Browsing by Author "Sagamiko, Thadei Damas"

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    Analysis of hodgkin-huxley model for the control of animal excitable cell volume
    (University of Dar es Salaam, 2010) Sagamiko, Thadei Damas
    Fourty-seven years ago, in 1963, Alan Hodgkin, Andrew Huxley, and Sir John Eccles were awarded the Nobel prize in physiology or medicine for their discoveries concerning the mechanisms involved in excitation and inhibition in the peripheral and central portions of the nerve cell membrane. They proved the transport of potassium and sodium ions through nerve membranes is possible due to the presence of ion selective channels that control biological electrical signling, and that the frequency of ion transport through the channels can be as high 108 per second. This work gives a short description of Hodgkin-Huxley model (HH- model) and presents a summary of its numerical analysis with focus on varying applied current as to different forms which are Constant (steady), Linear and Stochastic (unsteady).We have described Runge-Kutta method as a numerical method used to solve the model. However this method is incorporated in the softwares that are used to carry out numerical simulations. Results on numerical simulations of the model show that a fluctuating applied current with higher amplitude of oscillation causes an action potential to occur faster than the one with less amplitude of oscillation. Therefore the unsteady current with higher amplitude of oscillation is the best in testing the vitality of a cell and hence its volume control.
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    Modeling optimal control of a threatened prey-predator system: a case of Wildebeest-Lion Prey-Predator relationship in the Serengeti ecosystem
    (University of Dar es Salaam, 2016) Sagamiko, Thadei Damas
    It has been recognized that predator-prey interactions play an important role in the dynamics of species populations and their relationship has continued to be one of the dominant themes in both population ecology and mathematical ecology due to its universal existence and importance. This work presents an optimal control of wildebeest-lion prey-predator relationship in the Serengeti ecosystem. Two threatened prey-predator models with Holling Type II functional response and their control strategies are proposed. The first model considers poaching, retaliatory killings and drought as threats to the system with anti-poaching patrols, construction of strong bomas and dams being suggested as control strategies. The second model considers poaching, drought and disease as threats to the system with prey refuge factor. The disease control strategy is vaccination. Theoretical and optimal control numerical analyses are carried out. The possible impact of using combinations of three controls either one at a time or two at a time on the threatened system is examined. The best result is achieved by taking a combination of all controls. In addition, numerical results agrees with theoretical one in studying the effect of prey refuge which indicates that, its increase causes corresponding increase of the number of prey individuals saved and reducing the number of predator individuals saved due to loss of food. Cost-effectiveness is analyzed using incremental cost-effectiveness ratio where construction of dams and application of anti-poaching patrols are found to be more cost effective than other strategies for first and second model respectively. Finally, validation of model is done using Serengeti lion population density real data.