An SVIR model with vaccination and treatment as interventions and corresponding optimal control problem for these interventions is considered.
Total cost includes costs due to opportunity loss, vaccination efforts (4th degree nonlinear) and treatment efforts (quadratic).
Existence of controls is guaranteed analytically and corresponding optimal control functions are obtained analytically.
Three strategies are defined: A) with vaccination only; B) with vaccination and treatment, for control of disease and C) with treatment only.
Numerically we find: (i) strategy A)- less effective & expensive if vaccination is not highly effective; (ii) Strategy B)- best & least expensive.
Strategy B) not only minimizes cost burden due to opportunity loss and applied control policies but also keeps a tab on infective population.