School of Mathematics, Statistics and Actuarial Science
https://repository.maseno.ac.ke/handle/123456789/101
2022-01-27T11:35:39ZAnalysis of seasonal time series with Missing observations: A case of harvesting of fish in Lake Victoria Kenya.
https://repository.maseno.ac.ke/handle/123456789/4052
Analysis of seasonal time series with Missing observations: A case of harvesting of fish in Lake Victoria Kenya.
OTWANDE, Andrea
ABSTRACT
Time series is a measured observation recorded with time. This statistical procedure
is applicable in many fields of study including engineering and economics. The process of
collecting data sometimes faces a lot of challenges that may arise due to defective working
tools, misplaced or lost records and errors that are prone to occur. These problems can be
addressed by estimating the missing values so as to enable one to proceed with the analysis
and forecasting. The most commonly used approaches include the use of autoregressivemoving
average models developed by Box Jenkins, use of extrapolation or interpolation
under regression analysis and use of state space models where data is considered as a
combination of level, trend and seasonal components. This project intends to use the most
appropriate method of estimating missing values by using the direct method of imputation.
Incomplete secondary data obtained from the Ministry of fisheries and Development,
together with the Kenya Marine and Fisheries Research Institute are to be used to estimate
the gap left just before, during and immediately after the post election violence of the
year 2007/2008, a time when data could not be obtained and/or recorded. The original
time series data when analysed produced a SARIMA model (0,1,1)(2,0, 0h2 as the best
candidate for the lower segment. SARIMA (0,1,2)(0,0,1)12 was produced for the upper
segment using autoarima function in R package. The missing data were estimated using
forecast from the lower segment which was extended to the in sample forecast in the upper
segment. The regression test between predicted and the original values in upper segment
proves strong positive relationship indicating high level of accuracy on predictability of
the model used.
2013-01-01T00:00:00ZMultilevel Analysis Applied to Binary Data: Malaria Prevalence in Sauri Millenium Village, Kenya
https://repository.maseno.ac.ke/handle/123456789/3710
Multilevel Analysis Applied to Binary Data: Malaria Prevalence in Sauri Millenium Village, Kenya
LELERAI, L. Eliud
Millennium Villages Project is an initiative that is meant to demonstrate that the millennium
development goals could be achieved in an integrated approach in putting a combination of
interventions in place. Among these interventions are the health interventions of reducing the
prevalence of common diseases. Malaria is one of these common diseases. In 2005 Sauri
Millennium Village was started in western Kenya which was then followed by 13 other villages
across Africa. A baseline study was done in 2005 to measure the bench marks of the millennium
development goals indicators in the village. As part of these surveys, blood data was collected to
estimate the baseline prevalence of malaria in the Sauri Millennium village. This data was linked
to socioeconomic data to study factors affecting malaria prevalence. Malaria affects individuals
who are clustered in households and villages. In addition to individual effects, households and
villages have characteristics that influence malaria prevalence. The individual characteristics
under study were age and gender. The household characteristics were income and the education
status of the household the individual belongs. The village level factors were the counts of water
.
bodies and the area covered by woods of the villages. Logistic regression models were applied to
understand the determinants of malaria. Considering the multilevel structure of data, the analysis
goes beyond the single-level modelling and explores the value of multilevel modelling in
understanding the malaria risk factors. The analysis showed that malaria prevalence among the
population at baseline was about 50% and was similar for males and females. The results also
showed that malaria prevalence decreases with age. Income and education status of the
households were also found to have an effect on malaria prevalence. The utility of the multilevel
techniques in answering the research questions clearly demonstrated the value of statistical
techniques in understanding factors affecting health outcomes. The recognition of complex
structures of data in statistical modelling processes, yield reliable results that help health
strategists make informed decisions in taming malaria.
2014-01-01T00:00:00ZMathematical Model Incorporating Screening of Immigrants as A Control Against The Spread of Ebola
https://repository.maseno.ac.ke/handle/123456789/3707
Mathematical Model Incorporating Screening of Immigrants as A Control Against The Spread of Ebola
KW AMBOKA, Lilian
Ebola Disease Outbreak (EVD) is an acute and often fatal disease in humans and nonhuman primates (monkeys, gorillas and chimpanzees). The disease is caused by infection
with a virus of the family of Filoviridae, genus Ebolavirus. It's case fatality ratio ranges
from 25%-90% in humans. The number of travel-related cases in the absence of screening
exponentially increases with every successive outbreak.The objective of this study is to
develop a mathematical model incorporating screening of immigrants as a control against
the spread of Ebola. To achieve the objective of this study, a deterministic non-linear
mathematical model for the transmission dynamics of Ebola incorporating screening is
developed and analyzed. The analysis shows that the disease free equilibrium of the
model may not be globally asymptotically stable whenever Ro is less than unity. The Ger
Sgorin disc argument is used to show that the model has a unique, locally asymptotically
stable Endemic Equilibrium (EE). This means that given a small perturbation near the EE,
the system returns to EE. We present numerical simulation results in which we observe a
significant decrease in the number of Ebola infectives as a result of screening. Hence, we
can conclude that screening of immigrants should be considered alongside other control
and treatment measures for the effective management and control of Ebola.
This EVD outbreak, believed to have started in Guinea in March 2014 spread to Nigeria through an airline passenger, who arrived from Liberia. It also spread to Senegal by a
student from Guinea, who arrived by land transportation [9, 17]. The outbreak eventually
spread to other regions outside Africa. For instance, some Ebola-infected patients were
flown to the US, France, Germany, Norway, Spain and the UK [4, 17] for health-care
delivery. The US diagnosed its first imported travel-related Ebola case in September 2014
(by a person who had travelled to Dallas, Texas, from Liberia). The imported case, who
later died of the disease on 8 October 2014, resulted in the infection of two health-care
workers who cared for the deceased patient [12]. One of the cases flown to Spain also led
to an infection of healthcare workers [4]. A total of 17,942 cases, with 6,388 deaths were
reported to WHO as of December 2014.
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With this threat of international spread of such a highly infectious disease, compounded
by symptom overlap with common illnesses such as malaria, typhoid and flu, screening
of immigrants for EVD is imperative if its spread is to be kept under check.
2017-01-01T00:00:00ZAnalysis of young people’s career by use of Markov chains: case study of Kisumu city
https://repository.maseno.ac.ke/handle/123456789/1263
Analysis of young people’s career by use of Markov chains: case study of Kisumu city
OTIENO, Daniel Aoyi
It is the desire of every person to have a career. Not much thought has been taken by young people on how they can arrive at their future careers. The reason is mainly because they are not aware. As much as many people have attained their careers through education, not much consideration has been given to the other factors within education that leads one to his or her career. The study traced one's career from primary to present position. There are stages one follows to reach the career, which are called states in this study. The predicament of these young people is dealt with by use of Markov chains. A Markov chain is a process that consists of finite number of states, which are four in this study. The four states that were considered in this study are, KCPE, KCSE, College and Career. KCPE, KCSE and College are transient states, while career is the final state. Regardless of where they started from, they ended up in Career with different proportions. Transitional probabilities were used to form transitional probability matrix. The matrix so formed was used to find Fundamental Matrix. The fundamental matrix has given the expected number of times the process was in each transient state, that is, the means. About 16 percent of those who did KCPE, 10 percent of those who did KCSE and 99 percent of college graduates got career. This shows that not many get into career after KCPE. Further still fewer young people get into career after KCSE, this may be because most of them prefer to proceed to college before career. The variances associated with transition among KCPE, KCSE and College are 0.821685, 0.037049 and 0.0069. Their respective standard deviations are 0.906468, 0.192481 and 0.083066. The low values indicate that the values did not deviate much from the expected, except for KCPE. Those who don't intend to go to college should rather identify a career path after KCPE.
Masters' Thesis
2017-01-01T00:00:00Z