scholarly journals Optimal Control of the Lost to Follow Up in a Tuberculosis Model

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Yves Emvudu ◽  
Ramsès Demasse ◽  
Dany Djeudeu

This paper deals with the problem of optimal control for the transmission dynamics of tuberculosis (TB). A TB model that considers the existence of a new class (mainly in the African context) is considered: the lost to follow up individuals. Based on the model formulated and studied in the work of Plaire Tchinda Mouofo, (2009), the TB control is formulated and solved as an optimal control theory problem using the Pontryagin's maximum principle (Pontryagin et al., 1992). This control strategy indicates how the control of the lost to follow up class can considerably influence the basic reproduction ratio so as to reduce the number of lost to follow up. Numerical results show the performance of the optimization strategy.

2017 ◽  
Vol 6 (2) ◽  
pp. 137
Author(s):  
JONNER NAINGGOLAN

A tuberculosis model of SEIT type which incorporates treatment of infectives is considered. The population is divided into four compartments, that is: S are individuals in the susceptible compartment, E are individuals in the exposed compartments, I are individuals in the infected compartment, and T are individuals in the treatment compartments. For this model, controls on treatment is incorporated to reduce the actively infected individual compartments, via application of the Pontryagins Maximum Principle of optimal control theory. Numerical calculations with the approach of the Runge-Kutta method of fourth order can be seen that, the influence of the control treatment to more effectively reduce the number of individuals in the infected compartment compared with no controls. The basic reproduction ratio with control less compared with no controls.


Author(s):  
Mohamed Elhia ◽  
Omar Balatif ◽  
Lahoucine Boujallal ◽  
Mostafa Rachik

In this paper, we formulate an optimal control problem based on a tuberculosis model with multiple infectious compartments and time delays. In order to have a more realistic model that allows highlighting the role of detection, loss to follow-up and treatment in TB transmission, we propose an extension of the classical SEIR model by dividing infectious patients in the compartment (I) into three categories: undiagnosed infected (I), diagnosed patients who are under treatment (T) and diagnosed patients who are lost to follow-up (L). We incorporate in our model delays representing the incubation period and the time needed for treatment. We also introduce three control variables in our delayed system which represent prevention, detection and the efforts that prevent the failure of treatment. The purpose of our control strategies is to minimize the number of infected individuals and the cost of intervention. The existence of the optimal controls is investigated, and a characterization of the three controls is given using the Pontryagin's maximum principle with delays. To solve numerically the optimality system with delays, we present an adapted iterative method based on the iterative Forward-Backward Sweep Method (FBSM). Numerical simulations performed using Matlab are also provided. They indicate that the prevention control is the most effective one. To the best of our knowledge, it is the first work to apply optimal control theory to a TB model which considers infectious patients diagnosis, loss to follow-up phenomenon and multiple time delays.


2009 ◽  
Vol 40 (12) ◽  
pp. 13
Author(s):  
ALAN ROCKOFF
Keyword(s):  

2013 ◽  
Author(s):  
Danielle M. Lespinasse ◽  
Kristen E. Medina ◽  
Stacey N. Maurer ◽  
Samantha A. Minski ◽  
Renee T. Degener ◽  
...  

Diabetes ◽  
2020 ◽  
Vol 69 (Supplement 1) ◽  
pp. 1174-P
Author(s):  
RYAN MCDONOUGH ◽  
SARAH THOMAS ◽  
NICOLE RIOLES ◽  
OSAGIE EBEKOZIEN ◽  
MARK A. CLEMENTS ◽  
...  

2015 ◽  
Vol 6 (1and2) ◽  
Author(s):  
Kingstone Mutsonziwa

This paper is a follow-up article based on the first article titled Customers speak for themselves: A case of Customer Satisfaction in the four Main South African Banks. Customer satisfaction within the banking industry is very important in the South African context. Although banks are trying their best to give their customers the best service, it is important to continuously measure customer satisfaction and identify service attributes that contribute to overall customer satisfaction for the banks. The data used in the analysis is based on a quantitative survey of 500 randomly selected customers in Pretoria, Johannesburg, Durban and Cape Town were interviewed using a face to face methodology. The key drivers of overall customer satisfaction based on regression analysis for the different banks were helpfulness and innovativeness (ABSA), helpfulness, innovativeness of the bank, resolution of problems and investment advice (FNB), language usage and friendliness of service consultants (Nedbank), innovativeness of the bank, investment advice and use of language (Standard bank). These attributes were important to the overall customer satisfaction and need to be closely monitored by the management of these banks.


2019 ◽  
Vol 16 (1) ◽  
Author(s):  
Ahmad Aliyu ◽  
Babatunde Adelekan ◽  
Nifarta Andrew ◽  
Eunice Ekong ◽  
Stephen Dapiap ◽  
...  

Abstract Background Expanded access to antiretroviral therapy (ART) leads to improved HIV/AIDS treatment outcomes in Nigeria, however, increasing rates of loss to follow-up among those on ART is threatening optimal standard achievement. Therefore, this retrospective cross-sectional study is aimed at identifying correlates and predictors of loss to follow-up in patients commencing ART in a large HIV program in Nigeria. Methods Records of all patients from 432 US CDC Presidents Emergency Plan for AIDS Relief (PEPFAR) supported facilities across 10 States and FCT who started ART from 2004 to 2017 were used for this study. Bivariate and multivariate analysis of the demographic and clinical parameters of all patients was conducted using STATA version 14 to determine correlates and predictors of loss to follow-up. Results Within the review period, 245,257 patients were ever enrolled on anti-retroviral therapy. 150,191 (61.2%) remained on treatment, 10,960 (4.5%) were transferred out to other facilities, 6926 (2.8%) died, 2139 (0.9%) self-terminated treatment and 75,041 (30.6%) had a loss to follow-up event captured. Males (OR: 1.16), Non-pregnant female (OR: 4.55), Patients on ≥ 3-monthly ARV refills (OR: 1.32), Patients with un-suppressed viral loads on ART (OR: 4.52), patients on adult 2nd line regimen (OR: 1.23) or pediatric on 1st line regimen (OR: 1.70) were significantly more likely to be lost to follow-up. Conclusion Despite increasing access to anti-retroviral therapy, loss to follow-up is still a challenge in the HIV program in Nigeria. Differentiated care approaches that will focus on males, non-pregnant females and paediatrics is encouraged. Reducing months of Anti-retroviral drug refill to less than 3 months is advocated for increased patient adherence.


Neurosurgery ◽  
2004 ◽  
Vol 55 (3) ◽  
pp. 519-531 ◽  
Author(s):  
Erol Veznedaroglu ◽  
David W. Andrews ◽  
Ronald P. Benitez ◽  
M. Beverly Downes ◽  
Maria Werner-Wasik ◽  
...  

Abstract OBJECTIVE: Despite the success of stereotactic radiosurgery, large inoperable arteriovenous malformations (AVMs) of 14 cm3 or more have remained largely refractory to stereotactic radiosurgery, with much lower obliteration rates. We review treatment of large AVMs either previously untreated or partially obliterated by embolization with fractionated stereotactic radiotherapy (FSR) regimens using a dedicated linear accelerator (LINAC). METHODS: Before treatment, all patients were discussed at a multidisciplinary radiosurgery board and found to be suitable for FSR. All patients were evaluated for pre-embolization. Those who had feeding pedicles amenable to glue embolization were treated. LINAC technique involved acquisition of a stereotactic angiogram in a relocatable frame that was also used for head localization during treatment. The FSR technique involved the use of six 7-Gy fractions delivered on alternate days over a 2-week period, and this was subsequently dropped to 5-Gy fractions after late complications in one of seven patients treated with 7-Gy fractions. Treatments were based exclusively on digitized biplanar stereotactic angiographic data. We used a Varian 600SR LINAC (Varian Medical Systems, Inc., Palo Alto, CA) and XKnife treatment planning software (Radionics, Inc., Burlington, MA). In most cases, one isocenter was used, and conformality was established by non-coplanar arc beam shaping and differential beam weighting. RESULTS: Thirty patients with large AVMs were treated between January 1995 and August 1998. Seven patients were treated with 42-Gy/7-Gy fractions, with one patient lost to follow-up and the remaining six with previous partial embolization. Twenty-three patients were treated with 30-Gy/5-Gy fractions, with two patients lost to follow-up and three who died as a result of unrelated causes. Of 18 evaluable patients, 8 had previous partial embolization. Mean AVM volumes at FSR treatment were 23.8 and 14.5 cm3, respectively, for the 42-Gy/7-Gy fraction and 30-Gy/5-Gy fraction groups. After embolization, 18 patients still had AVM niduses of 14 cm3 or more: 6 in the 7-Gy cohort and 12 in the 5-Gy cohort. For patients with at least 5-year follow-up, angiographically documented AVM obliteration rates were 83% for the 42-Gy/7-Gy fraction group, with a mean latency of 108 weeks (5 of 6 evaluable patients), and 22% for the 30-Gy/5-Gy fraction group, with an average latency of 191 weeks (4 of 18 evaluable patients) (P = 0.018). For AVMs that remained at 14 cm3 or more after embolization (5 of 6 patients), the obliteration rate remained 80% (4 of 5 patients) for the 7-Gy cohort and dropped to 9% for the 5-Gy cohort. A cumulative hazard plot revealed a 7.2-fold greater likelihood of obliteration with the 42-Gy/7-Gy fraction protocol (P = 0.0001), which increased to a 17-fold greater likelihood for postembolization AVMs of 14 cm3 or more (P = 0.003). CONCLUSION: FSR achieves obliteration for AVMs at a threshold dose, including large residual niduses after embolization. With significant treatment-related morbidities, further investigation warrants a need for better three-dimensional target definition with higher dose conformality.


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