Department of Mathematics

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https://keffi.nsuk.edu.ng/handle/20.500.14448/3873

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Browsing Department of Mathematics by Author "Emmanuel, Atanyi Yusuf"

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    Mathematical prototype for the control of malaria by interrupting the life cycle of the Anopheles mosquito through the use of biological enemies in the larva, pupa and adult stages
    (Department of Mathematics, Nasarawa State University Keffi, 2023-01-19) Emmanuel, Atanyi Yusuf; Oduwole, H.K.; Umar, Mallam Abdulkarim
    Mathematical prototype to fight malaria by interrupting the life cycle of the Anopheles mosquito through the use of biological enemies in the larval, pupal and adult stages has been derived to eradicate larvae, pupae and adult Anopheles mosquitoes using natural predators. The new model is a control flowchart of the predator-prey interaction model in the mosquito life cycle, considering an open population of mosquitoes and predators. These models provide a osolid understanding of malaria control in our environment, especially when models are based on vector population ecology; and a solid understanding of transmission-relevant parameters and variables Model equations were derived using parameters and variables from the model Stability analysis of free equilibrium states was analyzed simultaneously using equilibrium point, Maple software, elimination and substitution methods. The number of larvae that pupate is almost zero, and the number ofp upae that turn into adults is minimal, and the number of adults that'escape to the vector stage is negligible, which means that thd life cycle could be disrupted at larval, pupal and adult stages with the introduction of natural enemies, with the natural implication 'there will be no adult Anopheles mosquito for transmission of the malaria. The contribution of this research to knowledge is to produce the model or the mathematical formula and the biologically sound methods that will contribute to the eradication of the adult Anopheles mosquito, which will also lead to° the eradication of malaria in our society.
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    Modelling the Effects of Three Natural Predators on the Aquactic and Adult Stages of Anopheles Mosquitoes in the Control of Malaria Transmission
    (Department of Mathematics, Nasarawa State University Keffi, 2023-01-16) Emmanuel, Atanyi Yusuf; Oduwole, H.K.; Umar, Mallam Abdulkarim
    Modelling the effects of three natural predators on the aquatic and adult anopheles’ mosquitoes in the control of malaria transmission was derived aimed’at "eradicating anopheles’ larva, pupa and adult anopheles' mosquito by introduction of natural predators ucopepods, tadpoles and purple martins” so that there should not be anopheles ’ adult mosquito for malaria transmission in our society. The new model is a control flow diagram of predator-prey interaction model in mosquito life-cycle. The population is sub-divided based on mosquito life- cycle and natural predators. Under a mosquito life-cycle, the population is divided into four compartments', * Egg compartment E(t), Larva compartment L(t), Pupa compartment P(t), and Adult compartment A(t), and natural predators, it is divided into three compartments’, namely; Copepods CP(t), Tadpoles TP(t) and Purple martins PM (t). From the stability analysis of steady state we observed that the model free equilibrium state is stable, implies that the equilibrium point or steady state is stable and the stability of the model (1) - (10) means, there will not be anopheles adult mosquito ip our society for malaria transmission and from the idea of Beltrami’s conditions and Diekmann condition, we observed that the Determinant of the Jacobian matrix is greater than zero {Det(J) > 0}, Trace of the Jacobian matrix is less than zero {Tr(j) < 0} and R0 < 1 which implies that the model disease free equilibrium state is stable. Hence the number of larva that transform to pupa ♦ is almost zero and the number of pupa that develop to adult is minimal and number of adult that escape to vector stage are inconsequential and microscopic and that means the life-cycle could be broken at the larva, pupa, and adult stages with the introduction of natural predators, with the natural implication there will not be anopheles adult mosquito for malaria transmission and we also use maple for symbolical and numerical solution and presented the results graphically.
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    The Pictorial Integral of Malaria Control with Maple
    (Department of Mathematics, Nasarawa State University Keffi, 2023-01-03) Emmanuel, Atanyi Yusuf; Oduwole, H.K.; Umar, Mallam Abdulkarim
    The pictorial integral of malaria control with maple has bepn derived to eradicate larvae, pupae and adult Anopheles mosquitoes using natural predators to eradicate "copepods, tadpoles and purple swallows" ( an organism that eats mosquitoes). The new model is a control flowchart of the predator-prey interaction model in the mosquito life cycle, considering an open population of mosquitoes and predators. These models provide a solid understanding of malaria control in our environment, especially when models are based on vector population ecology and a solid understanding of transmission-relevant parameters and variables Model equations were derived using parameters and variables from the model Stability analysis of free equilibrium states was analyzed simultaneously using equilibrium point, Maple software', elimination and substitution methods. Therefore, the number of larvae that pupate is almost zero, and the number of pupae that turn into adults is minimal, and the number of adults that escape to the vector stage is negligible, this means that the life cycle could be disrupted at the end of the larval, pupal and adult stages with the introduction of natural enemies, with the natural implication that there will be no adult Anopheles mosquito for transmission of the malaria, and we also use maple for the symbolic and numerical solution and graphically presented the results. . The contribution of this research to knowledge is to produce the mathematical formula and the biologically sound methods that will contribute to the eradication of the adult Anopheles mosquito, which will also lead to the eradication of malaria in our society. ,