Solutions of Impulsive Diffusion and Von-Foerster-Makendrick Models Using the B-Transform

Benjamin Oyediran  Oyelami; Samson Olatunji  Ale

doi:10.4236/am.2013.412223

Benjamin Oyediran Oyelami, Samson Olatunji Ale

Abstract: In this paper we explore the possibility of using the scientific computing method to obtain the inverse B-Transform of Oyelami and Ale [1]. Using some suitable conditions and the symbolic programming method in Maple 15 we obtained the asymptotic expansion for the inverse B-transform then used the residue theorem to obtain solutions of Impulsive Diffusion and Von-Foerster-Makendrick models. The results obtained suggest that drugs that are needed for prophylactic or chemotherapeutic purposing the concentration must not be allowed to oscillate about the steady state. Drugs that are to be used for immunization should not oscillate at steady state in order to have long residue effect in the blood. From Von-Foerster-Makendrick model, we obtained the conditions for population of the specie to attain super saturation level through the “dying effect” phenomenon ([2-4]). We used this phenomenon to establish that the environment cannot accommodate the population of the specie anymore which mean that a catastrophic stage t* is reached that only the fittest can survive beyond this regime (i.e. t > t*) and that there would be sharp competition for food, shelter and waste disposal etc.

Keywords: B-Transform; Impulsive Diffusion; Von-Foerster-Makendrick Models; Residue Theorem; Maple Symbolic Programme and Asymptotic Expansion

Cite this paper: Oyelami, B. and Ale, S. (2013) Solutions of Impulsive Diffusion and Von-Foerster-Makendrick Models Using the B-Transform. Applied Mathematics, 4, 1637-1646. doi: 10.4236/am.2013.412223.

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