School of Aerospace

Modelling Spatiotemporal Survival patterns and Survival Analysis of HIV-TB Co-Infected Patients in selected Counties in Kenya

2023-01-01T00:00:00Z

Modelling Spatiotemporal Survival patterns and Survival Analysis of HIV-TB Co-Infected Patients in selected Counties in Kenya Okemwa, Benard Onserio The illnesses tuberculosis (TB) and the human immunodeficiency virus/acquired immune deficiencies syndrome (HIV/AIDS), which result in approximately 10 million illnesses and 1.45 million fatalities each year, account for a sizeable share of the global burden. HIV survival rates are decreased by co-infection with TB because it is more difficult to manage and treat HIV. The objective of the project was to mimic in a few Kenyan counties the spatial-temporal survival dynamics of patients who also had TB and HIV infections. The study's specific objectives included comparing the survival rates of patients receiving ART and TB treatment in a few Kenyan counties with those receiving ART alone, analyzing geographic variations in associated patient deaths, demonstrating the spatial-temporal the distributions of HIV/TB fatalities, and using a Bayesian model to look into regional/county demographic factors associated with survival rates in a few Kenyan counties. A retrospective collaborative research methodology was used in the project. The patients who received co-therapy for TB and ART maintenance at medical hospital through January 1, 2015, and December 31, 2019, comprised the target population. This information was compiled using the National AIDS & STIs Control Program (NASCOP) database, which contains all the records of patients from the chosen Kenyan counties that had associated with HIV and TB. The Kaplan-Meier estimator was used to calculate the survival function. A Cox Proportional Hazard Regression Analysis was fitted in a multivariate analysis to assess subject survival trends and the influence of covariates on survival time. The fit of the data to the Cox proportionate hazard regression model is given by the log component likelihood function. The hazard ratios for every covariate data, under consideration were tested for statistical significance using the Log-rank, Score, and Wald tests. A Bayesian model was created to display the temporal and spatial variance in mortality hazard by County in Kenya. STATA 14.2 and Bayes 3.0.2 were used for the analysis. The results showed that 2,555 (7.9%) of the HIV and TB patients in Kenya reported passing away five years after starting ART. The mean duration of event incidence for the category receiving both ART and treatment for TB was 4 years, according to the mean surviving time for the resultant (dead) cases of 4 years. The study's log-rank test showed a p-value of 0.00, indicating that the two curves were statistically independent from one another. The p-value of 0.000, which was lower than the value of the p- value at the 5% significance threshold, demonstrates this. The probabilistic survival of those with HIV and TB mutual infection is thus impacted by ART and TB treatment. More persons with TB and HIV illnesses survived more time when they obtained both ART and antibiotics for TB compared to when they only received ART up until about the 750th day. Between 2015 and 2019, the study also discovered geographical disparities in the mortality rate for HIV-TB patients. The study also found that over a five-year period, the frequency of TB and HIV mortality varied in the selected Counties. The study discovered that ART and TB therapies, marital status, gender, WHO diagnostic stage, age, weight, and institution of residence are the key factors influencing HIV-TB patients' survival rates. Starting medicine later in the course of the medical condition may have less of an effect on lowering TB/HIV than targeted therapies in the initial few weeks and months after ART began. HIV-rationality. As a result, the use of ART and TB treatments, as well as demographic variables and geographic determinants, each have a statistically noteworthy impact on the life expectancy of HIV/TB infected as well individuals. The study urges the MoH to give preference to the use underlying ART and TB medication, the assessment of demographic traits, and spatial variables in order to increase survival

Bayesian hierarchical models with applications to cervical, oesophageal and lung cancers in Kenya's Counties

2022-01-01T00:00:00Z

Bayesian hierarchical models with applications to cervical, oesophageal and lung cancers in Kenya's Counties Waitara, Joseph Kuria Cancer is an event associated with space and time. Counties relative risks esti- mates can be obtained using Bayesian hierarchical models. The general objective of the research was to obtain county based estimates through Bayesian hierarchi- cal modeling of cervical, oesophageal and lung cancers in Kenya's counties from 2015 to 2016, period which complete data was available. Speci c objectives were: to model over-dispersion and conduct spatial correlations tests in order to model three cancer cases distribution in Kenya' counties; to model cervical cancer cases using Poisson-Gamma and spatial-temporal models; to model the e ects of co- variates on spatial-temporal distribution of oesophageal and lung cancer cases in Kenya's counties. The data was obtained from National Cancer Registry (NCR) which carried a 2 year retrospective study in ten counties. Cervical cancer cases were 1064, oesophageal cancer cases 1599 while lung cancer cases were 256. A simple Poisson log-linear model dispersion parameter for cervical was 31.202, oe- sophageal was 49.241 and lung cancer cases was 6.134 which were greater than 1 indicating over dispersion. Spatial correlation tests conducted for the three cancers revealed that there was no spatial auto correlations of the residuals since for cervical cancer p-value=0.2104>0.05, oesophageal p-value= 0.4155>0.05 while for lung cancer p-value=0.4120>0.05. The model revealed that the highest cervi- cal cancer relative risk was in Embu=7.92 and lowest in Bomet which was 1.53. The smoking and alcohol use interaction oesophageal cancer model revealed that Bomet=11.16 had the highest risk while Kiambu had the lowest relative risk 0.6. Smoking and alcohol use were signi cant risk factors of oesophageal cancer. The multiplicative e ect of smoking was 1.012, thus 1.2 % higher to smokers compared to non-smokers. Alcohol use was 1.0346 thus 3.5 % higher to alcohol users. The interaction model revealed that oesophageal cancer was 16.88 % higher to alcohol users while it was 4.60 % higher to smokers. The interaction model for lung cancer revealed that in Nairobi=5.97 had highest risk while lowest in Kakamega=0.1. In the lung cancer model the multiplicative e ect of smoking was 1.4021, indicating 40.21 % higher to smokers as compared to non-smokers, 1.3689 for alcohol use variable that is 36.89 % higher to alcohol users. In interaction model the e ect was 7.86 times higher for smokers. In conclusion, simple Poisson regression mod- els were not appropriate to model the three cancers due to over dispersion nature of the data sets. The spatial correlation tests revealed that there was no spatial auto correlation for the three types of cancer. Application of Bayesian hierarchical models enabled generation of relative risks and identi cation of the risk patterns of various counties, a major milestone since previous studies focused on speci c regions. We recommend that, since all counties had cervical cancer relative risk greater than 1, step up screening and avail vaccines to the appropriate groups. To mitigate oesophageal cancer, counties should create awareness on e ects of smok- ing and alcohol use. In case of lung cancer, counties with relative risks greater than 1 should disseminate information elaborating the e ects of smoking and alcohol use

Interplay of axis ratio on neutron flux in a spheroid nuclear reactor core using jacobi elliptic theta functions

2022-01-01T00:00:00Z

Interplay of axis ratio on neutron flux in a spheroid nuclear reactor core using jacobi elliptic theta functions Leting, Silas Kering The instantaneous neutron’s density in a reactor core is influenced by several factors. Some of them include the reactor material’s characteristics and the reactor configuration geometry properties. The role of the former has been well explored and understood while the latter continues to arouse interest in research and applications despite being poorly understood for some configuration types. In particular, spheroid configuration exhibits relatively higher robustness compared to other. However, the behavior of time dependent neutron flux at varying axis ratios and how the latter affects neutron leakage rates has not been well explored for this type of configuration. Therefore, this study is aimed at establishing how the axis ratio determines the behavior of neutron flux and neutron leakage rates. Specifically; modeling and determining the behavior of time dependent neutron diffusion flux in a spheroid reactor core at varying axis ratios, formulating the relationship between the axis ratio and neutron leakage rates and elaborating the behavior of neutron leakage rates for both spheroids at axis ratios equal, smaller and larger than unity. In order to carry out this, Fick’s law of diffusion was modified into a Jacobi elliptic theta function to describe the desired time dependent neutron diffusion problem in spheroid coordinates system. The quasi- radial component was adapted to represent the axis ratio and thereafter appropriate boundary conditions were imposed. Secondly, a relationship between neutron leakage rate and the axis ratio of spheroids was formulated using geometric buckling and neutrons thermal life time equations, and the results were evaluated for axis ratios equal, smaller and larger than unity with software used to solve all the formulated equations. It was found that neutrons diffuse outwards from the core towards the boundaries of the spheroid exhibiting the characteristics of Jacobi elliptic theta curves of the third kind. Various configurations of diffusion configurations were obtained that included ternary surfaces, continuous and discontinuous surfaces of various characteristics as the value of ‘n’ was varied. In addition, neutrons diffusion behavior along the quasi-angular component and the time component was found to be largely similar. In the investigation of neutron leakage rate versus the axis ratio, both configurations (with the same volume and same neutron leakage constant (k)) exhibited similar profile, although the neutron leakage rate for prolate was lower compared to that of oblate at axis ratios smaller than unity. In contrast, at axis ratios larger than unity, it was found that the neutrons leakage rate for prolate became greater than that of an oblate of the same volume. The results further showed that, at axis ratio larger than unity, the neutron leakage rate was mildly affected by the axis ratio of the spheroid. Finally, the values for neutron leakage rates for both prolate and oblate spheroids converged when the axis ratio was unity, for instance, the neutron leakage rates for both types of spheroids was 2.5 neutrons/square unit for neutron leakage constant of k = 200. The findings of this study could be utilized in the design of superior reactors with enhanced safety that can mitigate against nuclear accidents by varying core axis ratios in order to alter reactor criticality conditions. Further research needs to be conducted on multigroup neutron diffusion for a similar problem and determining the flux behavior for each type of spheroid separately

Application of bayesian vector autoregressive model in forecasting rainfall pattern in Kenya.

2022-01-01T00:00:00Z

Application of bayesian vector autoregressive model in forecasting rainfall pattern in Kenya. Gitonga, Harun Mwangi Time series modelling is of fundamental importance in forecasting weather that is basically one of the most technologically and scientifically challenging problems around the world currently. To make an accurate prediction is certainly one of the key challenges that meteorologists are facing all over the world. One of the most affected areas is the rainfall patterns, which is being influenced by global warming, causing drastic changes in its patterns that are characterized by either very high or low precipitation and temperature. These extreme changes have been identified as major global challenges of recent times. Meteorological scientist always tries to find means to understand the atmosphere of the Earth, and to develop accurate weather prediction models. Several methods have been used in weather prediction, which includes, Classical vector Autoregressive (VAR) models which perform only polynomial-time computation to compute the probability of the next fixed model parameters. While this is attractive, it means they cannot model distributions with a time varying data. They also have a problem with the curse of dimensionality. Recently, machine learning methods are assumed to be accurate techniques and have been widely used as an alternative to classical methods for weather prediction. With all these powerfulness and popularity machine learning methods are not perfect. They have several limitations where they require; massive datasets, enough time and resources, does not work well with high dimensional data and have high error vulnerability among others. Despite the availability of different models that are used by the meteorologists and other departments to make predictions, the same devastating scenarios of unpredictable weather changes are still being experienced. Therefore, robust models reliable for accurate predictions are needed on short- and long-term time scales to reduce potential risks and damages that may occur due to unexpected weather changes. These short comings are well addressed by the Bayesian Vector Autoregressive (BVAR) models. The purpose of this study was to develop a BVAR model for predicting rainfall patterns in Kenya. The specific objectives were to; perform diagnostic analysis of the weather variables; develop Bayesian Vector Autoregressive predictive model; conduct model performance analysis and apply the model to forecast the rainfall patterns in Kenya. The Augmented Dicker Fuller and Granger Causality tests were used for diagnostic analysis. The research adopted secondary data for a period of four years (2014-2018), which was sourced from Trans-African Hydro-Meteorological Observatory (TAHMO) and Kenya Meteorological stations. Bayesian Vector Autoregressive model was developed using multiple regression analysis in a system of equations. The model imposes structures through information prior beliefs on the parameters which were obtained from VAR models, likelihood models between the true parameters and the measured variables and the posterior distribution which is the conditional distribution of the parameter given the measurements. The model sensitivity was performed using the confusion matrix. The F-test was used to compare the variances of the actual and the predicted rainfall values. The data was analyzed using R-Statistical Software. The study found that; the data variables were stationary after at least the first differencing. Temperature, atmospheric pressure, wind speed and relative humidity were statistically significant (p < 0.05) determinants of rainfall in all five zones, while wind gust and radiation were significant in two zones, coast and arid areas. The BVAR model developed was statistically significant (R 2 = 0.9896). The performance of the model was adequate (RMSE= 86.81%) and its sensitivity was 82.52%, making it appropriate for forecasting. There was no significant difference between the variances of the actual and predicted values of rainfall (p = 0.3893) at the 5% level of significance in zone five. The study made the following conclusion, after at least the one differencing the weather variables were found to be stable, the developed model coefficients were found to be statistically significant, the model performance was good and it forecasting ability was termed as high. In conclusion, the Bayesian Vector Autoregressive model developed is suitable for forecasting rainfall patterns in Kenya. The study recommends adoption of the BVAR model by relevant authorities to predict rainfall. For further research the study recommends for use of more weather variables to make more accurate prediction. The study also recommends for development of dynamic weather model, which tests for the impulse response of weather variable in respect to change in other endogenous variables.