scholarly journals An Optimal Control Experiment for an SEIRS Epidemiological Model

2021 ◽  
Vol 18 (3) ◽  
pp. 3-14
Author(s):  
Tanner Snyder ◽  
Ryan Nierman
Keyword(s):  
Optimal Control ◽  
Control Experiment ◽  
Real Life ◽  
Epidemiological Model ◽  
Control Cost ◽  
Disease Epidemiology ◽  
Discrete Values ◽  
Finite Time Horizon ◽  
Parameter Values ◽  
Number Of Individuals

This work studies an optimal control model for a discrete-time Susceptible/Exposed/Infective/Removed/Susceptible (SEIRS) deterministic epidemiological model with a finite time horizon and changing population. The model presented converts a continuous SEIRS model that would typically be solved using differential equations into a discrete model that can be solved using dynamic programming. The discrete approach more closely resembles real life situations, as the number of individuals in a population, the rate of vaccination to be applied, and the time steps are all discrete values. The model utilizes a previously developed algorithm and applies it to the presented SEIRS model. To demonstrate the applicability of the algorithm, a series of numerical results are presented for various parameter values. KEYWORDS: Control; Cost; Discrete; Disease; Epidemiology; Minimization; Modeling; Optimality; SEIRS; Vaccination

scholarly journals Monitoring Robust Estimates for Compositional Data

2021 ◽  
Vol 50 (2) ◽  
pp. 16-37
Author(s):  
Valentin Todorov
Keyword(s):  
Compositional Data ◽  
Real Life ◽  
R Package ◽  
Diagnostic Tools ◽  
Data Set ◽  
Mahalanobis Distances ◽  
Robust Estimates ◽  
Real Life Data ◽  
Manufactured Exports ◽  
Parameter Values

In a number of recent articles Riani, Cerioli, Atkinson and others advocate the technique of monitoring robust estimates computed over a range of key parameter values. Through this approach the diagnostic tools of choice can be tuned in such a way that highly robust estimators which are as efficient as possible are obtained. This approach is applicable to various robust multivariate estimates like S- and MM-estimates, MVE and MCD as well as to the Forward Search in whichmonitoring is part of the robust method. Key tool for detection of multivariate outliers and for monitoring of robust estimates is the Mahalanobis distances and statistics related to these distances. However, the results obtained with thistool in case of compositional data might be unrealistic since compositional data contain relative rather than absolute information and need to be transformed to the usual Euclidean geometry before the standard statistical tools can be applied. Various data transformations of compositional data have been introduced in the literature and theoretical results on the equivalence of the additive, the centered, and the isometric logratio transformation in the context of outlier identification exist. To illustrate the problem of monitoring compositional data and to demonstrate the usefulness of monitoring in this case we start with a simple example and then analyze a real life data set presenting the technologicalstructure of manufactured exports. The analysis is conducted with the R package fsdaR, which makes the analytical and graphical tools provided in the MATLAB FSDA library available for R users.

Optimization

Speech Timing ◽  
2020 ◽  
pp. 190-237
Author(s):  
Alice Turk ◽  
Stefanie Shattuck-Hufnagel
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Hierarchical Control ◽  
Component Model ◽  
Multiple Factors ◽  
Key Features ◽  
Cost Of Time ◽  
The Cost ◽  
Parameter Values

This chapter introduces a theoretical framework, Optimal Control Theory, which will enable a phonology-extrinsic-timing-based, three-component model to determine values of controlled variables, and to model the influence of multiple factors on these parameter values. Key features of Optimal Control Theory models are discussed, as well as evidence for types of movement costs (including the cost of time) used in the models, and predictions of the models for the coordination of multiple effectors and hierarchical control. Finally, the chapter reviews Optimal Control Theory models currently used to account for timing phenomena in speech.

Dynamic testing resource allocation modeling for multi-release software using optimal control theory and genetic algorithm

2020 ◽  
Vol 37 (6/7) ◽  
pp. 1049-1069
Author(s):  
Vijay Kumar ◽  
Ramita Sahni
Keyword(s):  
Genetic Algorithm ◽  
Optimal Control ◽  
Resource Allocation ◽  
Real Life ◽  
Theoretic Approach ◽  
Numerical Illustration ◽  
Data Set ◽  
Allocation Model ◽  
Content Type ◽  
Software Firms

PurposeThe use of software is overpowering our modern society. Advancement in technology is directly proportional to an increase in user demand which further leads to an increase in the burden on software firms to develop high-quality and reliable software. To meet the demands, software firms need to upgrade existing versions. The upgrade process of software may lead to additional faults in successive versions of the software. The faults that remain undetected in the previous version are passed on to the new release. As this process is complicated and time-consuming, it is important for firms to allocate resources optimally during the testing phase of software development life cycle (SDLC). Resource allocation task becomes more challenging when the testing is carried out in a dynamic nature.Design/methodology/approachThe model presented in this paper explains the methodology to estimate the testing efforts in a dynamic environment with the assumption that debugging cost corresponding to each release follows learning curve phenomenon. We have used optimal control theoretic approach to find the optimal policies and genetic algorithm to estimate the testing effort. Further, numerical illustration has been given to validate the applicability of the proposed model using a real-life software failure data set.FindingsThe paper yields several substantive insights for software managers. The study shows that estimated testing efforts as well as the faults detected for both the releases are closer to the real data set.Originality /valueWe have proposed a dynamic resource allocation model for multirelease of software with the objective to minimize the total testing cost using the flexible software reliability growth model (SRGM).

scholarly journals Optimal Control of Rumor Spreading Model with Consideration of Psychological Factors and Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Liang’an Huo ◽  
Chenyang Ma
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Psychological Factors ◽  
Control Strategies ◽  
Information Age ◽  
Control Cost ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Official Information ◽  
Type Ii Functional Response

Rumors have rapidly increasing influence on the society as well as individual life in the information age. How to control the spread of such rumors effectively has become an urgent problem to be solved. In this paper, we consider an optimal control of rumor spreading model with psychological factors and time delay. Firstly, we introduce a realistic optimal control of rumor spreading model with consideration of Holling-type II functional response and time delay. Secondly, by introducing two control strategies of both promoting scientific knowledge and releasing official information, we formulate an optimal control problem to minimize both the number of ignorant individuals and spreaders and the control cost. Thirdly, we prove the existence and the necessary conditions of optimal control strategies theoretically based on Pontryagin’s maximum principle. Our results indicate that the proposed control strategies are effective in reducing the number of spreaders and ignorant individuals and minimizing control cost.

The Probable Datum Method (PDM): a technique for estimating the age of origination or extinction of nannoplankton

Paleobiology ◽  
10.1666/13072 ◽  
2014 ◽  
Vol 40 (4) ◽  
pp. 541-559 ◽  
Author(s):  
Jonathan D. Schueth ◽  
Klaus Keller ◽  
Timothy J. Bralower ◽  
Mark E. Patzkowsky
Keyword(s):  
Control Experiment ◽  
Sampling Error ◽  
Positive Control ◽  
Error Rates ◽  
Age Difference ◽  
Fossil Species ◽  
A New Technique ◽  
Local Range ◽  
Parameter Values

Accurate interpretation of origination and extinction of fossil species is crucial to answering a variety of questions in paleontology. Fossil datums, the observed age of first or last occurrences, are subject to sampling error as a result of preservation and low abundances near range endpoints. This sampling error can cause local range offset, an age difference between the observed first or last occurrence of a species and its true origination or extinction. Here, we develop and test a new technique, the Probable Datum Method (PDM), that can be used to assess the extent of local range offset for nannofossil species. The PDM estimates the original abundance of a taxon and its probable true age of first or last occurrence. The PDM uses a model in which original abundance is related to count abundance through preservation and the counting process. This model is empirically parameterized, including an experimental determination of false positive and error rates of a nannofossil count. The model is simulated then inverted to estimate likely original abundance and true datum age from count abundance data. We first test the PDM in a positive control experiment with known parameter values. This experiment shows that the PDM is robust and returns known values accurately. Next we apply the method to the origination of nannoplankton after the Cretaceous/Paleogene boundary to test whether first occurrences were synchronous between widely spaced locations. The PDM results suggest that observed diachrony of K/Pg originations cannot be explained by the effects of local range offset; rather, in some cases they indicate truly diachronous first occurrences between localities. Although the technique was developed to analyze nannoplankton ranges, the statistical nature of the PDM, its experimentally derived parameters, and its parsimonious nature should make it applicable to many micropaleontological studies that interpret patterns of origination and extinction.

scholarly journals Optimal Control and Cost-effectiveness Analysis of an HPV-Chlamydia Trachomatis co-infection model

2020 ◽  
Author(s):  
Andrew Omame ◽  
Celestine Uchenna Nnanna ◽  
Simeon Chioma Inyama
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Chlamydia Trachomatis ◽  
Reproduction Number ◽  
Population Level ◽  
Backward Bifurcation ◽  
Infection Model ◽  
Control Analysis ◽  
Number Of Individuals ◽  
Positive Population

In this work, a co-infection model for human papillomavirus (HPV) and Chlamydia trachomatis with cost-effectiveness optimal control analysis is developed and analyzed. The disease-free equilibrium of the co-infection model is \textbf{shown not to} be globally asymptotically stable, when the associated reproduction number is less unity. It is proven that the model undergoes the phenomenon of backward bifurcation when the associated reproduction number is less than unity. It is also shown that HPV re-infection ($\varepsilon\sst{p} \neq 0$) induced the phenomenon of backward bifurcation. Numerical simulations of the optimal control model showed that: (i) focusing on HPV intervention strategy alone (HPV prevention and screening), in the absence of Chlamydia trachomatis control, leads to a positive population level impact on the total number of individuals singly infected with Chlamydia trachomatis, (ii) Concentrating on Chlamydia trachomatis intervention controls alone (Chlamydia trachomatis prevention and treatment), in the absence of HPV intervention strategies, a positive population level impact is observed on the total number of individuals singly infected with HPV. Moreover, the strategy that combines and implements HPV and Chlamydia trachomatis prevention controls is the most cost-effective of all the control strategies in combating the co-infections of HPV and Chlamydia trachomatis.

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