scholarly journals Predicting and preventing measles epidemics in New Zealand: application of a mathematical model

2000 ◽  
Vol 124 (2) ◽  
pp. 279-287 ◽  
Author(s):  
M. G. ROBERTS ◽  
M. I. TOBIAS
Keyword(s):  
Mathematical Model ◽  
New Zealand ◽  
Optimal Timing ◽  
Extended Version ◽  
Critical Question ◽  
Immunization Campaign

A mathematical model of the dynamics of measles in New Zealand was developed in 1996. The model successfully predicted an epidemic in 1997 and was instrumental in the decision to carry out an intensive MMR (measles–mumps–rubella) immunization campaign in that year. While the epidemic began some months earlier than anticipated, it was rapidly brought under control, and its impact on the population was much reduced. In order to prevent the occurrence of further epidemics in New Zealand, an extended version of the model has since been developed and applied to the critical question of the optimal timing of MMR immunization.

scholarly journals Dynamic CO2 therapy in periodic breathing: a modeling study to determine optimal timing and dosage regimes

2009 ◽  
Vol 107 (3) ◽  
pp. 696-706 ◽  
Author(s):  
Yoseph Mebrate ◽  
Keith Willson ◽  
Charlotte H. Manisty ◽  
Resham Baruah ◽  
Jamil Mayet ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Sleep Apnea ◽  
Time Window ◽  
Central Sleep Apnea ◽  
Periodic Breathing ◽  
Optimal Time ◽  
Optimal Timing ◽  
Ventilatory Control ◽  
Dynamic Therapy ◽  
End Tidal

We examine the potential to treat unstable ventilatory control (seen in periodic breathing, Cheyne-Stokes respiration, and central sleep apnea) with carefully controlled dynamic administration of supplementary CO2, aiming to reduce ventilatory oscillations with minimum increment in mean CO2. We used a standard mathematical model to explore the consequences of phasic CO2 administration, with different timing and dosing algorithms. We found an optimal time window within the ventilation cycle (covering ∼1/6 of the cycle) during which CO2 delivery reduces ventilatory fluctuations by >95%. Outside that time, therapy is dramatically less effective: indeed, for more than two-thirds of the cycle, therapy increases ventilatory fluctuations >30%. Efficiency of stabilizing ventilation improved when the algorithm gave a graded increase in CO2 dose (by controlling its duration or concentration) for more severe periodic breathing. Combining gradations of duration and concentration further increased efficiency of therapy by 22%. The (undesirable) increment in mean end-tidal CO2 caused was 300 times smaller with dynamic therapy than with static therapy, to achieve the same degree of ventilatory stabilization (0.0005 vs. 0.1710 kPa). The increase in average ventilation was also much smaller with dynamic than static therapy (0.005 vs. 2.015 l/min). We conclude that, if administered dynamically, dramatically smaller quantities of CO2 could be used to reduce periodic breathing, with minimal adverse effects. Algorithms adjusting both duration and concentration in real time would achieve this most efficiently. If developed clinically as a therapy for periodic breathing, this would minimize excess acidosis, hyperventilation, and sympathetic overactivation, compared with static treatment.

Modeling Colorectal Cancer

2013 ◽  
pp. 53-75 ◽  
Author(s):  
Svetoslav Nikolov ◽  
Mukhtar Ullah ◽  
Momchil Nenov ◽  
Julio Vera Gonzalez ◽  
Peter Raasch ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Colorectal Cancer ◽  
Mathematical Model ◽  
Systems Biology ◽  
Numerical Simulations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Extended Version ◽  
Necessary And Sufficient ◽  
The Mathematical Model

Mathematical modeling is increasingly used to improve our understanding of colorectal cancer. In the first part of this chapter, the authors give a review of systems biology approaches to investigate colorectal cancer. In the second part, the mathematical model proposed by Johnston et al. (2007) is expanded to include time delays and analysed for its stability. For both models, the original and the extended version, the authors obtain the necessary and sufficient conditions for stability. This is confirmed by numerical simulations. Thus, some new mathematical and biological results are obtained.

scholarly journals Vitamin D status of newborns in New Zealand

2010 ◽  
Vol 104 (7) ◽  
pp. 1051-1057 ◽  
Author(s):  
Carlos A. Camargo ◽  
Tristram Ingham ◽  
Kristin Wickens ◽  
Ravi I. Thadhani ◽  
Karen M. Silvers ◽  
...  
Keyword(s):  
Vitamin D ◽  
New Zealand ◽  
Cord Blood ◽  
Vitamin D Supplementation ◽  
Optimal Timing ◽  
Vitamin D Status ◽  
Skeletal Health ◽  
Parental History ◽  
Low Levels ◽  
Apparently Healthy

Recognition of the important non-skeletal health effects of vitamin D has focused attention on the vitamin D status of individuals across the lifespan. To examine the vitamin D status of newborns, we measured serum levels of 25-hydroxyvitamin D (25(OH)D) in the cord blood of 929 apparently healthy newborns in a population-based study in New Zealand, a country at 41°S latitude, with strong anti-skin cancer (sun avoidance) campaigns and without vitamin D food fortification. Randomly selected midwives in two regions recruited children. The median cord blood level of 25(OH)D was 44 nmol/l (interquartile range, 29–78 nmol/l). Overall, 19 % of newborns had 25(OH)D levels < 25 nmol/l and 57 % had levels < 50 nmol/l; only 27 % had levels of 75 nmol/l or higher, which are levels associated with optimal health in older children and adults. A multivariable ordinal logistic regression model showed that the strongest determinants of low vitamin D status were winter month of birth and non-European ethnicity. Other determinants of low cord blood 25(OH)D included longer gestational age, younger maternal age and a parental history of asthma. In summary, low levels of vitamin D are common among apparently healthy New Zealand newborns, and are independently associated with several easily identified factors. Although the optimal timing and dosage of vitamin D supplementation require further study, our findings may assist future efforts to correct low levels of 25(OH)D among New Zealand mothers and their newborn children.

scholarly journals Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdon Atangana ◽  
Seda İğret Araz
Keyword(s):  
Mathematical Model ◽  
Statistical Analysis ◽  
Existence And Uniqueness ◽  
Extended Version ◽  
African Countries ◽  
Nonlocal Operators ◽  
Fractal Properties ◽  
Modeling And Forecasting ◽  
Near Future ◽  
Second Wave

AbstractUsing the existing collected data from European and African countries, we present a statistical analysis of forecast of the future number of daily deaths and infections up to 10 September 2020. We presented numerous statistical analyses of collected data from both continents using numerous existing statistical theories. Our predictions show the possibility of the second wave of spread in Europe in the worse scenario and an exponential growth in the number of infections in Africa. The projection of statistical analysis leads us to introducing an extended version of the well-blancmange function to further capture the spread with fractal properties. A mathematical model depicting the spread with nine sub-classes is considered, first converted to a stochastic system, where the existence and uniqueness are presented. Then the model is extended to the concept of nonlocal operators; due to nonlinearity, a modified numerical scheme is suggested and used to present numerical simulations. The suggested mathematical model is able to predict two to three waves of the spread in the near future.

Technology for Locating System of the Laying Pipe Manipulator

2009 ◽  
Vol 16-19 ◽  
pp. 25-29
Author(s):  
Dan Wang ◽  
Hong Yi Liu ◽  
Bin Li
Keyword(s):  
Mathematical Model ◽  
Control Theory ◽  
Product Development ◽  
Construction Site ◽  
Critical Question ◽  
Concrete Pipe ◽  
Locating System ◽  
The Mathematical Model ◽  
Test Result

The laying pipe manipulator is used to lay concrete pipe, and it solves the question of safety, quality, and efficiency in the pipe laying construction site, and the critical question of locating system is studied. The work principle and mathematical model of locating system were established, and the experiment of locating system was done. According to the test result, the work principle and mathematical model of locating system had turned out to be well adapted for requirement. The locating system of laying pipe manipulator can be applied to product development. The mathematical model of locating system supplies the basic control theory for the manipulator to lay and joint concrete pipe automatically.

scholarly journals Driving New Zealand’s Economic Relationship With Asia

2020 ◽  
Vol 16 (4) ◽  
Author(s):  
Simon Draper ◽  
James To
Keyword(s):  
Foreign Policy ◽  
New Zealand ◽  
Critical Question ◽  
Economic Relationship ◽  
Over Time

How does New Zealand’s engagement across the Asia region affect New Zealand’s prosperity and security? New Zealand’s approach to developing economic, political and people-to-people connections across Asia has changed considerably over the last few decades. This article seeks to highlight some of those changes, including how the New Zealand public’s perceptions of Asia have changed over time and how this has shaped New Zealand foreign policy. The critical question is whether enough is being done – across public, private and community sectors – to help position New Zealand as a highvalue partner in Asia for the long term.

scholarly journals On Backlund transformations of surfaces by extended Harry-Dym flow

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1823-1831
Author(s):  
Muhammed Sariaydin
Keyword(s):  
Mathematical Model ◽  
Bäcklund Transformation ◽  
Mapping Method ◽  
Bäcklund Transformations ◽  
Extended Version ◽  
Backlund Transformation ◽  
Backlund Transformations ◽  
Bonnet Surface ◽  
Schrodinger Flow ◽  
The Mathematical Model

The present paper deals with the introduction of Backlund transformations by extended Harry-Dym flow and with the aid of the extended version of the Riccati mapping method is obtained new solutions. Then, we give the Backlund transformation of the Schrodinger flow and obtain its the Bonnet surface. In finally, results obtained with the mathematical model are evaluated by applying to mathematica.

scholarly journals TMOD-33. AN INTEGRATED APPROACH COMBINING MATHEMATICAL AND GENOMIC METHODS TO REVEAL THE OPTIMAL TIMING OF THERAPEUTIC INTERVENTION IN WHO GRADE II DIFFUSE GLIOMA

2019 ◽  
Vol 21 (Supplement_6) ◽  
pp. vi270-vi270
Author(s):  
Kosuke Aoki ◽  
Takashi Yamamoto ◽  
Hiromichi Suzuki ◽  
Sachi Maeda ◽  
Melissa Ranjit ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Somatic Mutations ◽  
Integrated Approach ◽  
Exponential Model ◽  
Optimal Timing ◽  
Low Grade ◽  
Diffuse Glioma ◽  
Who Grade ◽  
Grade Ii

Abstract BACKGROUND In WHO grade II diffuse gliomas (low-grade gliomas, hereafter called LGGs), chemotherapy and radiotherapy contribute to prolonged survival but could induce somatic mutations. The optimal timing of treatment in LGGs remain poorly understood. To delineate this, we designed a mathematical model for tumor growth and investigate the association among the treatment, malignant transformation (MT), and the accumulation of somatic mutations revealed by whole exome sequencing (WES) in LGGs. METHODS Totally, 290 patients with LGGs between 1990 and 2018 were analyzed. We assessed the statuses of IDH mutation and 1p19q co-deletion in all tumors. Among all, 114 patients (39%) underwent MT during follow-up periods (mean: 82.6 months). Tumor volume was evaluated with FLAIR and/or T2-weighted MRI. MT was evaluated with contrast-enhanced MRI and/or pathological diagnosis. To investigate the number of somatic mutations in a cohort of LGGs and their patient matched recurrence, WES was performed on 88 serial samples collected at least two time-points from 39 patients. RESULTS Oligodendroglioma, IDH-mutant and 1p/19q-codeleted (OD) showed longer transformation-free survival compared to other subtypes. An exponential model was chosen to estimate growth rate in LGGs, since the exponential model provided a better fit to our data as compared to a linear model. The growth rate significantly decreased in the middle of chemotherapy and after radiotherapy. By contrast, these treatments increased the number of somatic mutations identified by WES and the rate of MT in each subtype. The increasing number of mutations in recurrent tumors showed strong correlation with the rise in MT rate. Based on the growth rate and the risk of MT, optimal timing of treatments could be calculated for each genetic subtype. CONCLUSIONS The mathematical model and WES analysis delineates the optimal timing of treatments in each subtype, which will help to decide the treatment for LGGs.

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