Browsing by Author "Lyimo, Jacob"

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    Modelling and analysis of a holling type ii stage structured predator-prey system in the presence of harvesting
    (University of Dar es Salaam, 2018) Lyimo, Jacob
    This study, developed and analyzed a stage structured predator-prey system in the presence of harvesting, whereby both involved species grow logistically and prey grows in two stages that is; immature and matured prey. Only matured prey species are consumed by predator and harvested. The aim is to analyze the effect of Harvesting and Predation on a Stage structured Predator-Prey system. It is shown that the solutions of the system are positive and bounded. The two populations co-exist if prey's growth rate, predator's growth and capturing rates are greater than, the threshold value R, it's death rate and threshold value A respectively. Local and global stabilities of all possible equilibrium points are discussed. The results show the co-existence equilibrium point is locally asymptotically stable whenever interior equilibrium point exists and predator's capturing rate is less than one. Also it is globally asymptotically stable if predator's growth rate is greater than death rate, the predator efficiency to convert prey biomass into fertility is less than one and prey's growth rate is less than the sum of harvesting and death rates. Finally some numerical solutions are carried out to support the analytic results. The results show that, predation and harvesting have negative impacts on population dynamics of predator-prey system.
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    Modelling and analysis of a holling type ii stage structured predator-prey system in the presence of harvesting
    (University of Dar es Salaam, 2018) Lyimo, Jacob
    This study, developed and analysed a stage structured predator-prey system in the presence of harvesting, whereby both involved species grow logistically and prey grows in two stages that is; immature and matured prey. Only matured prey species are consumed by predator and harvested. The aim is to analyze the effect of Harvesting and Predation on a Stage structured Predator-Prey system.It is shown that the solutions of the system are positive and bounded. The two populations co-exist if prey’s growth rate, predator’s growth and capturing rates are greater than, the threshold value R, it’s death rate and threshold value A respectively. Local and global stabilities of all possible equilibrium points are discussed. The results show the co-existence equilibrium point is locally asymptotically stable whenever interior equilibrium point exists and predator’s capturing rate is less than one. Also it is globally asymptotically stable if predator’s growth rate is greater than death rate, the predator efficiency to convert prey biomass into fertility is less than one and prey’s growth rate is less than the sum of harvesting and death rates.Finally some numerical solutions are carried out to support the analytic results. The results show that, predation and harvesting have negative impacts on population dynamics of predator-prey system.