through the environment.