Theses & Desertations

PREDICTIVE MODELING OF CHILD MORTALITY IN MIGORI AND NYAMIRA COUNTIES USING INDIRECT METHODS

Wed, 01 Jan 2025 00:00:00 GMT

PREDICTIVE MODELING OF CHILD MORTALITY IN MIGORI AND NYAMIRA COUNTIES USING INDIRECT METHODS OMARE, BRIAN Child mortality remains a critical public health challenge, particularly in developing countries like Kenya, where disparities in healthcare are stark across different regions. In counties such as Nyamira and Migori, persistent high rates of under-five child mortality demonstrate the need for more precise statistical predictions for and targeted interventions. Traditional methods for estimating child mortality, such as those derived from household surveys, are often hampered by issues like missing data and survivor bias, leading to inaccurate mortality estimates. This study sought to develop a comprehensive predictive model for under-five child mortality in Migori and Nyamira counties, Kenya, by incorporating temporal patterns and social determinants of health. Utilizing a retrospective cohort design, the study analyzed historical data from health records, census reports, and household surveys spanning 34 years (1989-2022). The analysis incorporated indirect estimation techniques to address data gaps and employed multiple linear regression, gradient boosting regressor, and spatio-temporal modeling to capture temporal and seasonal trends in child mortality. The multiple linear regression model was significant, explaining 89.9% of the change in neonatal mortality in Migori County and 80.6% of the variation in Nyamira County. Gradient boosting regressor performed optimally, accounting for 80.9% of the change in child mortality, indicating good predictive capability and suggesting that the chosen independent variables effectively capture the complexity of the response variable. Spatio-temporal modeling log-likelihood value of -111.87 indicated a relatively good fit, capturing the observed data well (pseudo-R-squared = 0.9415). Results indicated that infant mortality rates in both counties have fluctuated historically, with distinct seasonal trends influenced by factors such as disease prevalence and access to healthcare services. The temporal and seasonal analysis revealed that periods of increased respiratory complications and malaria prevalence corresponded with higher mortality rates. The study provides a methodological framework that can be adapted to other regions with comparable challenges. By addressing the limitations of traditional mortality estimation methods and leveraging advanced predictive modeling techniques, the study contributes to the ongoing efforts to improve child health outcomes in Kenya and beyond.

VECTOR AUTOREGRESSION MODELING OF MALARIA INCIDENCE AND MORTALITY RATES IN MIGORI COUNTY, KENYA

Wed, 01 Jan 2025 00:00:00 GMT

VECTOR AUTOREGRESSION MODELING OF MALARIA INCIDENCE AND MORTALITY RATES IN MIGORI COUNTY, KENYA CHACHA, PAUL JACKSON Malaria prevalence in poorer countries has been a persistent public health concern, disproportionately affecting vulnerable populations such as children and pregnant women. Despite notable progress in scaling up malaria control interventions in Kenya, malaria incidence rates continue to vary widely across counties, with endemic regions like Migori County experiencing persistent challenges. This study aimed to identify key factors associated with malaria incidence and mortality in Migori County using secondary data from the Kenya National Health Management System. Multiple statistical models, including regression, Vector Autoregression (VAR), and Vector Autoregression with Exogenous Variables (VARX), were applied to examine the temporal dynamics of malaria. While malaria incidence rates declined over time, mortality rates remained relatively stable. Regression results indicated that insecticide-treated net usage and effective treatment significantly influenced both incidence and mortality rates. However, model residuals showed substantial variability and signs of poor fit, highlighting the need for improved model specifications. The VAR model revealed issues of residual autocorrelation, while the VARX model, which incorporated exogenous variables, showed improved but still imperfect performance. Bayesian VAR (BVAR) models provided consistent findings across methodologies but also underscored ongoing challenges in modeling temporal malaria data accurately. Therefore, this study concludes that while current models offer valuable insights, they remain limited in capturing the full complexity of malaria dynamics. It recommends methodological enhancements, such as using advanced techniques like Generalized Method of Moments (GMM) or machine learning, conducting rigorous residual diagnostics, and incorporating environmental, socioeconomic, and behavioral variables. Expanding the dataset across regions and timeframes could also improve the robustness and generalizability of future research aimed at informing more effective malaria control strategies.

APPLICATION OF MIXTURE EXPERIMENT IN THE OPTIMIZATION OF CABBAGE (BRASSICA OLERACEA L.) YIELD USING SELECTED ORGANIC MANURE.

Mon, 01 Jan 2024 00:00:00 GMT

APPLICATION OF MIXTURE EXPERIMENT IN THE OPTIMIZATION OF CABBAGE (BRASSICA OLERACEA L.) YIELD USING SELECTED ORGANIC MANURE. CHIRCHIR, EMMANUEL K. Several products in practice are usually a combination of two or more ingredients put together. The rationale for conducting this research was to determine the optimum yield of Cabbage (Brassica oleracea L.) as affected by four types of manures which include; Chicken Manure (CM), Pig Manure (PM), Goat Manure (GM) and used Tea Leaves Manure (TLM) coded as 𝑋1,𝑋2,𝑋3 and 𝑋4 respectively in this study. The main objective that led to this research to be conducted was to come up with the best organic fertilizer or the mixture proportion that will maximize the yields of the crop. Utilizing the right quantities of manure would ultimately lead to the small-scale farmers having optimal yields and hence fetching increased profits from their farms. In this research, the moment matrix obtained from the information matrix whose primary source was the designs points was used based on D-Determinant, A-Average variance, E- Eigen value and T- Trace optimality criteria to select appropriate mixture experiment designs, which are the Simplex-Lattice Designs and Simplex-Centroid Design. The {4,4} Simplex-Lattice Design was employed in this research due to its lowest rank value of 1.0 compared with others. The final average weight of the crop was analyzed using the R statistical package. A second-order regression model was plotted with intercept set to zero. Data exploration was done by use of contour plot. This was essential in establishing the recommended proportions of the manure in their pure or binary blends that offered operating conditions. Different combinations of manure were tested. The results were comparably different because the selected manures had different nutrient components in them. The study concluded that component 𝑋2 (Pig manure) stood out to be the best single-component manure that yielded maximally with an average weight of 2.93 Kg and 2.86 Kg in the overall model and reduced model respectively. For the binary blends, a combination of component 𝑋1 (Chicken manure) and component 𝑋2 (Pig manure) gave the highest final weight of the crop, 1.16 Kg, with 0.3 and 0.7 working conditions respectively. The proposed levels of manure are recommended to the farmers for optimal yields with lower cost. This would increase income and, in the end, this would help in eradicating poverty, which is a menace to the economic growth of our country

MODELING THE RISK FACTORS OF MISCARRIAGE USING ADVANCED SURVIVAL ANALYSIS TECHNIQUES: CENSORED QUANTILE REGRESSION AND CURE MODEL

Mon, 01 Jan 2024 00:00:00 GMT

MODELING THE RISK FACTORS OF MISCARRIAGE USING ADVANCED SURVIVAL ANALYSIS TECHNIQUES: CENSORED QUANTILE REGRESSION AND CURE MODEL CHIBAYI, JOHN OLIVES Miscarriage is the involuntary termination of pregnancy before the fetus can survive outside the maternal uterus. The risk factors associated with the transition from a normal pregnancy to a complete miscarriage before 28 weeks of gestational age have not been exhaustively established. Use of logistic regression to assess the factors associated with spontaneous abortion excludes the longitudinal and incompleteness aspects of miscarriage data. Cox's model and the accelerated failure time model have the following drawbacks: Assumes a constant hazard ratio, model the hazard rate rather than the duration of survival, not robust in handling statistical outliers, cannot handle a data with cure fraction and lack flexibility. The main objective of the study was to model the risk factors associated with miscarriage using advanced survival analysis techniques; quantile regression and cure models. The study used secondary data from western Kenya's Kakamega County Teaching and Referral Hospital. The data collection period was January 1, 2019–December 31, 2020. The study used Kaplan-Meier, chi-squared and log-rank tests for independent analysis. The Cox proportional hazards (PH) model and parametric models were used to evaluate miscarriage data based on Akaike Information Criterion (AIC). A semi-parametric shared frailty model was used to examine unobserved variability among expecting women by residence. This study used cure rate and censored quantile regression models. Of the total sample of 6077, 248 mothers (4.1%) miscarried, while 5829 (95.9%) were censored. The significant factors identified by log rank test were ethnicity (𝑝 = 0.000), levels of education (𝑝 = 0.048), place of residence (𝑝 = 0.000), employment status (𝑝 = 0.004), malaria status (𝑝 = 0.000) and urinary tract infection (UTI) status (𝑝 = 0.000). The covariates in categorized form found significant by log rank were number of previous stillbirths (𝑝 = 0.000) and number of antenatal care (ANC) visits. The factors ethnicity, place of residence, malaria status, number of previous miscarriages, number of previous stillbirths and number of ANC visits were identified as the risk factors associated with miscarriages using cox model, parametric proportional hazards model and accelerated failure time models. The study found equivalent hazard ratios for Cox (PH) and accelerated failure time models but log-likely hood and the (AIC) showed that the Gompertz PH model had the best fit of the data. In comparison between the Cox and the censored quantile regression (CQR) models the factors; ethnicity, previous number of miscarriages, previous number of stillbirths, occupation status, and malaria infection, exhibited a statistically significant adverse effect on the duration of survival during the initial phases of pregnancy in the CQR model and not in cox model. The cure model showed that place of residency (𝑝 = 0.0034), ethnicity: kalenjin (𝑝 = 0.0008), kikuyu (𝑝 = 0.014) and luo (𝑝 = 0.04), number of prior miscarriages (𝑝 = 0.000), number of previous stillbirths (𝑝 = 0.000) and number of ANC visits (𝑝 = 0.000) statistically affect cure fraction. However these factors did not affect survival time, apart from the number of ANC visits (𝑝 = 0.001). The number of previous miscarriages, stillbirths, ANC visits, site of residency, and ethnic groups (Kalenjin, Kikuyu, and Luo) had cure probabilities of 54.88%, 47.09%, 76.09%, 87.16%, 39.33%, 44.78%, and 58.25%, respectively. The study concludes that there is association between certain explanatory variables and the time to miscarriages, the Gompertz (PH) regression model best fits this data set. Censored quantile regression model can show that certain variables had a significant effect on survival time in some point in pregnancy and reveal the dynamics of prognostic risk factors and their impact on patient survival over time. The cure model showed that these factors had effect on long-term survivors, on short-term trends there were little changes. The findings of this study will aid the government and healthcare authorities to plan and provide interventions to reduce miscarriages in Kenya.

MODELLING THE EFFECTS OF SOCIAL FACTORS ON POPULATION DYNAMICS USING AGE-STRUCTURED MODEL AS A MANAGEMENT STRATEGY

Mon, 01 Jan 2024 00:00:00 GMT

MODELLING THE EFFECTS OF SOCIAL FACTORS ON POPULATION DYNAMICS USING AGE-STRUCTURED MODEL AS A MANAGEMENT STRATEGY KEMEI, ZACHARY KIPKOECH This study used an age-structured model was used to investigate the effects of social factors to population dynamics. Apart from age, subset of time affecting the population dynamics of human beings, other social factors also contribute to this human population dynamic. Examples of such social factors includes food supply, level of education, availability of suitable shelter, level of poverty and availability of universal health care. The modified age-structured mathematical model was developed, with partial differential equations that consisted of three variables of age, time and social factors. The model was developed to predict the future population size using disjoint age groups namely: infants, juvenile, sub-adults, adults and old persons. In this study, the population dynamics was modelled, where population was put into age–structures and the transition rate was incorporated into new modified model. Method of separation of variables was applied to find the analytic solutions of the new modified age-structured model developed while method of Finite Difference Method (FDM) was used to discretize formulated mathematical model in both absence and presence of social factors. The two discretised forms of models were analytically solved using closed form iteration method. The Kenya Population Data 2019, was numerically substituted into the modified mathematical model using MATLAB, and the system numerically computed. The stability and the convergence of the discretised mathematical model obtained by Finite Difference Method was established using the Crank-Nicolson scheme and the condition for stability was obtained to be 𝛾 ≤ 1 2 and ∆𝛼 = 1. Numerical simulation in absence of social factors 𝛿 = 0, generated a triangular population pyramid, a characteristic of high birth rate, and high mortality rate and solutions obtained indicated that, the population is unstable, meanwhile the economic dependency ratio was obtained to be 1:2. Whereas with improved implementation of social factors 𝛿 > 0, the population stabilized at an optimum of 𝛿 ≥ 0.75, and the economic dependency ratio improved to 1:1.14, implying that, support by independent population towards the dependent population decreased. This results indicated that the social factors affects the mortality rate inversely and the birth rate and net-migration rates are affected directly, that is; the improvement in the provision of social factors leads to an increase in both birth and migration rates, and population structure gives a square population pyramid with characteristics of low birth rate and low mortality rate, like that of developed countries. Using social factors as population management strategy, the provision of social factors at an efficacy of = 0.75 , yields a lower birth rate of 𝛽𝑜𝑝𝑡 = 0.05104 down from 𝛽𝑜𝑙𝑑 = 0.05178 and a lower mortality rate of 𝜇𝑜𝑝𝑡 = 0.00184 from 𝜇𝑜𝑙𝑑 = 0.02786. The findings of obtained suggests a new method of managing and stabilizing population using social factors. The model also predicts the limiting optimal population size to be achieved due to improvement of social factors as 57,956,100 to be realized in 2054 after 35 years, up from 38,589,011 in 2019.

MATHEMATICAL MODELING OF HIV/AIDS DYNAMICS AMONG THE FISHERFOLK AS A VECTOR FOR HIV: A CASE STUDY OF LAKE VICTORIA METAPOPULATIONS

Thu, 01 Jun 2023 00:00:00 GMT

MATHEMATICAL 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.

MODELLING COVID-19 DYNAMICS (SPREAD AND CONTROL) AND THE EFFECTS OF A PREVENTIVE VACCINE

Fri, 01 Sep 2023 00:00:00 GMT

MODELLING 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 .

MODELING THE EFFECTS OF CROP SPACING AND INORGANIC FERTILIZER ON THE POTATO TUBER YIELD AND SIZE USING FIRST ORDER TWO-LEVEL FACTORIAL DESIGN

Wed, 01 Jun 2022 00:00:00 GMT

MODELING 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.

FORECASTING TUBERCULOSIS INFECTIONS USING ARIMA AND HYBRID NEURAL NETWORK MODELS AMONG CHILDREN BELOW 15 YEARS IN HOMA BAY AND TURKANA COUNTIES, KENYA

Tue, 01 Nov 2022 00:00:00 GMT

FORECASTING 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.

NUMERICAL SIMULATION OF EFFECTS OF VELOCITY AND DIFFUSION COEFFICIENT ON CONCENTRATION OF CONTAMINANTS IN FLUID FLOW

Sat, 01 Jan 2022 00:00:00 GMT

NUMERICAL 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.