Department of Mathematics and Computer Sciencehttp://41.89.164.27:8080/xmlui/handle/123456789/2102024-03-27T01:28:41Z2024-03-27T01:28:41ZMATHEMATICAL MODELING OF HIV/AIDS DYNAMICS AMONG THE FISHERFOLK AS A VECTOR FOR HIV: A CASE STUDY OF LAKE VICTORIA METAPOPULATIONSCHEPKWONY, JACOB KURUIhttp://41.89.164.27:8080/xmlui/handle/123456789/20702024-01-31T07:32:47Z2023-06-01T00:00:00ZMATHEMATICAL MODELING OF HIV/AIDS DYNAMICS AMONG THE FISHERFOLK AS A VECTOR FOR HIV: A CASE STUDY OF LAKE VICTORIA METAPOPULATIONS
CHEPKWONY, JACOB KURUI
HIV/AIDS pandemic has remained the leading causes of death among the sexually transmitted diseases. To date, there has been no cure, and all the intervention measures involve preventive and reduction of the severity of the spread. Several dynamics related to HIV/AIDS have been studied using mathematical models, but the study of the spread of HIV by a vector has not been exhausted. In this study, HIV/AIDS is considered as a human ‘vector borne’ disease, where both the host and the vector is affected. This is possible with the definition of Fisherfolk, as a unique group of people with significantly different disease characteristics, and thus seen to play the role of a vector in the transmission of HIV. This is based on reported high prevalence of HIV among the Fisherfolk, of up to 4 times of the rest of the susceptible. A mathematical model will be formulated, and analyzed to arrive at the following objectives. The first task was to formulate a mathematical model using differential equations to describe human HIV/AIDS disease dynamics of Fisherfolk and normal population around Lake Victoria. The formulated model was then analyzed for the well posedness, in terms of stability, positivity and boundedness to ensure feasible and realistic solutions. In order to optimize the controls, the system was then expressed as a linear programming problem, and used to determine the threshold values of parameters for optimality of disease control measures. Finally, the system was coupled and tested for synchronization, stability and robustness under small perturbation, through All-to-All coupling topology. The achievement of these objectives were realized with the use of the following methods; compartmental formulation of mathematical model, coupling using nearest neighbor and all to all configuration, and use of Lyapunov type numbers to test stability and robustness under small perturbation. The study results found using a system of eight ordinary differential equations that two equilibrium points exists, disease free equilibrium (DFE) and endemic equilibrium point (EEP). DFE was found to be asymptotically stable whenever 𝑅0<1. Intervention strategies like public health education and treatment were found to stabilize periodic solutions of EEP when 𝑅0>1. Synchronization manifold of all to all coupling configuration was determined to be stable under small perturbations with a coupling strength of 𝑘0≥1.1137. This means interaction of a minimum of 12% of the population will lead to synchronization of metapopulations, and therefore any intervention strategy should exceed a threshold of 12% of the population. The findings are valuable to public health and government for planning and budgeting on the desired cost of treating the public, together with other strategies of minimizing interaction through creation of markets, control of fishing points through licensing bottlenecks, and other mitigation strategies to reduce the scourge. This will improve the human resource capacity and improve on fish production in the region.
2023-06-01T00:00:00ZMODELLING COVID-19 DYNAMICS (SPREAD AND CONTROL) AND THE EFFECTS OF A PREVENTIVE VACCINEJEROP, RAELhttp://41.89.164.27:8080/xmlui/handle/123456789/20622024-01-30T07:54:35Z2023-09-01T00:00:00ZMODELLING COVID-19 DYNAMICS (SPREAD AND CONTROL) AND THE EFFECTS OF A PREVENTIVE VACCINE
JEROP, RAEL
Corona virus 2019 (COVID-19) have been pandemic both in Africa and the whole world. This work formulated and analyzed mathematical model of COVID-19 that monitors the temporal dynamics of the disease in the presence of preventive vaccine. The most effective ways of controlling the transmission of infectious disease is through vaccination and treatment. Due to transmission characteristics of COVID-19 , the population was divided into six classes. That is; susceptible(S), vaccinated (V), infective (I), hospitalized (H), home based care (𝐻𝐵) and recovery(R). In this thesis, non-linear system of differential equations governing the model was formulated to compute and were solved using quantitative analysis. Feasibility region and positivity of model variable was worked out in which the model is bounded so as to obtain the feasibility solution of the set and positivity of variables. The disease free equilibrium, local and global stability of the disease free equilibrium are discussed. The endemic equilibrium , local and global endemic equilibrium are determined. The model monitor reproduction number 𝑅𝑂 using next generation matrix method which describe the dynamics of the COVID-19.The disease free equilibrium is local asymptotically stable when basic reproduction number 𝑅𝑜<1 and unstable when basic reproduction number 𝑅𝑜>1. The numeric results obtained are determined graphically by use of MAPLE simulation method. The solution has been computed using numerical classical fourth order Runge Kutta integration method to gauge its effectiveness . The results indicated that; high vaccination coverage of 𝜑 =0.9 leads to high number of individuals recovering and low vaccination coverage of 𝜑=0.1 leads to high reproduction number hence the disease may not be eradicated .
2023-09-01T00:00:00ZEFFECT OF VACCINATION ON MATHEMATICAL MODELING OF COVID-19Jerop, RaelJulius, Maremwa S.Kandie, Joseph K.http://41.89.164.27:8080/xmlui/handle/123456789/19492023-09-18T12:07:15Z2023-02-01T00:00:00ZEFFECT OF VACCINATION ON MATHEMATICAL MODELING OF COVID-19
Jerop, Rael; Julius, Maremwa S.; Kandie, Joseph K.
Corona virus 2019 (Covid-19) have been endemic both in Africa and the whole world. In this paper we have formulated and analyze
mathematical model of covid-19 that monitors the temporal dynamics of the disease in the presence of preventive vaccine since the most
effective ways of controlling the transmission of infection disease is through vaccination and treatment. Due to transmission characteristics of
covid-19, we have divided the population into six classes. That is; susceptible(S), vaccinated (V), infective (I), hospitalized (H), home based care
( ) and recovery(R). We have formulated non-linear system of differentials equation governing the model to compute and solve using
quantitative analysis. Feasibility region, positivity of model variable, disease free equilibrium and local stability of the model are discussed. The
solution has been computed using numerical classical fourth order Runge Kutta integration method to gauge its effectiveness. The model monitor
reproduction number which describe the dynamics of the Covid-19.The disease fee equilibrium is local asymptotically stable when <
1 and unstable when > 1. MAPLE will be used to carry out the simulation and graphical results, then presented and discussed to explain the
solution of the problem.
2023-02-01T00:00:00ZDetecting Remote Access Network Attacks Using Supervised Machine Learning MethodWekesa, Cyruset. al...http://41.89.164.27:8080/xmlui/handle/123456789/19312023-07-11T06:53:04Z2023-01-01T00:00:00ZDetecting Remote Access Network Attacks Using Supervised Machine Learning Method
Wekesa, Cyrus; et. al...
Remote access technologies encrypt data to enforce policies and ensure protection. Attackers leverage such
techniques to launch carefully crafted evasion attacks introducing malware and other unwanted traffic to the internal
network. Traditional security controls such as anti-virus software, firewall, and intrusion detection systems (IDS) decrypt
network traffic and employ signature and heuristic-based approaches for malware inspection. In the past, machine learning
(ML) approaches have been proposed for specific malware detection and traffic type characterization. However,
decryption introduces computational overheads and dilutes the privacy goal of encryption. The ML approaches employ
limited features and are not objectively developed for remote access security. This paper presents a novel ML-based
approach to encrypted remote access attack detection using a weighted random forest (W-RF) algorithm. Key features
are determined using feature importance scores. Class weighing is used to address the imbalanced data distribution
problem common in remote access network traffic where attacks comprise only a small proportion of network traffic.
Results obtained during the evaluation of the approach on benign virtual private network (VPN) and attack network traffic
datasets that comprise verified normal hosts and common attacks in real-world network traffic are presented. With recall
and precision of 100%, the approach demonstrates effective performance. The results for k-fold cross-validation and
receiver operating characteristic (ROC) mean area under the curve (AUC) demonstrate that the approach effectively
detects attacks in encrypted remote access network traffic, successfully averting attackers and network in
2023-01-01T00:00:00ZApplication of ARIMA, and hybrid ARIMA Models in predicting and forecasting tuberculosis incidences among children in Homa Bay and Turkana Counties, KenyaSiamba, StephenOtieno, ArgwingsKoech, Juliushttp://41.89.164.27:8080/xmlui/handle/123456789/18282023-06-13T08:59:44Z2023-02-01T00:00:00ZApplication of ARIMA, and hybrid ARIMA Models in predicting and forecasting tuberculosis incidences among children in Homa Bay and Turkana Counties, Kenya
Siamba, Stephen; Otieno, Argwings; Koech, Julius
Tuberculosis (TB) infections among children (below 15 years) is a growing concern, particularly
in resource-limited settings. However, the TB burden among children is relatively
unknown in Kenya where two-thirds of estimated TB cases are undiagnosed annually. Very
few studies have used Autoregressive Integrated Moving Average (ARIMA), and hybrid
ARIMA models to model infectious diseases globally. We applied ARIMA, and hybrid
ARIMA models to predict and forecast TB incidences among children in Homa Bay and Turkana
Counties in Kenya. The ARIMA, and hybrid models were used to predict and forecast
monthly TB cases reported in the Treatment Information from Basic Unit (TIBU) system by
health facilities in Homa Bay and Turkana Counties between 2012 and 2021. The best parsimonious
ARIMA model that minimizes errors was selected based on a rolling window crossvalidation
procedure. The hybrid ARIMA-ANN model produced better predictive and forecast
accuracy compared to the Seasonal ARIMA (0,0,1,1,0,1,12) model. Furthermore,
using the Diebold-Mariano (DM) test, the predictive accuracy of ARIMA-ANN versus ARIMA
(0,0,1,1,0,1,12) model were significantly different, p<0.001, respectively. The forecasts
showed a TB incidence of 175 TB cases per 100,000 (161 to 188 TB incidences per
100,000 population) children in Homa Bay and Turkana Counties in 2022. The hybrid
(ARIMA-ANN) model produces better predictive and forecast accuracy compared to the single
ARIMA model. The findings show evidence that the incidence of TB among children
below 15 years in Homa Bay and Turkana Counties is significantly under-reported and is
potentially higher than the national average.
2023-02-01T00:00:00ZMODELING THE EFFECTS OF CROP SPACING AND INORGANIC FERTILIZER ON THE POTATO TUBER YIELD AND SIZE USING FIRST ORDER TWO-LEVEL FACTORIAL DESIGNKAPTICH, RONALD KAPKIAIhttp://41.89.164.27:8080/xmlui/handle/123456789/17792023-04-17T09:48:12Z2022-06-01T00:00:00ZMODELING THE EFFECTS OF CROP SPACING AND INORGANIC FERTILIZER ON THE POTATO TUBER YIELD AND SIZE USING FIRST ORDER TWO-LEVEL FACTORIAL DESIGN
KAPTICH, RONALD KAPKIAI
The essential nutrients for growth and productivity to all living organisms, specifically
plants are Nitrogen, Phosphorus and Potassium. However, there are other factors that
contribute to optimum yield of crops; these factors are land availability, farming
techniques, crop spacing, organic fertilization and climatic conditions. The current
research study investigated the optimal levels of potato tuber yield and size, recorded
the impact of crop spacing and inorganic fertilizers (nitrogen and phosphorus) as factors
of interest that are known to affect the production of potato crop, and to compare the
model fit using both full and fractional factorial experiment. A two-level full factorial
and the fractional factorial experiments 3 2 with three replicates were employed to
measure the impact of the selected factors on the potato tubers. The study used the
Randomized Complete Block Design (RCBD), where land acted as blocks and
treatments randomized within blocks. The first order models were fitted by using the
method of least squares. The data collected was subjected to data analysis using
descriptive statistics and Inferential Statistics ANOVA utilizing R statistical software.
The descriptive statistics was presented by use of frequency distribution tables. Results
indicate that the highest average optimum yield was 18.64 t ha-1 when nitrogen and
phosphorous were supplied at the higher rates of 80 kg ha-1 and 155 kg ha-1 respectively
with crop spacing of 65 cm by 20 cm and lowest average yield was 12.12 t ha-1 when
nitrogen and phosphorus were supplied at lower rates of 40 kg per hectare and 77 kg
per hectare respectively with spacing of 75 cm by 30 cm. Furthermore, the average
optimum size of potato tuber was recorded as 12.18 cm when nitrogen, and phosphorus
was supplied at 40 kg per hectare, and 155 kg per hectare with crop spacing of 75 cm
by 30 cm and smallest average size of potato tuber was recorded as 8.74 cm when
nitrogen, and phosphorus was supplied at lower rate of 40 kg per hectare and 77 kg per
hectare respectively with spacing of 65 cm by 20 cm. The effect crop spacing shows a
negative linear effect on the yield of potato tubers only but significant on both yield and
size of potato tuber whereas nitrogen (N) and phosphorus (P) shows positive linear
effects on both the yield and size of potato tuber with phosphorus being significant in
all models. Additionally, the use of fractional factorial experiment gave better model
fit 80% 2 R when compared to full factorial experiment 60% 2 R . The obtained
results are close to the national estimates on the yield of potato tuber which stands at
14 tons hectare and the global average of 17.2 tons per hectare respectively. The current
study will be important in designing the necessary interventions within country in order
to improve production of potato crop.
2022-06-01T00:00:00ZFORECASTING TUBERCULOSIS INFECTIONS USING ARIMA AND HYBRID NEURAL NETWORK MODELS AMONG CHILDREN BELOW 15 YEARS IN HOMA BAY AND TURKANA COUNTIES, KENYASIAMBA, STEPHEN NYONGESAhttp://41.89.164.27:8080/xmlui/handle/123456789/17392023-02-15T09:14:48Z2022-11-01T00:00:00ZFORECASTING TUBERCULOSIS INFECTIONS USING ARIMA AND HYBRID NEURAL NETWORK MODELS AMONG CHILDREN BELOW 15 YEARS IN HOMA BAY AND TURKANA COUNTIES, KENYA
SIAMBA, STEPHEN NYONGESA
Tuberculosis (TB) among children under the age of 15 is a significant public health problem, particularly in resource-constrained settings and is among top ten most dangerous causes of death worldwide, and ranks among the top five most lethal infectious agents in Kenya. However, the real burden of tuberculosis among children in Kenya is unclear. In modelling infectious diseases, Autoregressive Integrated Moving Average (ARIMA) and hybrid ARIMA models have been widely used. However, few studies in Kenya have utilized ARIMA or hybrid ARIMA models to model infectious diseases. This study sought to forecast TB infections in children under the age of 15 Homa Bay and Turkana Counties in Kenya using ARIMA and hybrid neural network models and specifically sought to compare the; performance of the models in predicting TB notification cases, accuracy produced by the models, and the forecasted temporal trends of TB notification cases among children below 15 years. The study hypothesized that the hybrid ARIMA-ANN model yields more accurate predictions and forecasts. The study used monthly TB confirmed cases reported for Homa Bay and Turkana Counties between 2012 and 2021. The ARIMA model was chosen using the Akaike Information and Bayesian Information Criteria. The ANN model was developed using the Multi-Layer Perceptrons (MLPs) three-layer feed-forward architecture. The hybrid ARIMA model was developed by combining the fitted cases using the ARIMA model and the residuals from the ANN. The hybrid ARIMA model (ARIMA-ANN) outperformed the single ARIMA(0,0,1,1,0,1,12) and ANN (1,1,2)[12] models in terms of predictive and forecast accuracy. The hybrid ARIMA model outperformed the ANN (1,1,2)[12] and ARIMA (0,0,1,1,0,1,12) models in terms of prediction accuracy, p<0.001. In Homa Bay and Turkana Counties, the 12-month predicted TB incidence of 175 to 198 infections per 100,000 children in 2022. The hybrid ARIMA model provides superior prediction accuracy and forecast performance. The findings of this study suggest that TB cases in children are underreported, and that the incidence of TB in children may be greater than previously assumed. Tuberculosis monitoring data needs to be re-evaluated in order to comprehend current inadequacies. To get the TB battle back on track, it is critical to reallocate critical resources to the National TB program.
2022-11-01T00:00:00ZMathematical modeling of flow of fertilizer-water mixture through soil and its effect on concentration and plant growthRutto, Kipkorir TimothyMaremwa, Julius ShichikhaKandie, Joseph Kipchirchirhttp://41.89.164.27:8080/xmlui/handle/123456789/16082022-03-29T09:14:52Z2021-01-01T00:00:00ZMathematical modeling of flow of fertilizer-water mixture through soil and its effect on concentration and plant growth
Rutto, Kipkorir Timothy; Maremwa, Julius Shichikha; Kandie, Joseph Kipchirchir
In this research we aim to demonstrate and explore how mathematical modeling can be used to aid
people gain knowledge and understanding of plants and, in particular, interactions between plants,
fertilizers, soil, and water. The primary objective is to convince members of the agricultural,
mathematical and biological culture of the need to work together in establishing mechanistic simulations
with quantitative data to help them understand flow of soil solutions and their effect on plant growth. The
mathematical models used are based on the fundamental knowledge of fluid flows and plant growth that
is necessitated by nutrient absorption from the soil by plant roots. Such models allow for a deeper
understanding of plant science at the most basic level and can aid us in dealing with real-world issues
such as food scarcity, soil pollution and global warming in developing countries, Kenya as a target. We
used mathematical model equations which have been made to describe fertilizer (contaminant) as well as
soil water flow, their concentrations, uptake by a plant root system and plant growth then solve the
equations by finite difference and volume methods with the help of MATLAB program. The technique of
explicit difference was used to solve the governing equations analytically. The results indicate that as
time of simulation increases, the concentration of fertilizer also increases thus increasing the growth
factor which in turn affects the length of plant growth
2021-01-01T00:00:00ZOn Unitary Invariance of Some Classes of Operators in Hilbert SpacesMuhati, Linety N.Khalagai, J. M.http://41.89.164.27:8080/xmlui/handle/123456789/16032022-03-24T07:05:21Z2020-01-01T00:00:00ZOn Unitary Invariance of Some Classes of Operators in Hilbert Spaces
Muhati, Linety N.; Khalagai, J. M.
It is a known fact in operator theory that two similar operators have equal spectra but they
do not necessarily have to belong to the same class of operators. However, under the
stronger relation of unitary equivalence it can be shown that two unitarily equivalent
operators may belong to the same class of operators. In this paper we endeavor to exhibit
some results on some pairs of operators which may belong to the same class under not only
unitary equivalence but also isometric and co-isometric equivalence.
2020-01-01T00:00:00ZNUMERICAL SIMULATION OF EFFECTS OF VELOCITY AND DIFFUSION COEFFICIENT ON CONCENTRATION OF CONTAMINANTS IN FLUID FLOWKIPNGETICH, LANGAThttp://41.89.164.27:8080/xmlui/handle/123456789/15822022-02-21T07:06:32Z2022-01-01T00:00:00ZNUMERICAL SIMULATION OF EFFECTS OF VELOCITY AND DIFFUSION COEFFICIENT ON CONCENTRATION OF CONTAMINANTS IN FLUID FLOW
KIPNGETICH, LANGAT
The study developed and implemented Implicit and explicit schemes for solving one
dimensional convection –diffusion equation modeling concentration of contaminant in a
fluid flow .The study uses method of lines and exact method to further verify the numerical
solution obtained. Stability of the scheme was analyzed and accuracy of the solution to the
contaminant transport equation was validated by exact solution. Graphical illustration of
the solution for varying velocity and diffusion coefficient is given, Errors in the methods
tabulated. The explicit method (EM) involved one unknown on left hand side (LHS) of the
scheme while implicit method (IM) involved several unknowns on LHS of the scheme and
method of lines (MOL) involved semi-discretization method. In the study, we examined
effect of velocity and diffusion coefficient on concentration of contaminant in a fluid
flowing .Comparison of solution from the methods stated was done. The developed,
numerical schemes were developed and MATLAB used generate and in analyze the results.
The results showed that concentration of contaminants increased inversely with fluid
velocity and directly with diffusion coefficient. Therefore, for proper treatment of water for
example, it is necessary to increase the flow velocities to reduce the concentration of
contaminants. The implicit Method significantly agreed to exact method to three decimals
than the explicit method which was much more inaccurate because of unconditional
stability. As Velocity increases the concentration of contaminant decreases and as diffusion
coefficient increases the concentration of contaminant increases.
2022-01-01T00:00:00Z