DSpace Repository :: Browsing by Author "Ngari, Cyrus G."

Browsing by Author "Ngari, Cyrus G."

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Analytical model for childhood pneumonia, a case study of Kenya
(Science Domain International, 2016) Ngari, Cyrus G.; Pokhariyal, G. P.; Koske, J. K.
Pneumonia is an infection of the lungs that is caused by bacteria, viruses, fungi, or parasites. For a long time to the best of our knowledge there have not been reliable mathematical model for childhood pneumonia in Kenya. This research study developed a deterministic model based on the Susceptible- Vaccinated-Infected-Treated-Recovered-Susceptible compartment classes. The study used the partial differentiation of control reproduction number toinvestigate effects of; environment, efficacy of vaccination drug and treatment. Model analysis indicates the system lie in feasible region, it is bounded, has no backward bifurcation and there exists unique endemic equilibrium point when control reproduction number is greater than unity. Local and global stability of the equilibrium points indicated that control reproduction has to be maintained at less than unity to eradicate the disease. Sensitivity analysis of the control reproduction number indicates that improved vaccination drug’s efficacy, attaining herd immunity, higher treatment rates and lower effects of environment are the best intervention strategies to lower impact of the pneumonia of the children under the age of five years in Kenya.
Aperture Maximization with Half-Wavelength Spacing, via a 2-Circle Concentric Array Geometry that is Uniform but Sparse
(2019-05) Kinyili, Musyoka; Kitavi, Dominic M.; Ngari, Cyrus G.
This paper proposes a new sensor-array geometry (the 2-circle concentric array geometry), that maximizes the array's spatial aperture mainly for bivariate azimuth-polar resolution of direction-of-arrival estimation problem. The proposed geometry provides almost invariant azimuth angle coverage and o ers the advantage of full rotational symmetry (circular invariance) while maintaining an inter-sensor spacing of only an half wavelength (for non-ambiguity with respect to the Cartesian direction cosines). A better-accurate performance in direction nding of the proposed array grid over a single ring array geometry termed as uniform circular array (UCA) is hereby analytically veri ed via Cram er-Rao bound analysis. Further, the authors demonstrate that the proposed sensor-array geometry has better estimation accuracy than a single ring array.
Cramer-Rao Bound of Direction Finding Using a Uniform Hexagonal Array
(2019-06) Ndiritu, Grace Wakarima; Kitavi, Dominic M.; Ngari, Cyrus G.
Direction-of-arrival (DOA) estimation is a key area of sensor array processing which is encountered in many important engineering applications. Although various studies have focused on the uniform hexagonal array for direction nding, there is a scanty use of the uniform hexagonal array in conjunction with Cram er-Rao bound for direction nding estimation. The advantage of Cram er- Rao bound based on the uniform hexagonal array: overcome the problem of unwanted radiation in undesired directions. In this paper, the direction-of-arrival estimation of Cram er-Rao bound based on the uniform hexagonal array was studied. The proposed approach concentrated on deriving the array manifold vector for the uniform hexagonal array and Cram er-Rao bound of the uniform hexagonal array. The Cram er-Rao bound based on the uniform hexagonal array was compared with Cram er-Rao bound based on the uniform circular array. The conclusions are as follows. The Cram er-Rao bound of uniform hexagonal array decreases with an increase in the number of sensors. The comparison between the uniform hexagonal array and uniform circular array shows that the Cram er-Rao bound of the uniform hexagonal array was slightly higher as compared to the Cram er-Rao bound of the uniform circular array. The analytical results are supported by graphical representation.
Cramer-Rao Bound of Direction Finding Using Uniform Arc Arrays
(2019) Nyokabi, Veronicah; Kitavi, Dominic M.; Ngari, Cyrus G.
Direction-of-Arrival estimation accuracy using arc array geometry is considered in this paper. There is a scanty use of Uniform Arc Array (UAA) in conjunction with Cram er-Rao bound (CRB) for Direction-of-Arrival estimation. This paper proposed to use Uniform Arc Array formed from a considered Uniform Circular Array (UCA) in conjunction with CRB for Direction-of-Arrival estimation. This Uniform Arc Array is obtained by squeezing all sensors on the Uniform Circular Array circumference uniformly onto the Arc Array. Cram er-Rao bounds for the Uniform Arc Array and that of the Uniform Circular Array are derived. Comparison of performance of the Uniform Circular Array and Uniform Arc Array is done. It was observed that Uniform Arc Array has better estimation accuracy as compared to Uniform Circular Array when number of sensors equals four and ve and azimuth angle ranging between π 9 7 and π and also 18 10 9 π and 25 18π. However, UCA and UAA have equal performance when the number of sensors equals three and the azimuth angle ranging between 0 and 2π. UCA has better estimation accuracy as compared to UAA when the number of sensors equals four and ve and the azimuth angle ranging between π 2 and π and also 32 π and 2π
Estimated numerical results for the deterministic model of the under five years pneumonia in Kenya
(2016) Ngari, Cyrus G.; Pokhariyal, G. P.; Koske, J. K.
In this paper the numerical results are estimated for childhood pneumonia deterministic model, using Kenyan data. The estimates of data and parameters from Kenya Health information system, ministry of Health of Kenya and UNICEF for the years 2012 and 2013 were fitted in the developed model using Matlab software. The estimated numerical value for control reproduction number (Rc) and basic reproduction number (Ro) were obtained as 9.31808 and 22.5914 respectively, by substituting estimated parameters in the expression for the determined analytical results. The herd immunity was estimated as 95.57% using the basic reproduction number. Impact of treatment value was found to be found to be positive. Sensitivity analysis of the control reproduction number indicates that improved vaccination drug’s efficacy, attaining herd immunity, higher treatment rates and lower effects of environment are the best intervention strategies to lower impact of the pneumonia of the children under the age of five years in Kenya.
A model for childhood Pneumonia Dynamics
(Asian online journals, 2014) Ngari, Cyrus G.; Malonza, David M.; Muthuri, Grace G.
This paper presents a deterministic model for pneumonia transmission and uses the model to assess the potential impact of therapy. The model is based on the Susceptible-Infected-Treatment-Susceptible compartmental structure with the possibility of infected individual recovering from natural immunity. Important epidemiological thresholds such as the basic and control reproduction numbers ( 𝑅𝑜and 𝑅𝑐 respectively) and a measure of treatment impact are derived. Infection free point was found to be locally stable but globally unstable. We found that if the control reproduction number is greater than unity, then there is a unique endemic equilibrium point and it is less than unity, the endemic equilibrium point is globally asymptotically stable, and pneumonia will be eliminated. Numerical simulations using Matlab software suggest that, besides the parameters that determine the basic reproduction number, natural immunity plays an important role in pneumonia transmissions and magnitude of the public health impact of therapy. Further, treatment regimens with better efficacy holds great promise for lowering the public health burden of pneumonia disease.
Modeling Influence Tribal Coalitions in Kenya Presidential Politics: A Case Study of Kikuyu-Kalenjin versus Luo-Kamba
(Science Domain International, 2016-04) Ngari, Cyrus G.
A deterministic model was developed to describe the two dominant tribal coalition based voting bloc (A and B) and other tribes (C). The first order nonlinear ordinary differential equations were deduced using predator-prey equations. The system was established to lie in feasible region. The coalition free steady state was determined. The conditions necessary for local stabilities of steady states were determined using Routh-Hurwitz criteria for stability. The condition necessary for global stability of steady state were determined using Lyapunov function. The estimated numerical bound of the registered voters was obtained as 27871013. Numerical simulation was carried out using 2013 general election scenario.
Modeling Kenya Domestic Radicalization like A Disease Incorporating Rehabilitation Centers
(Academic Research Publishing Group, 2016) Ngari, Cyrus G.
The study presents a deterministic model for radicalization process in Kenya and use the model to assess impact of rehabilitation centers to radicalization burden. The possibility of other drivers of radicalization to individuals who are not religious fanatics, and also individuals in rehabilitated subclass continuing being violent was considered. The model incorporated rehabilitation of the radicalized but peaceful individuals in subclass R (t), and also radicalized but violent individuals in subclass T (t), allowing recovery of individuals in subclass R (t) from the intervention of good clergies. The stationary points were computed, their stabilities investigated and important thresholds determining the progression of the radicalization evaluated. The model sensitivity indices indicate that high intervention rates hold great promise to reduce the radicalization burden.
Modeling Scramble for other tribes votes by the three main tribal voting blocs in Kenya Presidential elections
(2016) Ngari, Cyrus G.
A deterministic model was formulated to describe the tribal based voting blocs in Kenya presidential politics using four compartmental classes: Kikuyu (K), Luo (L), AKalenjin (A) and other tribes (T). The first order nonlinear ordinary differential equations governing the dynamics were developed using Lokta-Voltera equations (Predator-Prey interspecific competition). Model analysis was carried out. The possibility of at most four tribal bloc equilibrium points was predicted using Descartes’s rule of sign. The stabilities of the equilibrium points were predicted using Routh-Hurwitz criteria, eigenvalues of Jacobi matrix and Lyapunov function. The estimated bound for valid votes in Kenya was obtained as 21212503 for the next five general elections and numerical simulations were carried .The result indicates that anti-tribalism civic education on new voters’ holds great promise to reverse the trend in future.
Modelling Vaccination and Treatment of Childhood Pneumonia and Their Implications
(Science Domain International, 2018-07) Ngari, Cyrus G.
This paper presents a deterministic model for pneumonia transmission and uses the model to assess the potential impact of the vaccination, treatment and efficacy of vaccination drugs in lowering the public health impact of the pneumonia disease. The model is based on the Susceptible-Vaccinated-Infected- Treated compartmental classes of children less than five years. There is possibility of the non-severely infected recovering from natural immunity. Model analysis indicates the system lie in the positive region, solution is bounded and there exist unique positive endemic equilibrium point whenever control reproduction number is greater than unity. Important epidemiological thresholds such as the basic and control reproduction number are determined. Disease-free point equilibrium points are determined. Local and Global stability of equilibrium points will be investigated. Sensitivity analysis of the reproduction numbers indicated higher vaccination drug efficacy vaccination, treatment and recoveries from natural immunity hold great promise in lowering pneumonia impact. Estimated numerical result indicated impact of treatment is positive. Numerical simulation was carried to predict the dynamics of the system.
Multinomial Logistic Modelling of Socio-Economic Factors Influencing Spending Behavior of University Students
(2019-06) Akelo, Jacqueline Gogo; Mbunzi, Stephen M.; Ngari, Cyrus G.
This study aims at determining the use of Multinomial Logistic Regression (MLR) model which is one of the important methods for categorical data analysis. This model particularly deals with one nominal or ordinal response variable that has more than two categories. Despite the fact that many researchers have applied this model in data analysis in many areas, for instance behavioral, social, health, and educational, a study on spending habits of University students have never been done. To identify the model by practical way, we conducted a survey research among students from University of Embu. Segment of the population of students in undergraduate level, a sample of 376 was selected. We employed the use stratified random sampling and simple random sampling without replacement in each stratum. The response variable consisted of five categories. Four of explanatory variables were used for building the primary (MLR) model. The model was tested through a set of statistical tests to ensure its appropriateness for the data. From the results, the study reveals that year of study, family financial level, gender and school are significant factors in explaining spending habits of students. Despite the fact that gender is one of the deterministic factors of financial behavior of student, this model identified family level of income as a major deterministic factor. Conclusively, using MLR model accurately defines the relationship between the group of explanatory variables and the response variable. It also identifies the effect of each of the variables, and we can predict the classification of any individual case. The researchers recommend that, the Universities peer counselling department, should hold trainings on the basis of major determinant of financial spending behavior i.e. family financial level.
Numerical simulation of the deterministic model of the under-five year’s pneumonia in Kenya
(2016) Ngari, Cyrus G.; Pokhariyal, G. P.; Koske, J. K.
In this paper the numerical simulation of the childhood pneumonia deterministic model are determined. The estimated parameters and the under-five year’s population data for year 2013 was used to simulate the developed deterministic model, using Matlab inbuilt ordinary differential equation (ode) solver. Graphical results predicting the dynamics of the under-five year’s pneumonia were obtained for a period of twenty years. Simulations indicated that sustained vaccination and treatment are likely to reduce the burden of the under-five year’s pneumonia over a period twenty years.
Parameterization and Forecasting of Childhood Pneumonia Model Using Least Square Approximation, Lagrange Polynomial and Monte Carlo Simulation
(2020-09) Ngari, Cyrus G.; Kitavi, Dominic M.
espite a study by [1] proposing a simple model of under five years pneumonia, doubt lingers regarding its reliability, sufficiency and validity. The research question is whether the model is valid for use or not? The objectives of this study were to: incorporate exit rate from under five-year age bracket in the model, use Kenya data to parameterize the model, taking into account the uncertainties and finally to predict the dynamics of pneumonia. The model was rescaled through nondimensionalization. Data was fitted using theory of general solutions of nonlinear Ordinary differential equations, numerical differentiation using Lagrange polynomials and least square approximation method. Uncertainties due to disparities and round off errors were simulated using Monte Carlo simulation. Predictions of dynamics of pneumonia were carried out using MATLAB inbuilt ode solvers. Excel software was used to predict dynamics of discrete ordinary differential equations and to fit data. The basic reproduction number () and effective reproduction number () were obtained as 61 and 7 respectively. Iteration of uncertainties on R was carried out 1000 times by Monte Carlo simulation. The maximum and minimum R were obtained as 90 and 55, respectively. Using MATLAB software and effective reproduction number, the ratio of infective class to the total population and the ratio of class under treatment to the total population will remain constant at 0.095 and 0.2297 respectively for the years 2021, 2022 and 2023. Research result indicted that it is more effective and efficient to use effective reproduction number () than basic reproduction number () in mathematical modelling of Infectious diseases whenever study focuses on proportion of population. On basis of large absolute errors in fitting data to model, findings cast doubt on model formulation and/or observed data.
Parameters and States Estimates of COVID-19 Model Using Lagrange Polynomial, Least Square Approximation and Kenya Quarantine Data
(2020-10-09) Ngari, Cyrus G.; Muthuri, Grace G.; Mirgichan, James K.
Aims/ Objectives: To develop a compartment based mathematical model, fit daily quarantine data from Ministry of Health of Kenya, estimate individuals in latency and infected in general community and predict dynamics of quarantine for the next 90 days. Study Design: Cross-sectional study. Place and Duration of Study: 13thMarch 2020 to 30th June 2020. Methodology: The population based model was developed using status and characteristic of COVID-19 infection. Quarantine data up to 30/6/2020 was fitted using integrating and differentiating theory of odes and numerical differentiation polynomials. Parameter and state estimates was approximated using least square. Simulations were carried out using ode Matlab solver. Daily community estimates of individuals in latency and infected were obtained together with daily estimate of rate of enlisting individual to quarantine center and their proportions were summarized. Results: The results indicated that maximum infection rate was equal 0.892999 recorded on 28/6/2020, average infection rate was 0.019958 and minimum 0.00012 on 26/6/2020. Conclusion: Predictions based on parameters and state averages indicated that the number of individuals in quarantine are expected to rise exponentially up to about 26,855 individuals by 130th day and remain constant up to 190th day.
A Simple model for the ethnic, sub ethnic, clan and religion based politics in Kenya presidential elections
(2016) Ngari, Cyrus G.
A simple deterministic model with Kenya specific attributes was developed to describe the ethnic based voting blocs. Four compartmental classes: Agikuyu (A), Luo (L), Kalenjin (K) and the Rest (R) were formulated, and first order linear ordinary differential equations(ODE) deduced. The model was established to lie in the feasible region. Ethnic free equilibrium points (EFP) and ethnic bloc equilibrium point were determined. The condition necessary for the stability of the ethnic free equilibrium was established. The condition necessary for the global stability of the ethnic bloc equilibrium point was determined using lyapunov function. The estimated bound for valid votes in Kenya was obtained as 2014500 for the next 30 general election. Numerical simulation suggests that the Rest (R) class will dominate in numerical strength for the next 30 general elections. The result suggests that recruitment of new voters along ethnic plays a key role in persistence of ethnic voting pattern and effort should be focused there to reverse the trend in future.
Simulation of a Deterministic Model of HIV Transmission between Two Closed Patches
(2020-09) Mirgichan, James Khobocha; Ngari, Cyrus G.; Karanja, Stephen
Numerical simulation of a deterministic model of HIV transmission between major cities in Kenya is carried out. The model considered two closed patches connected by the commuter movements of truck drivers being the agents of HIV transmission. The transmission kernel being the function of distance between the patches is ignored. The numerical algorithms are applied in the solution of a nonlinear firstorder differential equations. The algorithms are implemented with the aid of MATLAB solver which has an in- built mechanism of Runge Kutta method of fourth order. Numerical simulation indicated the population dynamics of the patches, effect of migration on female sex workers and model reproduction number. The findings of the study were that the migration of the truck drivers between two closed patches contributed significantly to the spread of HIV. In this regard, it was recommended that, stakeholders should target the truck driving population and towns along the transport corridors to mitigate the growing HIV infections and integrate the truck drivers in the national health strategy.
A Theoretical Model of Corruption Using Modified Lotka Volterra Model A Perspective of Interactions between Staff and Students
(2020-09) Kawira, Mercy; Ngari, Cyrus G.; Karanja, Stephen
Corruption is the misuse of power or resources for private gain. This undermines economic development, political stability, and government legitimacy, the society fabric, allocation of resources to sectors crucial for development, and encourages and perpetuates other illegal opportunities. Despite Mathematical modeling being a powerful tool in describing real life phenomena it still remains unexploited in the fight of corruption menace. This study uses Lotka Volterra, predator-prey equations to develop a model to describe corruption in institutions of higher learning, use the developed model to determine its equilibria, determine the condition for stability of the equilibria and finally carry out the simulation. The corrupt students and staff act as predators while their non-corrupt counterparts act as prey in the paper. Theory of ordinary differential equations was used to determine steady states and their stability. Mathematica was used for algebraic analysis and Matlab was used for numerical analysis and simulation. Analytical result suggested multiple steady state however numerical result confirmed that the model has four steady states. Numerical bifurcation analysis suggests the possibility of backward of corrupt staff when is about 39. Numerical simulation points to an increasing trend on corrupt staff and decrease trend on corrupt student. This study concludes that more focus should be put to staff than students in curbing the spread of corruption. Future study should strive to fit this model in real data
Tuberculosis model, a case study of tigania west, Kenya
(2016) Muthuri, Grace G.; Malonza, David; Ngari, Cyrus G.
Tuberculosis (TB) is a bacterial disease caused by mycobacterium tuberculosis. Many mathematical models for TB have been developed but not specifically for Kenya. This study develops a deterministic model based on Susceptible–Exposed–Active–Treated compartments classes. The model analyses the stability of the disease free equilibrium by analyzing the basic (R0) and control (RC) reproduction number and the endemic equilibrium point (EEP) which shows that the model is stable when RC< 1 and there exist an EEP when RC is less than one. Sensitivity analysis of the model was investigated using the partial derivatives of (RC) with respect to treatment which shows that high rate of treatment reduces the control reproduction number so is the best intervention method in Kenya.

Browsing by Author "Ngari, Cyrus G."

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