  In this paper, we derive and analyse a model for the control of arboviral
diseases which takes into account an imperfect vaccine combined with some other
mechanisms of control already studied in the literature. We begin by analyse
the basic model without controls. We prove the existence of two disease-free
equilibrium points and the possible existence of up to two endemic equilibrium
points (where the disease persists in the population). We show the existence of
a transcritical bifurcation and a possible saddle-node bifurcation and
explicitly derive threshold conditions for both, including defining the basic
reproduction number, R 0 , which determines whether the disease can persist in
the population or not. The epidemiological consequence of saddle-node
bifurcation (backward bifurcation) is that the classical requirement of having
the reproduction number less than unity, while necessary, is no longer
sufficient for disease elimination from the population. It is further shown
that in the absence of disease--induced death, the model does not exhibit this
phenomenon. We perform the sensitivity analysis to determine the model
robustness to parameter values. That is to help us to know the parameters that
are most influential in determining disease dynamics. The model is extended by
reformulating the model as an optimal control problem, with the use of five
time dependent controls, to assess the impact of vaccination combined with
treatment, individual protection and vector control strategies (killing adult
vectors, reduction of eggs and larvae). By using optimal control theory, we
establish optimal conditions under which the disease can be eradicated and we
examine the impact of a possible combined control tools on the disease
transmission. The Pontryagin's maximum principle is used to characterize the
optimal control. Numerical simulations, efficiency analysis and cost
effectiveness analysis show that, vaccination combined with other control
mechanisms, would reduce the spread of the disease appreciably, and this at low
cost.
