TITLE:
Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function
AUTHORS:
Aboudramane Guiro, Dramane Ouedraogo, Harouna Ouedraogo
KEYWORDS:
Discrete Model, Delay, Lyapunov Functional, Nonlinear Incidence, Backward Difference Scheme, Local Stability, Global Stability
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.9,
September
18,
2018
ABSTRACT: In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization
is one. The dynamical properties are investigated (positivity and
the boundedness of solution). By constructing the Lyapunov function, the
general incidence function f must satisfy certain assumptions, under which,
we establish the global stability of endemic equilibrium when R0 >1. The
global stability of diseases-free equilibrium is also established when R0 ≤1.
In addition we present numerical results of the continuous and discrete model
of the different class according to the value of basic reproduction number R0.