An improved two-step method in stochastic differential equation's structural parameter estimation

Non-parametric modelling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline characterised by the truncated power series basis with Bayesian approach is considered in the first step of a two-step method for estimating the structural parameters for stochastic differential equation (SDE). Previous methodology revealed the selection of knot and order of spline can be done heuristically based on a scatter plot. To overcome the subjective and tedious process of selecting the optimal knot and order of spline, an algorithm is proposed. A single optimal knot is selected out of all the points with exception of the first and the last data and the least value of Generalised Cross Validation is calculated for each order of spline. The spline model is later utilised in the second step to estimate the stochastic model parameters. In the second step, a non-parametric criterion is proposed for estimating the diffusion parameter of SDE. Linear and non-linear SDE consisting of Geometric Brownian Motion (GBM) for the former and logistic together with Lotka Volterra (LV) model for the later are tested using the two-step method for both simulated and real data. The results show high percentage of accuracy with 99.90% and 96.12% are obtained for GBM and LV model respectively for diffusion parameters of simulated data. This verifies the viability of the two-step method in the estimation of diffusion parameters of SDE with an improvement of a single knot selection

On estimate of Malaysian mortality rates using interpolation methods

Life table is a table that shows mortality experience of a nation. However, in Malaysia, the information in this table is provided in the five-years age groups (abridged) instead of every one-year age. Hence, this study aims to estimate the one-year age mor- tality rates from the abridged mortality rates using several interpolation methods. We applied Kostaki method and the Akima spline method to five sets of Malaysian group mortality rates ranging from period of 2012 to 2016. The result were then compared with the one-year mortality rates. We found that the method by Akima is the best method for Malaysian mortality experience as it gives the least minimum of sum of square errors. The method does not only provide a good fit but also, shows a smooth mortality curve

Parameter estimation of stochastic differential equation

Non-parametric modeling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline with Bayesian approach is considered in the first step of a two-step method in estimating the structural parameters for stochastic differential equation (SDE). The selection of knot and order of spline can be done heuristically based on the scatter plot. To overcome the subjective and tedious process of selecting the optimal knot and order of spline, an algorithm was proposed. A single optimal knot is selected out of all the points with exception of the first and the last data which gives the least value of Generalized Cross Validation (GCV) for each order of spline. The use is illustrated using observed data of opening share prices of Petronas Gas Bhd. The results showed that the Mean Square Errors (MSE) for stochastic model with parameters estimated using optimal knot for 1,000, 5,000 and 10,000 runs of Brownian motions are smaller than the SDE models with estimated parameters using knot selected heuristically. This verified the viability of the two-step method in the estimation of the drift and diffusion parameters of SDE with an improvement of a single knot selection

Oral health knowledge, practice and dental plaque maturity status of hearing-impaired children

Hearing impairment is an unseen handicapped that lead to communication barriers which might impede knowledge transfer. The aim of this study was to compare the oral health knowledge, practice and dental plaque maturity between hearing-impaired (HI) and normal children. A cross sectional study was conducted among children aged 7-14 years old. The HI children were recruited from a special school for the deaf while the normal children were from the primary and secondary schools in Bachok, Kelantan. The oral health knowledge and practice was assessed by face to face interview whilst the dental plaque maturity status was evaluated using GC Tri Plaque ID Gel™ (TPID). The data was analysed using IBM SPSS version 22. HI children had poor oral health knowledge and oral health practice compared to normal children (p<0.05). HI children had significantly more matured plaque compared to normal children with mean (SD) DPMS of 1.8 (0.57) and 1.3 (0.20), respectively (p<0.001). In conclusion, there were poor oral health knowledge, poor oral hygiene practice and high plaque maturity among HI children

Parameter estimation of Stochastic Logistic Model : Levenberg-Marquardt Method

In this paper, we estimate the drift and diffusion parameters of the stochas- tic logisticmodels for the growth of Clostridium Acetobutylicum P262 using Levenberg- Marquardt optimization method of non linear least squares. The parameters are esti- mated for five different substrates. The solution of the deterministic models has been approximated using Fourth Order Runge-Kutta and for the solution of the stochastic differential equations, Milstein numerical scheme has been used. Small values of Mean Square Errors (MSE) of stochastic models indicate good fits. Therefore the use of stochastic models are shown to be appropriate in modelling cell growth of Clostridium Acetobutylicum P26

Boundary-layer flow and heat transfer of Blasius and Sakiadis problems in nanofluids with partial slip and thermal convection

This study aims to investigate the steady two-dimensional laminar boundary layer flow past a fixed (Blasius) or past a moving (Sakiadis) semi-infinite flat plate in water-based nanofluids with partial slip and thermal convective boundary condition. The similarity equations are solved numerically for three types of metallic or non-metallic nanoparticles such as copper (Cu), alumina (Al2O3), and Titania (TiO2) in the base fluid of water with the Prandtl number Pr = 6.2 to investigate the effect of the solid volume fraction parameter ???? of the nanofluids. The governing partial differential equations are transformed into a system nonlinear ordinary differential equation using a similarity transformation which is then solved numerically using a shooting method in Maple software. The numerical results are presented in tables and graphs for the skin friction coefficient Cf and local Nusselt number Nu which represents the heat transfer rate at the surface as well as the velocity and temperature profile for a range of various parameters such as nanoparticles volume fraction, slip parameter and Biot number. The results indicate that the solid volume fraction affects the fluid flow and heat transfer characteristics

The influence of climate factors on hand-foot-mouth disease: a five-state study in Malaysia

Hand, foot, and mouth disease (HFMD) has become an important public health problem worldwide due to its tendency to cause outbreaks and human death. The outbreak of HFMD with clinical and fatal complications has been noticed in the Asia Pacific region since the late 1990s. The increasing evidence of climate change effect on HFMD has motivated the need for further investigations. Numerous previous studies conducted in several countries have established a significant association between climate factors and HFMD. However, there are currently only a few studies in Malaysia addressing these issues. Therefore, this study aimed to examine the link between climate factors and the occurrences of HFMD in five states representing each region of Malaysia by using a generalized linear model approach. The weekly HFMD cases and four climate variables, including temperature, humidity, rainfall, and wind speed, were examined. The findings indicate that climate variables significantly influence HFMD in Malaysia; however, it varies between states as different states experience different climates. Additionally, the results revealed that humidity and temperature were the primary climate factors affecting the incidence of HFMD in Malaysia. This study could guide policymakers, health agencies, and local communities in determining the most effective prevention and control strategies

A systematic review of the statistical methodology used in establishing the link between climate factors and HFMD incidence

Hand, foot, and mouth disease (HFMD) is a common infectious disease caused by two main viruses, namely Coxsackievirus A16 and Human Enterovirus 71. It has been a significant public health disease and a substantial burden all over the world since 1969. Prior studies have shown that climate factors are significantly associated with HFMD cases by using various statistical methods. Therefore, this study aims to review the scientific studies related to climate and HFMD and hence, address the analytical techniques used. This study only includes quantitative studies from peer-reviewed and original papers published in international and national journals from the years 1957 to 2020. In total, there were 522 articles identified; however, there were only 29 studies that linked climate change and HFMD. Based on the articles reviewed, the modelling analysis technique, which includes the Generalized Linear Model (GLM), the Generalized Additive Model (GAM), and the Generalized Additive Mixed Model (GAMM), represents the most popular analysis in identifying the association between HFMD and climate factors. The temperature and humidity showed the greatest impact on the occurrence of HFMD, and the suitable incubation period for all climatic factors was not more than three weeks

DNA Strand Patterns on Aluminium Thin Films

A new patterning method using Deoxyribose Nucleic Acid (DNA) strands capable of producing nanogaps of less than 100 nm is proposed and investigated in this work. DNA strands from Bosenbergia rotunda were used as the fundamental element in patterning DNA on thin films of aluminium (Al) metal without the need for any lithographic techniques. The DNA strands were applied in buffer solutions onto thin films of Al on silicon (Si) and the chemical interactions between the DNA strands and Al creates nanometer scale arbitrary patterning by direct transfer of the DNA strands onto the substrate. This simple and cost-effective method can be utilized in the fabrication of various components in electronic chips for microelectronics and Nano Electronic Mechanical System (NEMS) applications in general

Exponential growth model and stochastic population models: a comparison via goat population data

A population dynamic model explains the changes of a population in the near future, given its current status and the environmental conditions that the population is exposed to. In modelling a population dynamic, deterministic model and stochastic models are used to describe and predict the observed population. For modelling population size, deterministic model may provide sufficient biological understanding about the system, but if the population numbers become small, then a stochastic model is necessary with certain conditions. In this study, both types of models such as exponential, discrete-time Markov chain (DTMC), continuous-time Markov chain (CTMC) and stochastic differential equation (SDE) are applied to goat population data of small size. Results from the simulations of stochastic realizations as well as deterministic counterparts are shown and tested by root mean square error (RMSE). The SDE model gives the smallest RMSE value which indicate the best model in fitting the data