TITLE:
Solutions of Impulsive Diffusion and Von-Foerster-Makendrick Models Using the B-Transform
AUTHORS:
Benjamin Oyediran Oyelami, Samson Olatunji Ale
KEYWORDS:
B-Transform; Impulsive Diffusion; Von-Foerster-Makendrick Models; Residue Theorem; Maple Symbolic Programme and Asymptotic Expansion
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.12,
December
3,
2013
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.