Browsing by Author "Okongo, M. O."

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Mathematical Analysis of a Comprehensive HIV AIDS Model: Treatment versus Vaccination
(HIKARI Ltd,, 2013) Okongo, M. O.; Kirimi, J.; Murwayi, A. L. Murwayi; Muriithi, D. K.
A comprehensive deterministic HIV/AIDS transmission model incorporating social behaviour, treatment, vaccination, stages of infection, age structures, discrete time delay and vertical transmission is presented and rigorously analyzed. Two age structures are considered with group one consisting of children aged (0 - a) years and group two consisting of adults aged (a) years and above. In this study we investigate wether a trade-off exists between vaccination and treatment. Numerical simulations shows that treatment that does not reduce infectiousness is worse than when the treatment is not applied at all, however when coupled with effective counseling, then it is very effective in combating the spread of the disease and finally eliminating it. A trade off seems to exists between vaccination and treatment and therefore careful considerations should be made when vaccination and treatment is to be applied together because a combination of the two could be counterproductive or helpful depending on how it is implemented.
Mathematical Modeling of Host - Pest Interac- Tions in Stage-Structured Populations: A Case of False Codling Moth [Thaumatotibia Leucotreta ]
(Scitech Research Organisation(SRO)., 2021) Ochwach, J. O.; Okongo, M. O.; Muraya, M. M.
False codling moth (FCM) (Thaumatotibia lucotreta ) is a significant pest due to its potential eco- nomic impact on many susceptible fruits in most temperate regions of the world. Efforts to control the codling moth in the past mostly relied on the use of broad spectrum insecticide sprays, which has resulted in the development of insecticide resistance, and the disruption of the control of secondary pests. Understanding the dynamic of this pest is of great in importance in order to effectively employ the most effective control strategies. In this study, a mathematical model of host-false codling moth interactions is developed and qualitatively analysed using stability theory of system of differential equations. The basic offspring number with respect to FCM free equilibrium is obtain using next generation matrix. The condition for local and global asymptotic stability of FCM free and coexis- tence equilibria are established. The model is analysed numerically and graphically represented to justify the analytical results.
MATHEMATICAL MODELING OF STERILE INSECT TECHNIQUE FOR CONTROL OF FALSE CODLING MOTH
(Chuka University, 2022) Ochwach, J. O.; Okongo, M. O.; Muraya, M.
The Sterile Insect Technique (SIT) is a biological and nonpolluting method of control of pest population in a farm. This method relies on the release of sterile male False Codling Moth (FCM) in order to reduce the population fertile female FCM in the farm. In this study a mathematical model that simulates the interaction between the susceptible host, sterile male FCM and the wild FCM population is developed. The local and global stability analysis of the model is analyzed and found to be asymptotically stable when . A threshold number of sterile insect FCM above which the control of FCM is effective is determined. The results are reorganized as possible strategies for control of FCM and illustrated.