School of Mathematics, Statistics and Actuarial Sciencehttps://repository.maseno.ac.ke/handle/123456789/1012024-03-28T17:33:55Z2024-03-28T17:33:55ZMathematical modeling of Dual protection and art Adherence for a high risk HIV PopulationORIEDO, Indayi Samsonhttps://repository.maseno.ac.ke/handle/123456789/59862024-02-14T14:41:10Z2023-01-01T00:00:00ZMathematical modeling of Dual protection and art Adherence for a high risk HIV Population
ORIEDO, Indayi Samson
The spread of HIV/AIDS remains a major concern to public health enthusiasts
world over. In spite of interventions such as medical male circumcision,
condom use, treatment using Antiretroviral Therapy (ART), as
well as use of Pre-Exposure Prophylaxis, the number of new HIV/AIDS
infections in Sub-Sahara Africa remains high. This may be attributed
to factors such as PrEP failure and inconsistency in condom use especially
among the high risk group. The e ectiveness of condoms depends
on quality and proper use, while the success of ART largely depends on
adherence. Mathematical models for these interventions exist in literature.
However the challenges associated with the use of a single approach
consequently necessitate the use of dual protection for better outcome
against infection especially for the high risk population. In this study, a
mathematical model for dual protection, incorporating PrEP and Condom
use, and ART adherence is formulated, based on a system of ordinary
di erential equations and analyzed. The results obtained from stability
analysis indicate that provided the basic reproductive number (R0) is less
than unity, the disease free equilibrium point is both locally and globally
asymptotically stable, while provided that R0 is greater than unity,
the endemic equilibrium point is locally asymptotically stable. Sensitivity
analysis showed that the most sensitive parameter is 1, the mean contact
rate with undiagnosed infectives. Numerical simulation results revealed
that dual protection and ART adherence are key in the ght against the
spread of HIV among the high risk population. These ndings will help in
reducing the number of new HIV infections as well as lower the infectivity
of those who are already infected.
Master's Thesis
2023-01-01T00:00:00ZApproximations of ruin probabilities under financial constraints.ODIWUOR, Calvine Otienohttps://repository.maseno.ac.ke/handle/123456789/57382023-06-22T14:45:32Z2022-01-01T00:00:00ZApproximations of ruin probabilities under financial constraints.
ODIWUOR, Calvine Otieno
This thesis studies the approximate ruin probabilities under financial constraints which in- clude the rate of inflation, constant interest rate, and taxation. When the surplus falls below zero, the insurance company is technically considered ruined. The main objective of the study included; to establish a risk model which takes into account all the financial con- straints,to establish analytically, the formula for the approximation of ruin probabilities for both exponentially and sub-exponentially distributed claims, to compare the approximate ruin probabilities from our model and those of the classical Cram´er-Lundberg model, and finally to compare the convergence of Pareto and Log-normal distributions for the formu- lated model. An extensive review of literature is done and much attention is given to the research by Albrecher and Hipp whose research successfully formulates Lundberg’s (classi- cal) risk process in presence of tax. A risk model is formulated in the present study whose premium inflow is influenced by inflation and a constant interest rate. We thereafter in- voke the Albrecher and Hipp loss-carried-forward tax scheme from which an approximation of probability of ruin for the light tailed (exponential) distribution is derived for an exact solution. Then, a suitable formula for the claims with sub-exponential distribution is also derived using the Pollaczek-Khintchine formula. Simulations are hence done using R and Microsoft Excel in this regard. The results show that approximating ruin probability when taking into account all the three financial constraints gives desirable results as compared to those of classical Lundberg model. The comparison between the two heavy-tailed distribu- tions under the concept of limiting density ratio, shows that a Log-normal density exhibit a lighter tail, thus converges faster. However, the model is open for further improvements, specifically to incorporate a stochastic rates of interest. The results of this study will hence guide the policymakers and the insurance industry to make informed decisions to help guard against future ruin as witnessed in local insurance companies in Kenya and globally.
Masters Thesis
2022-01-01T00:00:00ZOperation of mutation on Polar quiversOYENGO, Michael Obiero Michael Obierohttps://repository.maseno.ac.ke/handle/123456789/52612022-05-17T06:55:59Z2009-01-01T00:00:00ZOperation of mutation on Polar quivers
OYENGO, Michael Obiero Michael Obiero
In recent times, there has been a lot of interest in the study of quivers,
both by mathematicians and theoretical physicists. We introduce a new
concept of polar quivers and their mutation. The idea of polar quivers
arises from the concept of anomaly free R-charges in theoretical physics.
Mutation of polar quivers is build on mutation quivers with potential,
which was defined by Derksen, Weyman and Zelevinsky. An R-charge assigns
angles to the arrows of a quiver. In a polar quiver we assign angles
and positive non-zero integers to vertices and impose conditions equivalent
to the anomaly conditions for R-charges. We then establish that
mutation of a polar quiver will give a polar quiver if and only if a simple
additional condition is satisfied. We use families of quivers linked by mutation,
from the work of Stern, as our source of examples. The results of
this study have applications in geometry and theoretical physics.
2009-01-01T00:00:00ZNorms of tensor products and elementary OperatorsODERO, Beatrice Adhiambhttps://repository.maseno.ac.ke/handle/123456789/52602022-05-17T06:50:28Z2009-01-01T00:00:00ZNorms of tensor products and elementary Operators
ODERO, Beatrice Adhiamb
In this thesis, we determine the norm of a two-sided symmetric operator
in an algebra. More precisely, .we investigate the lower bound of the operator
using the injective tensor norm. Further, we determine the norm of the inner
derivation on irreducible C*-algebra and confirm Stampfli's result for these
algebras.
2009-01-01T00:00:00ZOn norms of elementary operatorsNYAARE , Benard Okelohttps://repository.maseno.ac.ke/handle/123456789/52572022-05-17T06:16:38Z2009-01-01T00:00:00ZOn norms of elementary operators
NYAARE , Benard Okelo
The study of elementary operators has been of great interest to many
mathematicians for the past two decades. Of special interest has been to
determine the norms of these operators. The norm problem for elementary
operators involves finding a formula which describes the norm of an elementary
operator in terms of its coefficients. The upper estimates of these
norms are easy to find but approximating these norms from below has
proved to be difficult in generaL Several mathematicians have produced
known results for special cases on the lower estimates, for example, Mathieu
found that for prime C*-algebras, the coefficient is ~, Stacho and Zalar
obtained 2( v'2-1) for standard operator algebras on Hilbert spaces, Cabrera
and Rodriguez obtained 20!I2 for JB* -algebras while Timoney came up
with a formula involving the tracial geometric mean to calculate the norm
of elementary operators. An operator T: A ~ A is called an elementary
operator if T can be expressed in the formZ'[z) = L~=Iaixbi, \j x E A
where A is an algebra and tu, b; fixed in A. The norm of an operator T
is defined by IITII= sup{IITxll : x E H, Ilxll = I} where H is a Hilbert
space. The purpose of this study therefore, has been t,o determine the
lower estimate of the norm of the basic elementary operator on a' C*-
algebra through tensor products. To do this we needed to have a good
background knowledge on functional analysis, general topology, operator
theory and C*-algebras by understanding the existing theorems and relevant
examples especially on tensor product norms. We used the approach
of tensor products in solving our particular problem. We hope that the
results obtained shall be useful to applied mathematicians and physicists
especially in quantum mechariics.
2009-01-01T00:00:00ZMathematics of Pesticide Adsorption in a Porous Medium: Convective-Dispersive Transport with steady state water flow In two DimensionWETOYl, A.Seth Harrissonhttps://repository.maseno.ac.ke/handle/123456789/52512022-05-12T12:08:44Z2007-01-01T00:00:00ZMathematics of Pesticide Adsorption in a Porous Medium: Convective-Dispersive Transport with steady state water flow In two Dimension
WETOYl, A.Seth Harrisson
The transport of solutes through porous media where chemicals undergo adsorption or
change process on the surface of the porous materials has been a subject of research over
years. Usage of pesticides has resulted in production of diverse quantity and quality for
the market and disposal of excess. material has also become an acute problem. The
concept of adsorption is essential in determining the movement pattern of pesticides in
soil in order to asses the effect of migrating chemical, from their disposal sites, on the
quality of ground water. In the study of movement of pesticides in the soil, the
mathematical models so far developed only consider axial movement. The contribution of
radial movement to the overall location of solutes in the porous media seems to have
been disregarded by researchers in this field. The objective of this study is to close this
gap by developing a mathematical model to determine the combine radial and axial
movement of pesticides due to Convective - Dispersive transport of pesticides with
steady - state water flow in a porous media.
The methodology will involve determining the comprehensive dispersion equation
accounting for both axial and radial movement of solutes in the porous media and finding
the solution of the governing equation using finite difference methods. The solution of
this equation will be applied to the data from experiments carried out on adsorption and
movement of selected pesticides at hi~h concentration by soil department, University of
Florida, Gainesville U.S.A. We will confme our study to single - Region Flow and
Transport.
2007-01-01T00:00:00ZNumerical solution of Korteweg-de vries equationONAM, Joel Otienohttps://repository.maseno.ac.ke/handle/123456789/52502022-05-12T11:57:59Z2008-01-01T00:00:00ZNumerical solution of Korteweg-de vries equation
ONAM, Joel Otieno
The Kotteweg-de Vrr-es(KdV)is a mathematical model of waves on shallow
water surfaces. The mathematical theory behind the KdV equation
is rich and interesting, and, in the broad sense, is a topic of active mathematical
research. The equation is named after Diederik Korteweg and
Gustav de Vries,
It has long been known that conservative discretization schemes for
the KdV and other nonlinear equations tend to become numericrtlly unstable.
Although finite difference approximations have been used, there
are always instabilities of the solutions obtained,
In this work we solved the Korteweg-ds Vries (KdV) equation using an
explicit finite difference method, subject. to various boundery conditions
which are travelling wave solutions to the KdV equation. The methodology
involved carefully designing conservative finite difference discretization
that can remain stable and deliver sharp solution profiles fora long
time. We then determined the accuracy of the finite diffurence scheme by
comparing the graphical outputs of the numerical results.
2008-01-01T00:00:00ZOn a generalized q-numerical RangeMusundi, Sammy Wabombahttps://repository.maseno.ac.ke/handle/123456789/52492022-05-12T11:48:03Z2008-01-01T00:00:00ZOn a generalized q-numerical Range
Musundi, Sammy Wabomba
We 'consider numerical ranges of a bounded linear operator on complex
Hilbert spaces. Many properties of the classical numerical range are
known. We investigate the properties of the q-numerical range in relation
to those of the classical numerical range. We also establish the
relationship between the q-numerical range and the algebra q-numerical
range. Furthermore, we extend the results of the classical numerical range
and q-numerical range to the C-numerical range and investigate how the
C-numerical range is an explicit generalization of both the classical numerical
range and q-numerical range.
2008-01-01T00:00:00ZForecasting Kenya’s inflation rate using a Varma for price of imported crude oil and Kenya’s previous inflation rate time seriesAMISI, Pascal Oumahttps://repository.maseno.ac.ke/handle/123456789/52332022-05-11T08:47:09Z2021-01-01T00:00:00ZForecasting Kenya’s inflation rate using a Varma for price of imported crude oil and Kenya’s previous inflation rate time series
AMISI, Pascal Ouma
Inflation is the persistent rise in the prices of selected goods and services over time.
The rate of inflation measures economic performance of a country and is an important
economic indicator to economists of any given government. High rates of inflation lead to
slow economic growth and has the effect of lowering the living standards of a population
by eroding their purchasing power. In the period November 2016 to June 2017, Kenya
experienced an unprecedented rise in the inflation rate to a high of 11.7% causing harsh
economic and social repercussions to her population [5]. To cushion its population against
such strain, the government should be able to estimate and predict the rate of inflation.
Previous research by Bilal Kargi for Turkey’s case [6] indicates a relationship between the
changes in price levels of imported crude oil and the rate of inflation. The objective of this
study was to determine if there is a long-run relationship between Kenya’s Inflation rate
and the price of imported crude oil, fit a VARMA (p,q) model and use the fitted model
to forecast Kenya’s inflation rate using the previous rates of inflation and the price of
imported crude oil since there was a cointegrated association between the two time series.
This will enable the government plan strategically for the mid- and long-term effects of
inflation in Kenya. Cross-correlation analysis was used to determine whether there is a
significant correlation between the two time series and a test of cointegration was used
to determine a significant association. A VARMA model was fitted to the data using
the SCM approach. The study showed that there exists a moderate negative correlation
between the two time series with a correlation coefficient of -0.21, with a p-value of < 0.05
that implies that the correlation is statistically significant. The study further showed that
there is a moderate statistically significant association between the two time series at lags
6 and that there exists cointegration and dependencies between the price of imported
crude oil and the Kenya’s Inflation rate by a CADF test which a statistically significant
Dickey Fuller Statistic of −8.3394, with a p − value = 0.01, implying cointegrating association
between the two time series. A VARMA (2, 1) model was fitted to the data and
used to forecast Kenya’s inflation rates to six steps (months) behind for comparison to
the actual available data and further a eleven-steps ahead forecast. The forecasts were
accurate with a Mean Absolute Error (MAE) of 0.66% which are good forecasts according
to [17] for planning purposes. From the study results it shows that there exists a
statistically significant association between the price of crude oil and Kenya’s previous
inflation rates and therefore used in forecasting future Kenya’s inflation rates. This study
therefore provides better inflation forecasts(Kenya) to be used for strategical planning for
the mid- and long-term effects of inflation by the government.
2021-01-01T00:00:00ZA correlation study on the effect of Non-conditional cash transfer on poverty Alleviation among older persons in Emuhaya sub- county, KenyaMWANIGA, Josphinehttps://repository.maseno.ac.ke/handle/123456789/52312022-05-11T08:20:20Z2021-01-01T00:00:00ZA correlation study on the effect of Non-conditional cash transfer on poverty Alleviation among older persons in Emuhaya sub- county, Kenya
MWANIGA, Josphine
The world is experiencing growth in the number of older persons with those aged 60 years and above projected to double from 1.4 billion in 2015 to 2.8 billion in 2050. According to the Kenya Population and Housing Census, there were 1.3 million people who were above 65 years of age in 2009 with a declining mortality rate from 11/1000 in 2007 to 8.93/1000 in 2011 an indication that the number of those aging in Kenya is expected to increase significantly by 2030. In Vihiga County, the population of older persons aged 65 years and above stood at 33,475 by 2013. The growing numbers of older persons in Kenya have increased social, economic and political pressure necessitating introduction of various social protection programs which include non-conditional cash transfer initiatives. Although several studies show that cash transfer programs have a positive effect on access to food, healthcare and shelter, the studies focused on conditional cash transfers creating uncertainty on the effect of non-conditional cash transfers such as Older Persons Cash Transfer (OPCT) on poverty alleviation. This study investigated the effect of non-conditional cash transfer on poverty alleviation among older persons in Emuhaya Sub-County, Kenya. Specifically, the study determined the effect of OPCT on access to food among older persons in Emuhaya Sub-County, Kenya. It also established the effect of OPCT on access to health care among older persons as well as effect of OPCT on quality of shelter among older persons. Case study research design was employed with a target population comprising of 1067 OPCT beneficiaries with a sample size of 290 obtained using Yamane formula which was obtained by simple random sampling and the participants were stratified based on the wards. Descriptive and inferential data analysis techniques were employed to define the participants' characteristics and established the effect of non-conditional cash transfers on poverty alleviation. The study established that there exists a positive correlation between OPCT and access to food with r=0.281 and p- value=0.00. The study also established that there exists a positive correlation between OPCT and access to health care with r=0.120 and p-value=0.004. The study also found a positive correlation between OPCT and access to a quality shelter with r=0.162 and p-value=0.000. The odds ratio predicted by the model for improved access to food, health care and quality was 1.534, 2.388 and 1.793 respectively. The study concluded that OPCT alleviates poverty. The recommendation for the study was that a large sample size should be considered to access poverty alleviation among the older persons on the OPCT program. Secondly since household size differ, this affects the quantity of food from the household and therefore the cash provided should put this in mind to ensure that the household have improved food access. Lastly, improved access to health care had a weak correlation with cash transfer and in order to strengthen the correlation the government should pay NHIF for all beneficiaries and not a sample.
2021-01-01T00:00:00Z