  In this paper, we derive and analyze a compartmental model for the control of
arboviral diseases which takes into account an imperfect vaccine combined with
individual protection and some vector control strategies already studied in the
literature. After the formulation of the model, a qualitative study based on
stability analysis and bifurcation theory reveals that the phenomenon of
backward bifurcation may occur. The stable disease-free equilibrium of the
model coexists with a stable endemic equilibrium when the reproduction number,
R 0 , is less than unity. Using Lyapunov function theory, we prove that the
trivial equilibrium is globally asymptotically stable; When the disease--
induced death is not considered, or/and, when the standard incidence is
replaced by the mass action incidence, the backward bifurcation does not occur.
Under a certain condition , we establish the global asymptotic stability of the
disease--free equilibrium of the full model. Through sensitivity analysis, we
determine the relative importance of model parameters for disease transmission.
Numerical simulations show that the combination of several control mechanisms
would significantly reduce the spread of the disease, if we maintain the level
of each control high, and this, over a long period.
