Stochastic Simulation Model Research Articles

Comparing statistical methods for detecting and estimating waning efficacy of rotavirus vaccines in developing countries

ABSTRACT Introduction Vaccination has significantly reduced morbidity and mortality resulting from rotavirus infection worldwide. However, rotavirus vaccine efficacy (VE) appears to wane over the first 2 years since vaccination, particularly in developing countries. Statistical methods for detecting VE waning and estimating its rate have been used in a few studies, but comparisons of methods for evaluating VE waning have not yet been performed. In this work we present and compare three methods – Durham’s method, Tian’s method, and time-dependent covariate (TDC) method – based on generalizations of the Cox proportional hazard model. Methods We developed a new stochastic agent-based simulation model to generate data from a hypothetical rotavirus vaccine trial where the protective efficacy of the vaccine may vary over time. Input parameters to the simulation model were obtained from studies on rotavirus infections in four developing countries. We applied each of the methods to four simulated datasets and compared the type-1 error probabilities and the powers of the resulting statistical tests. We also compared estimated and true values of VE over time. Results Durham’s method had the highest power of detecting true VE waning of the three methods. This method also provided quite accurate estimates of VE in each period and of the per-period drop in VE. Conclusions Durham’s method is somewhat more powerful than the other two Cox proportional hazards model-based methods for detecting VE waning and provides more information about the temporal behavior of VE.

Analysis of 11,430 recombinant protein production experiments reveals that protein yield is tunable by synonymous codon changes of translation initiation sites.

Recombinant protein production is a key process in generating proteins of interest in the pharmaceutical industry and biomedical research. However, about 50% of recombinant proteins fail to be expressed in a variety of host cells. Here we show that the accessibility of translation initiation sites modelled using the mRNA base-unpairing across the Boltzmann's ensemble significantly outperforms alternative features. This approach accurately predicts the successes or failures of expression experiments, which utilised Escherichia coli cells to express 11,430 recombinant proteins from over 189 diverse species. On this basis, we develop TIsigner that uses simulated annealing to modify up to the first nine codons of mRNAs with synonymous substitutions. We show that accessibility captures the key propensity beyond the target region (initiation sites in this case), as a modest number of synonymous changes is sufficient to tune the recombinant protein expression levels. We build a stochastic simulation model and show that higher accessibility leads to higher protein production and slower cell growth, supporting the idea of protein cost, where cell growth is constrained by protein circuits during overexpression.

On the distribution of the time-integral of the geometric Brownian motion

We study the numerical evaluation of several functions appearing in the small time expansion of the distribution of the time-integral of the geometric Brownian motion as well as its joint distribution with the terminal value of the underlying Brownian motion. A precise evaluation of these distributions is relevant for the simulation of stochastic volatility models with log-normally distributed volatility, and Asian option pricing in the Black–Scholes model. We derive series expansions for these distributions, which can be used for numerical evaluations. Using tools from complex analysis, we determine the convergence radius and large order asymptotics of the coefficients in these expansions. We construct an efficient numerical approximation of the joint distribution of the time-integral of the gBM and its terminal value, and illustrate its application to Asian option pricing in the Black–Scholes model.

Ecosystem carbon balance in the Hawaiian Islands under different scenarios of future climate and land use change

The State of Hawai‘i passed legislation to be carbon neutral by 2045, a goal that will partly depend on carbon sequestration by terrestrial ecosystems. However, there is considerable uncertainty surrounding the future direction and magnitude of the land carbon sink in the Hawaiian Islands. We used the Land Use and Carbon Scenario Simulator (LUCAS), a spatially explicit stochastic simulation model that integrates landscape change and carbon gain-loss, to assess how projected future changes in climate and land use will influence ecosystem carbon balance in the Hawaiian Islands under all combinations of two radiative forcing scenarios (RCPs 4.5 and 8.5) and two land use scenarios (low and high) over a 90 year timespan from 2010 to 2100. Collectively, terrestrial ecosystems of the Hawaiian Islands acted as a net carbon sink under low radiative forcing (RCP 4.5) for the entire 90 year simulation period, with low land use change further enhancing carbon sink strength. In contrast, Hawaiian terrestrial ecosystems transitioned from a net sink to a net source of CO2 to the atmosphere under high radiative forcing (RCP 8.5), with high land use accelerating this transition and exacerbating net carbon loss. A sensitivity test of the CO2 fertilization effect on plant productivity revealed it to be a major source of uncertainty in projections of ecosystem carbon balance, highlighting the need for greater mechanistic understanding of plant productivity responses to rising atmospheric CO2. Long-term model projections such as ours that incorporate the interactive effects of land use and climate change on regional ecosystem carbon balance will be critical to evaluating the potential of ecosystem-based climate mitigation strategies.

Quantifying the Impact of Inspection Processes on Production Lines through Stochastic Discrete-Event Simulation Modeling

Inspection processes are becoming more and more popular beyond the manufacturing industry to ensure product quality. Implementing inspection systems in multistage production lines brings many benefits in productivity, quality, and customer satisfaction. However, quantifying the changes necessary to adapt the production to these systems is analytically complicated, and the tools available lack the flexibility to visualize all the inspection strategies available. This paper proposed a discrete-event simulation model that relies on probabilistic defect propagation to quantify the impact on productivity, quality, and material supply at the introduction of inspection processes in a multistage production line. The quantification follows lean manufacturing principles, providing from quite basic quantity and time elements to more comprehensive key performance indicators. The flexibility of discrete-event simulation allows for customized manufacturing and inspection topologies and variability in the tasks and inspection systems used. The model is validated in two common manufacturing scenarios, and the method to analyze the cost-effectiveness of implementing inspection processes is discussed.

Gradient‐based criteria for sequential experiment design

AbstractComputer experiments are often used as inexpensive alternatives to real‐world experiments. Statistical metamodels of the computer model's input‐output behavior can be constructed to serve as approximations of the response surface of the real‐world system. The suitability of a metamodel depends in part on its intended use. While decision makers may want to understand the entire response surface, they may be particularly keen on finding interesting regions of the design space, such as where the gradient is steep. We present an adaptive, value‐enhanced batch sequential algorithm that samples more heavily in such areas while still providing an understanding of the entire surface. The design points within each batch can be run in parallel to leverage modern multi‐core computing assets. We illustrate our approach for deterministic computer models, but it has potential for stochastic simulation models as well.

Reconstructing a COVID-19 outbreak within a religious group using social network analysis simulation in Korea.

OBJECTIVESWe reconstructed a coronavirus disease 2019 (COVID-19) outbreak to examine how a large cluster at a church setting spread before being detected and estimate the potential effectiveness of complying with mask-wearing guidelines recommended by the government.METHODSA mathematical model with a social network analysis (SNA) approach was used to simulate a COVID-19 outbreak. A discrete-time stochastic simulation model was used to simulate the spread of COVID-19 within the Sarang Jeil church. A counterfactual experiment using a calibrated baseline model was conducted to examine the potential benefits of complying with a mask-wearing policy.RESULTSSimulations estimated a mask-wearing ratio of 67% at the time of the outbreak, which yielded 953.8 (95% confidence interval [CI], 937.3 to 970.4) cases and was most consistent with the confirmed data. The counterfactual experiment with 95% mask-wearing estimated an average of 45.6 (95% CI, 43.4 to 47.9) cases with a standard deviation of 20.1. The result indicated that if the church followed government mask-wearing guidelines properly, the outbreak might have been one-twentieth the size.CONCLUSIONSSNA is an effective tool for monitoring and controlling outbreaks of COVID-19 and other infectious diseases. Although our results are based on simulations and are thus limited, the precautionary implications of social distancing and mask-wearing are still relevant. Since person-to-person contacts and interactions are unavoidable in social and economic life, it may be beneficial to develop precise measures and guidelines for particular organizations or places that are susceptible to cluster outbreaks.

New standards in stochastic simulations of dairy cow disease modelling: Bio-economic dynamic optimization for rational health management decision-making

Bioeconomic models applied to animal health issues are now commonly observed in literature. This section of literature is very heterogeneous and the underlying methods are very diverse, from very simple methods (partial budgeting) to very complex ones. The objective of the present study is to build a new dynamic stochastic optimisation bioeconomic model applied to the dairy cow sector, that goes beyond some limitations usually found in methods used up to now. First, based on a critical literature review, we highlight four issues of bio-economic stochastic simulation models (BESSMs) applied to dairy cow diseases at the farm level. These models appear as partial (the farm system is not considered as a whole), unbalanced (between the economic and biological parts of the model), closed (to the farm environment) and only partially dynamic. To address these 4 main issues and improve the methodological standards in the microeconomics of dairy cow health management, we secondly develop a new bio-economic sequential optimization model (BESOM), called DairyHealthSim. DairyHealthSim aims to better consider both the context of decision-making and the farming system dynamics to define the best health management strategies in a given context. The biological part of the model simulates the complex dairy production cycle with a holistic approach. It is defined on a cow-week basis, and the weekly probabilities for all cow events, including production, reproduction and diseases, are simulated. The economic part of the model is a mean-variance optimization framework that dynamically represents the farmer's input allocation decision process under constraints. The biological and economic parts are closely integrated and the model is running with back and forth between the 2 parts of the bioeconomic model. Third, an application involving farmers' strategies related to biological risk management, labour willingness and market demand is proposed for dairy production and mastitis management. The results highlight the added value of the farming system-driven system coupled to economic optimization approach. DairyHealthSim identifies the optimal scenario for the entire ten-year simulation period or is based on yearly optimization (sequential modelling). The two different optimal solutions found show the usefulness of considering the dynamics and complexities of the actual field situation. The opportunity cost between the best and alternative solutions demonstrates that some solutions are economic equivalents. In conclusion, compared to approaches where the outcome is reduced to the monetary impact of diseases, DairyHealthSim is far more precise and appropriate for supporting decision-making.

PopART-IBM, a highly efficient stochastic individual-based simulation model of generalised HIV epidemics developed in the context of the HPTN 071 (PopART) trial.

Mathematical models are powerful tools in HIV epidemiology, producing quantitative projections of key indicators such as HIV incidence and prevalence. In order to improve the accuracy of predictions, such models need to incorporate a number of behavioural and biological heterogeneities, especially those related to the sexual network within which HIV transmission occurs. An individual-based model, which explicitly models sexual partnerships, is thus often the most natural type of model to choose. In this paper we present PopART-IBM, a computationally efficient individual-based model capable of simulating 50 years of an HIV epidemic in a large, high-prevalence community in under a minute. We show how the model calibrates within a Bayesian inference framework to detailed age- and sex-stratified data from multiple sources on HIV prevalence, awareness of HIV status, ART status, and viral suppression for an HPTN 071 (PopART) study community in Zambia, and present future projections of HIV prevalence and incidence for this community in the absence of trial intervention.

An evaluation of strategies for restoring a degraded New Zealand scallop fishery using stochastic dynamic simulation modelling

A decision-theoretical approach was used to evaluate strategies to rebuild a severely depleted scallop (Pecten novaezelandiae) populations in the Tasman Bay and Golden Bay of New Zealand. These strategies were: no intervention, cessation of seabed bottom contact fishing, and reduction of sediment and nutrient runoff from surrounding land through on-farm practices. Our approach combined outputs of estimated effects of on-farm practices on erosion and nutrient reduction with a stochastic dynamic model of the scallop populations. The most effective individual intervention is eliminating bottom contact fishing through dredging and trawling which increased scallop biomass on average by 73% compared to the no intervention scenario. Although on-farm practices have reduced sedimentation and nutrient runoff significantly (28–36% and 2%, respectively), they have no effect on scallop biomass if implemented individually and led to only marginal improvements in scallop biomass if implemented alongside cessation of bottom contact fishing (2–4%). Although our results showed, on average, substantial recovery in the scallop population when reducing seabed bottom contact and water pollution, the large uncertainty boundaries makes it unclear whether these improvements would be realized. The long-term success of such strategies will depend on the available habitat being able to sustain high densities of healthy scallop adults and recruits, a situation that has been posited in our analysis. Where scallop juvenile survival is compromised by sedimentation, nutrient pollution, or other exogenous influences, proposed interventions may be insufficient to aid recovery.

Economic impact of adding a second prostaglandin F2α treatment during an Ovsynch protocol using a meta-analytical assessment and a stochastic simulation model

Incomplete luteal regression after treatment with a single dose of PGF2α during an Ovsynch protocol decreases fertility to timed artificial insemination (AI). An additional treatment with PGF2α 24 h after the first dose has been recommended to increase the proportion of cows with complete luteal regression and subsequent pregnancy per AI (P/AI). This is, however, associated with additional costs of labor and product. The objective was to develop a stochastic partial budget model to estimate the economic impact of an additional PGF2α treatment on d 8 during an Ovsynch protocol in primiparous and multiparous cows. A systematic review of the literature and a meta-analytical assessment was performed to evaluate the effects of adding a second PGF2α treatment during the Ovsynch protocol on P/AI in lactating dairy cows. Thirteen randomized controlled experiments from 11 published manuscripts including 9,735 cows were used. We were able to retrieve information regarding parity from 9 experiments from 7 manuscripts (2,367 primiparous cows and 5,356 multiparous cows). An additional dose of PGF2α yielded a 5.60 risk difference in P/AI [95% confidence interval (CI) = 3.69-7.52]. In primiparous cows and multiparous cows, an additional dose of PGF2α yielded a 4.24 (95% CI = 0.31-8.17) and a 5.31 risk difference in P/AI (95% CI = 2.75-7.87). Revenue was based on the associated improvement in reproductive performance because of an increase in P/AI multiplied by the value of a pregnancy (PGVAL). Median PGVAL was €252, ranging from €42 (fifth percentile) to €623 (95th percentile). Based on parity, median PGVAL was €205 (5th percentile = €43; 95th percentile = €651) and €264 (5th percentile = €88; 95th percentile = €598) for primiparous (n = 1,252) and multiparous cows (n = 3,003), respectively. Using a stochastic simulation model with 10,000 iterations, adding a second PGF2α dose on d 8 was more profitable (€7.76/cow; 5th percentile = €0.01; 95th percentile = €29.40) compared with a single PGF2α administration on d 7. In primiparous cows, adding a second PGF2α treatment was more profitable (€1.99/cow; 5th percentile = -€3.08; 95th percentile = €22.52) in 67% of all simulated iterations. In multiparous cows, adding a second PGF2α treatment was more profitable (€7.92/cow; 5th percentile = -€0.09; 95th percentile = €28.22) in 95% of all simulated iterations. In conclusion, there was a clear benefit of an additional PGF2α treatment during the Ovsynch protocol on P/AI (+5.6 percentage units). Despite additional costs for hormones and labor, an additional treatment with PGF2α on d 8 was more profitable in 95% of all scenarios because of the associated increase in fertility. It turned out, however, that adding a second PGF2α treatment was more profitable in multiparous cows compared with primiparous cows.

Optimal budget allocation for stochastic simulation with importance sampling: Exploration vs. replication

This article investigates a budget allocation problem for optimally running stochastic simulation models with importance sampling in computer experiments. In particular, we consider a two-level (or nested) simulation to estimate the expectation of the simulation output, where the first-level draws random input samples and the second-level obtains the output given the input from the first-level. The two-level simulation faces the trade-off in allocating the computational budgets: exploring more inputs (exploration) or exploiting the stochastic response surface at a sampled point in more detail (replication). We study an appropriate computational budget allocation strategy that strikes a balance between exploration and replication to minimize the variance of the estimator when importance sampling is employed at the first-level simulation. Our analysis suggests that exploration can be beneficial than replication in many practical situations. We also conduct numerical experiments in a wide range of settings and wind turbine case study to investigate the trade-off.

Pharmacokinetics of Ceftazidime in Children and Adolescents with Obesity.

The aim of this study was to evaluate ceftazidime pharmacokinetics (PK) in a cohort that includes a predominate number of children and adolescents with obesity and assess the efficacy of competing dosing strategies. A population PK model was developed using opportunistically collected plasma samples. For each dosing strategy, model-based probability of target attainment (PTA) estimates were computed for study participants using empirical Bayes estimates. In addition, the effects of body size and renal function on PTA were evaluated using stochastic model simulations with virtually generated subjects. Twenty-nine participants, 24 of whom were obese, contributed data towards the analysis. The median (range) age, body weight, and body mass index of participants were 12.2 years (2.3-20.6), 59.2 kg (8.4-121), and 25.2kg/m2 (13.8-42.9), respectively. Administration of 50mg/kg intravenously (IV) every 8 hours (q8h; max 6g/day) or 40mg/kg IV q6h (max 6g/day) resulted in PTA values of ≥90% (minimum inhibitory concentration 8mg/L) for the subset of obese participants with estimated glomerular filtration rates (GFR) ≥~80mL/min/1.73m2. However, for both regimens, stochastic model simulations denoted lower PTA values (<90%) with increasing body weight forvirtual subjects with GFR ≥120mL/min/1.73m2. Alternatively, permitting for a maximum daily dose of 8g/day using a 40mg/kg IV q6h regimen provided PTA values that were near or above target (90%) forvirtual subjects between 10 to 120kg with GFR ≥80mL/min/1.73m2. Our analysis suggests administration of 40mg/kg IV q6h (max 8g/day) maximizes PTA in children and adolescents with obesity and GFR ≥80mL/min/1.73m2. Clinicaltrials.gov Identifier: NCT01431326.

Stochastic event simulation model for quantitative prediction of road tunnel downtime

Given the importance of road tunnels in a transportation network, it is essential to quantitatively assess and predict tunnel functionality loss due to disruptive events. In this study, a stochastic event simulation model was developed to evaluate the resilience of tunnel infrastructure, quantified using a functionality metric as a function of loss in traffic capacity and its duration. The model consists of individual modules to account for disruptive events that cause tunnel closures. In this paper, the mechanism and probabilistic models used for each simulation module are presented. A simulation for Eisenhower tunnel, Colorado, was conducted using the proposed method as a validation case study. The results showed that the proposed model could simulate realistic tunnel operation status. While the validation was made for a specific tunnel, the model was designed to be applied to the resilience analysis of any road tunnel with defined design and operation parameters.

Simulation Analyses of End-Around Taxiway Operations under Four Different Runway and Taxiway Choices

End-around taxiways (EAT) have been implemented at four major U.S. airports to increase the safety and throughput of parallel runway systems. This paper proposes two new runway and taxiway choices that become possible because of EATs. Instead of using the inboard runway to take off, the departing aircraft could use the outboard runway and use the EAT as the taxi-out path. A discrete-event stochastic simulation model simulates the operations of four different runway and taxiway choices. Two experiments compare the performance of the four choices on average taxi times, average fuel consumption per taxi, and number of runway crossings. In general, the results indicate that using the outboard runway to take off and the EAT as a taxi-out path would yield benefits in both taxi-in and taxi-out performance, as well as enhancing runway safety. Using the outboard runway to land and the EAT as a taxi-in path would yield benefit in taxi-out performance and runway safety at the expense of a longer taxi-in time. Concerns related to using the EAT as the taxi-out path, as well as potential future research topics, are discussed.

Reproducible parallel inference and simulation of stochastic state space models using odin, dust, and mcstate.

State space models, including compartmental models, are used to model physical, biological and social phenomena in a broad range of scientific fields. A common way of representing the underlying processes in these models is as a system of stochastic processes which can be simulated forwards in time. Inference of model parameters based on observed time-series data can then be performed using sequential Monte Carlo techniques. However, using these methods for routine inference problems can be made difficult due to various engineering considerations: allowing model design to change in response to new data and ideas, writing model code which is highly performant, and incorporating all of this with up-to-date statistical techniques. Here, we describe a suite of packages in the R programming language designed to streamline the design and deployment of state space models, targeted at infectious disease modellers but suitable for other domains. Users describe their model in a familiar domain-specific language, which is converted into parallelised C++ code. A fast, parallel, reproducible random number generator is then used to run large numbers of model simulations in an efficient manner. We also provide standard inference and prediction routines, though the model simulator can be used directly if these do not meet the user's needs. These packages provide guarantees on reproducibility and performance, allowing the user to focus on the model itself, rather than the underlying computation. The ability to automatically generate high-performance code that would be tedious and time-consuming to write and verify manually, particularly when adding further structure to compartments, is crucial for infectious disease modellers. Our packages have been critical to the development cycle of our ongoing real-time modelling efforts in the COVID-19 pandemic, and have the potential to do the same for models used in a number of different domains.

Reproducible parallel inference and simulation of stochastic state space models using odin, dust, and mcstate

State space models, including compartmental models, are used to model physical, biological and social phenomena in a broad range of scientific fields. A common way of representing the underlying processes in these models is as a system of stochastic processes which can be simulated forwards in time. Inference of model parameters based on observed time-series data can then be performed using sequential Monte Carlo techniques. However, using these methods for routine inference problems can be made difficult due to various engineering considerations: allowing model design to change in response to new data and ideas, writing model code which is highly performant, and incorporating all of this with up-to-date statistical techniques. Here, we describe a suite of packages in the R programming language designed to streamline the design and deployment of state space models, targeted at infectious disease modellers but suitable for other domains. Users describe their model in a familiar domain-specific language, which is converted into parallelised C++ code. A fast, parallel, reproducible random number generator is then used to run large numbers of model simulations in an efficient manner. We also provide standard inference and prediction routines, though the model simulator can be used directly if these do not meet the user’s needs. These packages provide guarantees on reproducibility and performance, allowing the user to focus on the model itself, rather than the underlying computation. The ability to automatically generate high-performance code that would be tedious and time-consuming to write and verify manually, particularly when adding further structure to compartments, is crucial for infectious disease modellers. Our packages have been critical to the development cycle of our ongoing real-time modelling efforts in the COVID-19 pandemic, and have the potential to do the same for models used in a number of different domains.

A planetary mill modelling in chaotic mode

Consider a random walk in a regular m-polygon inscribed in the unit circle. The movement of the point to a randomly selected vertex determines the new position of the point. The point passes a prescribed distance and stops. For such a process, there is a limit distribution of the probabilities of the position of the point. This algorithm was used for modelling different processes. Now we apply it for high-energy ball milling. The impact frequency spatial distribution calculated with the stochastic model simulation has coincided with the distribution predicted by the distinct element method. The real granulometric analysis also can be explained by the model.

Risk-oriented simulation of the long logistics supply chains in developing enterprises

The paper defines and solves the urgent problem of research of long logistics supply chains in developing enterprises. Due to the distribution of the production system as well as to the presence of a large number of remote suppliers of materials, raw materials and components supply plans are threatened. Supply disruptions in their turn may affect the plans of the main production resulting in possible fines, economic losses, and disruptions in supply of manufactured articles to the markets of high-tech and science-intensive products. To study threats and vulnerabilities in supply logistics the risk-oriented approach that considers potential threats using past statistics and expert assessments has been proposed. The objective of the paper is to develop a risk-oriented method to study the existing threats and assess their impact on the vulnerabilities of the logistics chains of the distributed production system. Due to the complexity of the problematic logistics task, the study is conducted in three different stages: development of the method to simulate the risks in long supply chains; identification of possible bottlenecks in the transport system of supply logistics; threat simulation and vulnerability analysis in supply logistics. To model the risks, an agent model is used, in which the accumulation of risks is carried out by passing orders in the transport system. To simulate bottlenecks, a simulation event model is used, in which large queues that occur in the transport system are analyzed. A stochastic simulation model is used to model threats and vulnerabilities. The new scientific results are risk-oriented method of long logistics supply chains simulation; simulation of supply logistics threats and vulnerabilities. Mathematical methods used: risk theory; simulation event modeling; agent modeling; queuing theory. The proposed approach as a set of developed simulation models should be used to plan the supply of developing production.

Risk analysis of natural water resources scarcity based on a stochastic simulation model in the hilly area of southwest China

Risk analysis of natural water resources scarcity based on a stochastic simulation model in the hilly area of southwest China