RP-Department of Mathematics

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Browsing RP-Department of Mathematics by Author "Chepkwony, Isaac"

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    Investigating the Impact of TB or COVID-19 Infections on a Population Suffering from TB/COVID-19 Coinfection
    (Asian Journal of Probability and Statistics, 2024) Githinji, Mary Ng’endo; Chepkwony, Isaac
    The discovery that the spread of tuberculosis reduced significantly in the last two years has been associated with the preventive measures placed to combat the spread of COVID-19. This shows a string correlation between the spread of COVID-19 and tuberculosis in any population. It is worth noting that tuberculosis and COVID-19 are among the leading most deadly diseases in the world today. The correlation in their spread also leaves us to believe that the spread of one can enhance the spread of the other. Hence, we propose the situation where a population is co-infected with the two diseases. The mathematical model is formulated using conservative laws and the resulting model analysed. The stability of the co-infection is analysed and the non-negativity conditions for the solution is established. It is found that tuberculosis sub-population reaches the highest capacity when the recruitment into the COVID-19 subpopulation is the lowest while the COVID 19 sub-population is attained when the rate of recruitment into the COVID-19 subpopulation is the highest.
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    A Mathematical Model of Rabies Transmission Dynamics in Dogs Incorporating Public Health Education as a Control Strategy -A Case Study of Makueni County
    (Sciencedomain International, 2020) Musaili, Jane S.; Chepkwony, Isaac
    Rabies is a zoonotic viral disease that affects 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 efficient vaccines for controlling the disease. In this project, we developed SIRS mathematical model using a system of ordinary differential equations from the model to study the transmission dynamics of rabies virus in 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 done using Matlab indicated that education of the public on administration of both pre and post exposure vaccines to dogs and responsible dog ownership