Browsing by Author "Arop, Martin"

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    Determining important parameters in Ebola epidemics
    (International Journal of Sciences: Basic and Applied Research (IJSBAR), 2016) Arop, Martin; Luboobi, Livingstone; Nannyonga, Betty
    The dynamics of Ebola can best be understood using a mathematical model that determines its dynamics in the community. The model designed in this study explicitly incorporates the latency period, the different transmission compartments, and immigration and emigration effects. The steady states of the system are analysed for existence of equilibria and their stability investigated. From qualitative analysis of the model, it is established that a disease-free equilibrium exists and is stable when ℛ0<1. When ℛ0>1, an endemic equilibrium state exists and is stable. Results show further that the model undergoes a hopf bifurcation at the endemic equilibrium and exhibits periodic oscillations. Sensitivity analysis shows that the most effective control measures are increasing hospitalization and reducing transmission rates. The numerical simulations performed demonstrated the theoretical results.
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    Optimal actuator placement for control of vibrations induced by pedestrian-bridge interactions
    (Mathematics in Applied Sciences and Engineering, 2023-09-03) Arop, Martin; Kasumba, Henry; Kasozi, Juma; Berntsson, Fredrik
    In this paper, an optimal actuator placement problem, with a linear wave equation as the constraint, is considered. In particular, this work presents the framework for finding the best location of actuators depending upon the given initial conditions, and where the dependence on the initial conditions is averaged out. The problem is motivated by the need to control vibrations induced by pedestrian-bridge interactions. An approach based on the shape optimization techniques is used to solve the problem. Specifically, the shape sensitivities involving a cost functional are determined using the averaged adjoint approach. A numerical algorithm based on these sensitivities is used as a solution strategy. Numerical tests illustrate the theoretical results.