Global dynamics and bifurcation analysis of a fractional-order SEIR
epidemic model with saturation incidence rate
Abstract
The present paper studies a fractional-order SEIR epidemic model for the
transmission dynamics of infectious diseases such as HIV and HBV that
spreads in the host population. The total host population is considered
bounded, and Holling type-II saturation incidence rate is involved as
the infection term. Using the proposed SEIR epidemic model, the
threshold quantity, namely basic reproduction number R0, is obtained
that determines the status of the disease, whether it dies out or
persists in the whole population. The model’s analysis shows that two
equilibria exist, namely, disease-free equilibrium (DFE) and endemic
equilibrium (EE). The global stability of the equilibria is determined
using a Lyapunov functional approach. The disease status can be verified
based on obtained threshold quantity R0. If R0 < 1, then DFE
is globally stable, leading to eradicating the population’s disease. If
R0 > 1, a unique EE exists, and that is globally stable
under certain conditions in the feasible region. The Caputo type
fractional derivative is taken as the fractional operator. The
bifurcation and sensitivity analyses are also performed for the proposed
model that determines the relative importance of the parameters into
disease transmission. The numerical solution of the model is obtained by
the generalized Adams- Bashforth-Moulton method. Finally, numerical
simulations are performed to illustrate and verify the analytical
results.