Browsing by Author "Ochwach, Jimrise O."

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Mathematical Modeling of Host - Pest Interactions in Stage-Structured Populations: A Case of False Codling Moth [Thaumatotibia leucotreta]
(Scitech Research Organisation (SRO), 2021-09) Ochwach, Jimrise O.; Okongo, Mark O.; Muraya, Moses M.; ; ;
False codling moth (FCM) (Thaumatotibia lucotreta) is a significant pest due to its potential economic 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 coexistence equilibria are established. The model is analysed numerically and graphically represented to justify the analytical results.
A NOTE ON THE BASIC REPRODUCTION NUMBER: NOVEL CORONA VIRUS (2019-nCOV)
(Chuka University, 2021) Ochwach, Jimrise O.; Okongo, Mark O.; Muraya, Moses
The basic reproductive number, R 0, is the expected number of secondary infections produced by a single individual during his or her entire infectious period, in a completely susceptible population. This concept is fundamental to the study of epidemiology and within-host pathogen dynamics. It is often used as a threshold parameter that can predicts whether an infection will spread or not. Since the outbreak of 2019 novel corona virus disease (COVID-19) in Wuhan and other cities of China the growth and spread of this disease is of a growing global concern. Many studies have been carried out and are continued to be carried to model the spread and subsequent control of the disease. In this paper, we give a brief overview of common methods of formulating R 0 from deterministic, non-structured models. Finally, we survey the recent use of R 0 in assessing the spread of novel corona virus
Stability Analysis of the Modified Advection-Dispersion Model for Nitrate Leaching into Groundwater
(2020) Ochwach, Jimrise O.; Musundi, Sammy W.; Okong’o, Mark O.
Nitrogen is a vital nutrient that enhances plant growth which has motivated the intensive use of nitrogen-based fertilizers to boost crop productivity. However, Pollution by nitrate is a globally growing problem due to the population growth, increase in the demand for food and inappropriate Nitrogen application. The complexities and challenges in quantifying nitrate leaching have led to development of a range of measurement and modeling techniques. However, most of them are not widely applied due to their inaccuracy. This calls for new approaches in which nitrate leaching can be analysed in order to give better understanding of nitrate fate and transport process for proper management of groundwater. This study presents a mathematical model to analyse nitrate leaching into groundwater from the advection-dispersion equation. The advection-dispersion equation is modified by incorporating soil porosity and volumetric water content of the soil. The stability of the model has been performed by the Von Neumann stability condition after performing descritization using the Cranck-Nicolson scheme and finite difference scheme. The model is conditionally stable for all ranges of angle(κ), when Von Neumann stability condition is applied for both the Cranck-Nicolson scheme and finite difference scheme. The results provide science-based input into best alternative mathematical model which can be used to analyse leaching of nitrate into groundwater.