Browsing by Author "Samson, Michael"

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    Harvesting of a single-species (nile tilapia) system incorporating stage structure and toxicity using a delay model
    (University of Dar es Salaam, 2012) Samson, Michael
    Great attention has been paid by many researchers to study the dynamical behavior of single-species stage structured models under the influence of toxicant. Wu and Chen (2009) studied a single species stage structured system incorporating both toxicant and harvesting without taking into account a delay time for the population to progress from immature to maturity stage. This study therefore by considering a delay time, a single species (Nile Tilapia) delayed stage-structured model incorporating both toxicant and harvesting was formulated and analyzed to study its dynamics. The model consisted of two developmental stages, namely immature and mature populations. Both qualitative methods and numerical simulation have been employed to analyses the model. In qualitative analysis, the trivial and two nontrivial steady states were obtained. Both trivial and nontrivial steady states were found to be asymptotically stable. The interior nontrivial steady state was found to be globally asymptotically stable. The graphs obtained from simulation of the model depict this phenomenon as well. It was also found that as toxicant level increases both populations of immature and mature Nile Tilapia decrease with a possibility of extinct. We then considered the system with the variable harvest effect. We explored the existence of bionomic equilibrium and also found three bionomic steady states. The bionomic (interior) steady state was found to be a stable spiral. Numerical simulation also illustrates the stable spiral and global stability of the bionomic equilibrium. Lastly, the optimal harvesting policy was established by employing Pontryagm's maximum principle. It was recommended that all the government of the nations around Lake Victoria to have stern regulations that avoid dumping of toxicant substances in the lake and also to create fish regulatory board that will control harvesting of Nile Tilapia.