Author(s)

Petros Kelkile Desalegn, Samuel Mwalili, John Mango

Department of Mathematics, Pan Africa University Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya.

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.

Basic Reproduction Ratio, Lyapunov Function, Meta-Population, Disease-Free and the Endemic Equilibrium

Desalegn, P. , Mwalili, S. and Mango, J. (2018) Stability Analysis of a Deterministic Epidemic Model in Metapopulation Setting. Advances in Pure Mathematics, 8, 219-231. doi: 10.4236/apm.2018.83011.