Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection

A human respiratory syncytial virus surveillance system was implemented in Florida in 1999, to support clinical decision-making for prophylaxis of premature newborns. Recently, a local periodic SEIRS mathematical model was proposed in [Stat. Optim. Inf. Comput. 6 (2018), no.1, 139--149] to describe real data collected by Florida's system. In contrast, here we propose a non-local fractional (non-integer) order model. A fractional optimal control problem is then formulated and solved, having treatment as the control. Finally, a cost-effectiveness analysis is carried out to evaluate the cost and the effectiveness of proposed control measures during the intervention period, showing the superiority of obtained results with respect to previous ones.Comment: This is a preprint of a paper whose final and definite form is with 'Chaos, Solitons & Fractals', available from [http://www.elsevier.com/locate/issn/09600779]. Submitted 23-July-2018; Revised 14-Oct-2018; Accepted 15-Oct-2018. arXiv admin note: substantial text overlap with arXiv:1801.0963

Optimal Control and Sensitivity Analysis of a Fractional Order TB Model

A Caputo fractional-order mathematical model for the transmission dynamics of tuberculosis (TB) was recently proposed in [Math. Model. Nat. Phenom. 13 (2018), no. 1, Art. 9]. Here, a sensitivity analysis of that model is done, showing the importance of accuracy of parameter values. A fractional optimal control (FOC) problem is then formulated and solved, with the rate of treatment as the control variable. Finally, a cost-effectiveness analysis is performed to assess the cost and the effectiveness of the control measures during the intervention, showing in which conditions FOC is useful with respect to classical (integer-order) optimal control.Comment: This is a preprint of a paper whose final and definite form is with 'Statistics Opt. Inform. Comput.', Vol. 7, No 2 (2019). See [http://www.IAPress.org]. Submitted 09/Sept/2018; Revised 10/Dec/2018; Accepted 11/Dec/2018. arXiv admin note: text overlap with arXiv:1801.09634, arXiv:1810.0690

The Transition to College Process in PR-CETP Scholars

This article describes a study about the experiences of a group of students during the transition from high school to college. The students are future teachers who evidenced a high level of academic achievement in high school and received merit scholarships from the Puerto Rico Collaborative for Excellence in Teacher Preparation (PR-CETP). Two groups of students were compared: those who sustained a high GPA during their freshman year, and those who did not and, therefore, no longer qualified for the scholarship. The study was carried out through focused interviews with eight students, from three universities, four of whom maintained the scholarship and four who did not. Findings indicate that the main problems encountered were academic and social, and that the students received support from their families during the entire process. Regarding formal support, they pointed out that they felt highly satisfied with the services provided by PR-CETP and the universities, but they also pointed out (particularly those who lost the scholarship) that they needed additional services from the universities. They suggested, for example, better tutoring, and social activities among the scholars. The interviewed students, in general, consider that they faced the transition successfully since most of them described their academic, emotional, and social status as satisfactory at the time of the interviews

Fractional-order modelling and optimal control of cholera transmission

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.publishe

Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB

In this article, we develop a simple mathematical GNU Octave/MATLAB code that is easy to modify for the simulation of mathematical models governed by fractional-order differential equations, and for the resolution of fractional-order optimal control problems through Pontryagin's maximum principle (indirect approach to optimal control). For this purpose, a fractional-order model for the respiratory syncytial virus (RSV) infection is considered. The model is an improvement of one first proposed by the authors in [Chaos Solitons Fractals 117 (2018), 142--149]. The initial value problem associated with the RSV infection fractional model is numerically solved using Garrapa's fde12 solver and two simple methods coded here in Octave/MATLAB: the fractional forward {Euler's} method and the predict-evaluate-correct-evaluate (PECE) method of Adams--Bashforth--Moulton. A fractional optimal control problem is then formulated having treatment as the control. The fractional Pontryagin maximum principle is used to characterize the fractional optimal control and the extremals of the problem are determined numerically through the implementation of the forward-backward PECE method. The implemented algorithms are available on GitHub and, at the end of the paper, in appendixes, both for the uncontrolled initial value problem as well as for the fractional optimal control problem, using the free GNU Octave computing software and assuring compatibility with MATLAB. The developed Octave/Matlab code is available at [https://github.com/SilverioRosa/numres-focp]This research was funded by The Portuguese Foundation for Science and Technology (FCT—Fundação para a Ciência e a Tecnologia), grants number UIDB/50008/2020 (S.R.) and UIDB/04106/2020 (D.F.M.T.).publishe

VLBA Determination of the Distance to Nearby Star-forming Regions. IV. A Preliminary Distance to the Proto-Herbig AeBe Star EC 95 in the Serpens Core

Using the Very Long Base Array, we observed the young stellar object EC 95 in the Serpens cloud core at eight epochs from 2007 December to 2009 December. Two sources are detected in our field and are shown to form a tight binary system. The primary (EC 95a) is a 4-5 M_⊙ proto-Herbig AeBe object (arguably the youngest such object known), whereas the secondary (EC 95b) is most likely a low-mass T Tauri star. Interestingly, both sources are non-thermal emitters. While T Tauri stars are expected to power a corona because they are convective while they go down the Hayashi track, intermediate-mass stars approach the main sequence on radiative tracks. Thus, they are not expected to have strong superficial magnetic fields, and should not be magnetically active. We review several mechanisms that could produce the non-thermal emission of EC 95a and argue that the observed properties of EC 95a might be most readily interpreted if it possessed a corona powered by a rotation-driven convective layer. Using our observations, we show that the trigonometric parallax of EC 95 is π = 2.41 ± 0.02 mas, corresponding to a distance of 414.9^(+4.4)_ (–4.3) pc. We argue that this implies a distance to the Serpens core of 415 ± 5 pc and a mean distance to the Serpens cloud of 415 ± 25 pc. This value is significantly larger than previous estimates (d ~ 260 pc) based on measurements of the extinction suffered by stars in the direction of Serpens. A possible explanation for this discrepancy is that these previous observations picked out foreground dust clouds associated with the Aquila Rift system rather than Serpens itself