TITLE:
Stability Analysis of a Deterministic Epidemic Model in Metapopulation Setting
AUTHORS:
Petros Kelkile Desalegn, Samuel Mwalili, John Mango
KEYWORDS:
Basic Reproduction Ratio, Lyapunov Function, Meta-Population, Disease-Free and the Endemic Equilibrium
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.3,
March
14,
2018
ABSTRACT: We present in this article an epidemic model with
saturated in metapopulation setting. We develop the mathematical modelling of
HIV transmission among adults in Metapopulation setting. We discussed the
positivity of the system. We calculated the reproduction number, If for , then each infectious individual in Sub-Population j infects on average less than one
other person and the disease is likely to die out. Otherwise, if for , then each infectious individual in Sub-Population j infects on average more than one
other person; the infection could therefore establish itself in the population
and become endemic. An epidemic model, where the presence or absence of an
epidemic wave is characterized by the value of both ideas of
the inner equilibrium point of stability properties are discussed.