isaac chepkwony | Kenyatta University, Nairobi (original) (raw)
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Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a DECLARATION I declare that the thesi... more Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a DECLARATION I declare that the thesis which I hereby submit for the award of MHSC in Heritage and Cultural Tourism in the University of Pretoria is my own original work and has not been previously submitted for the award of any degree or examination at any other University. Irene Chebet Chepkwony. © © U Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a iii DEDICATION To my dear mother Mrs. Hellen Chepkwony, who has been very supportive and toiled to make sure I completed this Masters degree successfully. © © U Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a © © U Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a v Africa. I was aware of the financial challenge I was going to face but she made me believe it was going to be well. She has been of great help both financially and emotionally. Mummy toiled so hard to raise enough finances for me to be able to go through my studies in South Africa. Not a single day did I lack anything. Special thanks also go to my dear husband Dr. Jackson Cheruiyot Korir for his support and encouragement for the four years that I was away. He read every bit of my work and gave me positive criticisms and often helped with my work. His financial support cannot also go unmentioned as he financed my education and the many air tickets to Kenya every year. I will not forget to thank my siblings for their patience with me and forsaking some of their dreams so that my parents could spare some cash for my upkeep in South Africa. Finally, my sincere appreciation to all my friends and relatives for the various supports they gave me during my studies.
Journal of Advances in Mathematics and Computer Science
Cancer is a menace to public health globally. Human Papillomavirus (HPV) is a sexually transmitte... more Cancer is a menace to public health globally. Human Papillomavirus (HPV) is a sexually transmitted virus and has been linked to several cancers such as cervical cancer, anal cancer, oropharyngeal cancer and neck cancer. In this research a mathematical model based on a system of ordinary differential equations is formulated to study the impact of an effective mass media awareness campaigns on the spread of HPV infections under vaccination in Kenya. The basic reproduction number is computed using the next generation matrix method. The equilibrium points of the model are determined and their stability investigated. The results of stability analysis show that the HPV free equilibrium is locally asymptotically stable when Ro < 1 and the endemic equilibrium point existed if Ro < 1. We used the center manifold theory to investigate the nature of bifurcation. The investigation identified that the bifurcation parameter θ changes from negative to positive, changes its stability from st...
International journal on future revolution in computer science & communication engineering, Jul 31, 2019
European Journal of Mathematics and Statistics
Human Papillomavirus (HPV), a sexually transmitted virus is a collection of more than 40 types of... more Human Papillomavirus (HPV), a sexually transmitted virus is a collection of more than 40 types of viruses, some of which are linked to several cancers. HPV type 16 and HPV type 18 are accountable for 70% of cervical cancer cause. Besides cervical cancer, HPV has been linked to several cancers such as anal cancer, oropharyngeal cancer and neck cancer. Mathematical models have been used in the evaluation of control strategies and making of health policies. Very few mathematical models have been developed on HPV awareness in Kenya. In this study we developed a deterministic model on the impact of HPV infection under vaccination. In this model we incorporated an ineffective media awareness. We computed the equilibrium points of the model and local and global stability analysis was conducted on the reproduction number. The numerical simulation results show that the HPV infections continue to stay in the community due to the ineffective mass media awareness. Sensitivity analysis show that...
Distributed control of a cochlea model ∗
Journal of Advances in Mathematics and Computer Science
Tungiasis is a disease that mostly affects the children,the disabled,alcoholics and the aged in K... more Tungiasis is a disease that mostly affects the children,the disabled,alcoholics and the aged in Kenya and other parts of the world.Despite the intensive research that has been doneon tungiasis disease,the disease remains a threat in Muranga County.In this research, weformulated a model which is mathematical in nature and derived a system of ordinary differentialequations from it,which we used to study the dynamics of tungiasis disease, incorporating properhygiene as a control measure.The basic reproduction number, R0, is calculated using the nextgeneration matrix.We determined the equilibrium points of the model and also carried out theirstability analysis. From stability, both disease free equilibrium and endemic equilibrium points of the model were found to be locally asymptotically stable when R0 < 1 and R0…
Mathematical theory and modeling, 2019
In this study the effects on temperature on applying variable pressure gradient to a MHD fluid fl... more In this study the effects on temperature on applying variable pressure gradient to a MHD fluid flowing between two plates in an inclined magnetic field was carried out. It involved an unsteady hydromagnetic fluid flowing through two plates where the upper plate was porous and moving with a constant velocity in a direction that is contrary to fluid flow direction. The lower plate was non-porous and stationary. In the past years, research studies relating to MHD fluid flow through plates have been done. The information obtained from these studies have been implemented in various industrial systems for instance designing of electromagnetic meters and MHD pumps. However these research studies have been carried out when the pressure gradient was a constant and none when the pressure gradient was a variable, hence the reason why we carried out this investigation. The objective of this project was to determine the effect on temperature on applying variable pressure gradient to a MHD flow i...
Measles virus is a member paramyxoviridae within the genus of morbillivirus. Its genome consist o... more Measles virus is a member paramyxoviridae within the genus of morbillivirus. Its genome consist of approximately 16,000 bases of non-segmented single stranded negative sense RNA. This means that the virus is transcribed immediately upon entry into the cell. The virus spreads from person to person through the release of the aerosol droplets. In this paper, we investigate the transmission of measles virus using the five compartments of susceptible, vaccinated, exposed, infectious and recovered individuals with demographic factors. We give the mathematical model describing the transmission of the measles virus. The results of the model analysis showed that the model has a unique disease free equilibrium (DFE) which is locally asymptotically stable when R0 < 1 and unstable when R0 > 1. We further carried out numerical simulation of the model to investigate the effect of vaccination on the transmission dynamics of the virus. The results showed that there exist a minimum value of th...
Epidemic modeling is an important theoretical approach for investigating the transmission dynamic... more Epidemic modeling is an important theoretical approach for investigating the transmission dynamics of infectious diseases. It formulates mathematical models to describe the mechanisms of disease transmissions and dynamics of infectious agents and then informs the health control practitioners the likely impact of the control methods. In this paper we investigate the spread of an infectious disease in a human population structured into n-patches. The population is initially fully susceptible until an infectious individual is introduced in one of the patches. The interaction between patches is dominated by movement of individuals between patches and also the migration of individuals and therefore any infection occurring in one patch will have a force of infection on the susceptible individuals on the other patches. We build a mathematical model for a metapopulation consisting of n patches. The patches are connected by movement of individuals. For n = 2, we obtained the basic reproducti...
British Journal of Mathematics & Computer Science, 2015
Journal of Advances in Mathematics and Computer Science
Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are respon... more Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are responsible for 99% of human rabies cases and the disease is always fatal once the symptoms appear. In Kenya the disease is still endemic despite the fact that there are ecient vaccines for controlling the disease. In this project, we developed SIRS mathematical model using a system of ordinary dierential equations from the model to study the transmission dynamics of rabies virusin dogs using public health education as a control strategy. The reproduction number R0 was calculated using the Next Generation Matrix. Both disease free and endemics equilibrium points were determined and their stability analysis performed. From the stability analysis results it was found out that the disease free equilibrium point is both locally and globally asymptotically stable when R0 < 1 and the endemic equilibrium point is both locally and globally asymptotically stable when R0 > 1. Numerical simulations...
International Journal of Advances in Scientific Research and Engineering
We investigate shear banding phenomena in the plane Couette flow of viscoelastic fluids.The visco... more We investigate shear banding phenomena in the plane Couette flow of viscoelastic fluids.The viscoelastic fluids are modelled via the Giesekus constitutive equations with stress diffusion. The nonlinear and coupled systems of equations, comprising the momentum equation and the constitutive equations, are solved numerically using semi-implicit finite difference methods. The effects of the fluid parameters on the flow variables are also investigated. Under certain values of the material parameters, we observe formation of shear bands in plane Couette flow.
International Journal of Advances in Scientific Research and Engineering
A fractional-order HTLV type-1 model with transmission from an infected cell to uninfected cell a... more A fractional-order HTLV type-1 model with transmission from an infected cell to uninfected cell and also through mitosis is constructed and investigated. The requirements for the existence of equilibrium points are established. We have generalized the integer theorem introduced by LaSalle into the fractional system and given some adequate requirements for the infection-free equilibrium plus chronic equilibrium being globally asymptotically stable. We employed a numerical technique established for changing the fractional-order derivative to the integer-order derivative to work out the HTLV type-1 model. Numerical simulations are given to illustrate our results. The fractional-order derivatives are defined using the Caputo definition.
Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a DECLARATION I declare that the thesi... more Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a DECLARATION I declare that the thesis which I hereby submit for the award of MHSC in Heritage and Cultural Tourism in the University of Pretoria is my own original work and has not been previously submitted for the award of any degree or examination at any other University. Irene Chebet Chepkwony. © © U Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a iii DEDICATION To my dear mother Mrs. Hellen Chepkwony, who has been very supportive and toiled to make sure I completed this Masters degree successfully. © © U Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a © © U Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a v Africa. I was aware of the financial challenge I was going to face but she made me believe it was going to be well. She has been of great help both financially and emotionally. Mummy toiled so hard to raise enough finances for me to be able to go through my studies in South Africa. Not a single day did I lack anything. Special thanks also go to my dear husband Dr. Jackson Cheruiyot Korir for his support and encouragement for the four years that I was away. He read every bit of my work and gave me positive criticisms and often helped with my work. His financial support cannot also go unmentioned as he financed my education and the many air tickets to Kenya every year. I will not forget to thank my siblings for their patience with me and forsaking some of their dreams so that my parents could spare some cash for my upkeep in South Africa. Finally, my sincere appreciation to all my friends and relatives for the various supports they gave me during my studies.
Journal of Advances in Mathematics and Computer Science
Cancer is a menace to public health globally. Human Papillomavirus (HPV) is a sexually transmitte... more Cancer is a menace to public health globally. Human Papillomavirus (HPV) is a sexually transmitted virus and has been linked to several cancers such as cervical cancer, anal cancer, oropharyngeal cancer and neck cancer. In this research a mathematical model based on a system of ordinary differential equations is formulated to study the impact of an effective mass media awareness campaigns on the spread of HPV infections under vaccination in Kenya. The basic reproduction number is computed using the next generation matrix method. The equilibrium points of the model are determined and their stability investigated. The results of stability analysis show that the HPV free equilibrium is locally asymptotically stable when Ro < 1 and the endemic equilibrium point existed if Ro < 1. We used the center manifold theory to investigate the nature of bifurcation. The investigation identified that the bifurcation parameter θ changes from negative to positive, changes its stability from st...
International journal on future revolution in computer science & communication engineering, Jul 31, 2019
European Journal of Mathematics and Statistics
Human Papillomavirus (HPV), a sexually transmitted virus is a collection of more than 40 types of... more Human Papillomavirus (HPV), a sexually transmitted virus is a collection of more than 40 types of viruses, some of which are linked to several cancers. HPV type 16 and HPV type 18 are accountable for 70% of cervical cancer cause. Besides cervical cancer, HPV has been linked to several cancers such as anal cancer, oropharyngeal cancer and neck cancer. Mathematical models have been used in the evaluation of control strategies and making of health policies. Very few mathematical models have been developed on HPV awareness in Kenya. In this study we developed a deterministic model on the impact of HPV infection under vaccination. In this model we incorporated an ineffective media awareness. We computed the equilibrium points of the model and local and global stability analysis was conducted on the reproduction number. The numerical simulation results show that the HPV infections continue to stay in the community due to the ineffective mass media awareness. Sensitivity analysis show that...
Distributed control of a cochlea model ∗
Journal of Advances in Mathematics and Computer Science
Tungiasis is a disease that mostly affects the children,the disabled,alcoholics and the aged in K... more Tungiasis is a disease that mostly affects the children,the disabled,alcoholics and the aged in Kenya and other parts of the world.Despite the intensive research that has been doneon tungiasis disease,the disease remains a threat in Muranga County.In this research, weformulated a model which is mathematical in nature and derived a system of ordinary differentialequations from it,which we used to study the dynamics of tungiasis disease, incorporating properhygiene as a control measure.The basic reproduction number, R0, is calculated using the nextgeneration matrix.We determined the equilibrium points of the model and also carried out theirstability analysis. From stability, both disease free equilibrium and endemic equilibrium points of the model were found to be locally asymptotically stable when R0 < 1 and R0…
Mathematical theory and modeling, 2019
In this study the effects on temperature on applying variable pressure gradient to a MHD fluid fl... more In this study the effects on temperature on applying variable pressure gradient to a MHD fluid flowing between two plates in an inclined magnetic field was carried out. It involved an unsteady hydromagnetic fluid flowing through two plates where the upper plate was porous and moving with a constant velocity in a direction that is contrary to fluid flow direction. The lower plate was non-porous and stationary. In the past years, research studies relating to MHD fluid flow through plates have been done. The information obtained from these studies have been implemented in various industrial systems for instance designing of electromagnetic meters and MHD pumps. However these research studies have been carried out when the pressure gradient was a constant and none when the pressure gradient was a variable, hence the reason why we carried out this investigation. The objective of this project was to determine the effect on temperature on applying variable pressure gradient to a MHD flow i...
Measles virus is a member paramyxoviridae within the genus of morbillivirus. Its genome consist o... more Measles virus is a member paramyxoviridae within the genus of morbillivirus. Its genome consist of approximately 16,000 bases of non-segmented single stranded negative sense RNA. This means that the virus is transcribed immediately upon entry into the cell. The virus spreads from person to person through the release of the aerosol droplets. In this paper, we investigate the transmission of measles virus using the five compartments of susceptible, vaccinated, exposed, infectious and recovered individuals with demographic factors. We give the mathematical model describing the transmission of the measles virus. The results of the model analysis showed that the model has a unique disease free equilibrium (DFE) which is locally asymptotically stable when R0 < 1 and unstable when R0 > 1. We further carried out numerical simulation of the model to investigate the effect of vaccination on the transmission dynamics of the virus. The results showed that there exist a minimum value of th...
Epidemic modeling is an important theoretical approach for investigating the transmission dynamic... more Epidemic modeling is an important theoretical approach for investigating the transmission dynamics of infectious diseases. It formulates mathematical models to describe the mechanisms of disease transmissions and dynamics of infectious agents and then informs the health control practitioners the likely impact of the control methods. In this paper we investigate the spread of an infectious disease in a human population structured into n-patches. The population is initially fully susceptible until an infectious individual is introduced in one of the patches. The interaction between patches is dominated by movement of individuals between patches and also the migration of individuals and therefore any infection occurring in one patch will have a force of infection on the susceptible individuals on the other patches. We build a mathematical model for a metapopulation consisting of n patches. The patches are connected by movement of individuals. For n = 2, we obtained the basic reproducti...
British Journal of Mathematics & Computer Science, 2015
Journal of Advances in Mathematics and Computer Science
Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are respon... more Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are responsible for 99% of human rabies cases and the disease is always fatal once the symptoms appear. In Kenya the disease is still endemic despite the fact that there are ecient vaccines for controlling the disease. In this project, we developed SIRS mathematical model using a system of ordinary dierential equations from the model to study the transmission dynamics of rabies virusin dogs using public health education as a control strategy. The reproduction number R0 was calculated using the Next Generation Matrix. Both disease free and endemics equilibrium points were determined and their stability analysis performed. From the stability analysis results it was found out that the disease free equilibrium point is both locally and globally asymptotically stable when R0 < 1 and the endemic equilibrium point is both locally and globally asymptotically stable when R0 > 1. Numerical simulations...
International Journal of Advances in Scientific Research and Engineering
We investigate shear banding phenomena in the plane Couette flow of viscoelastic fluids.The visco... more We investigate shear banding phenomena in the plane Couette flow of viscoelastic fluids.The viscoelastic fluids are modelled via the Giesekus constitutive equations with stress diffusion. The nonlinear and coupled systems of equations, comprising the momentum equation and the constitutive equations, are solved numerically using semi-implicit finite difference methods. The effects of the fluid parameters on the flow variables are also investigated. Under certain values of the material parameters, we observe formation of shear bands in plane Couette flow.
International Journal of Advances in Scientific Research and Engineering
A fractional-order HTLV type-1 model with transmission from an infected cell to uninfected cell a... more A fractional-order HTLV type-1 model with transmission from an infected cell to uninfected cell and also through mitosis is constructed and investigated. The requirements for the existence of equilibrium points are established. We have generalized the integer theorem introduced by LaSalle into the fractional system and given some adequate requirements for the infection-free equilibrium plus chronic equilibrium being globally asymptotically stable. We employed a numerical technique established for changing the fractional-order derivative to the integer-order derivative to work out the HTLV type-1 model. Numerical simulations are given to illustrate our results. The fractional-order derivatives are defined using the Caputo definition.