Analytical solution of the fractional and global stability of multicompartment non-linear epidemic model

Abstract

In this paper the Multicompartment epidemiological model assumes that, given a con-
tagious illness, a population can be partitioned into individuals that are susceptible to the illness,
infected by the illness, and recovered from the illness.S(t) Number of individuals at time t susceptible
to the illness; I(t);i = 1,2,3,4 Number of individuals at time t infected with the illness.RS(t) Total
number of survivors of the illness at time t , RD(t) Total number of deaths due to the illness at time t.
The stability of a disease-free status equilibrium and the existence of endemic equilibrium can
be determined by the ratio called the basic reproductive number. Laplace-adomian decomposition
method is used to compute an analytical solution of the model study. This paper study the equilibrium,
local , global stability under certain conditions.