Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/999
Title: A VARIABLE HUMAN POPULATION MODEL FOR MALARIA DISEASE WITH DIRECT TRANSMISSION
Authors: IYARE, B.S.E
OSAGIEDE, F.E.U
Issue Date: 2011
Publisher: International Journal of Academic Research
Series/Report no.: 3;5
Abstract: In the modeling of malaria, many of the contributors have always assumed that malaria disease is only transmitted to the human population through infected mosquitoes. However, this assumption is not always true because evidences have shown that direct transmission is through blood transmission. Using the idea of Liming Cai and Xuezhi Li, (2010) a variable human population model for malaria disease with direct transmission is formulated. We showed that our model is mathematically wellposed and has a unique solution. We showed that the stability of the meter in the model can be controlled by a threshold parameter R0. That is, if   H1 m m H H2        Meaning, if 1 0 R  , the disease can persist in the population, and if   H1 m m H H2        , that is, 1 0 R  , the disease-free equilibrium point E0 exists and its locally stable. We proved the global stability of our model using the Lyapunov function and showed that disease-free equilibrium point Eo is globally asymptotically stable when 1 0 R  . The endemic disease free equilibrium was also established when 1 0 R  .
URI: http://hdl.handle.net/123456789/999
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