In [20], a mixed regular and impulsive vaccination action is proposed for a SEIR epidemic mode model which involves also mixed point and distributed delays.
In the first days, approximately until the sixth day as it can be seen in Figure 8, none vaccination action is applied.
The periodic impulsive, rather than regular, vaccination action proposed in [18, 19], can be got from (1.1)–(1.5) with while adding either corresponding "culling" action, or, alternatively, a less drastic "partial removal of susceptible from the habitat" action.
where, and are, respectively, the susceptible, vaccinated, exposed, infected (or infective or infectious), and recovered populations, is the total population being the sum of the above ones, and is a constant vaccination action.
Note that the observation stage is short compared to the observation/control stage; thus the vaccination action can begin a few days later than the infection is detected in the host population.
For example, Sabin [19] controlled successfully measles and poliomyelitis throughout Central and South America, and another example of successful application of this strategy is the U.K. vaccination action against measles in [20].
Thus, there is at least one endemic equilibrium point at which the susceptible, vaccinated, infected, exposed, and recovered populations are positive and the vaccinated population is zero if and only if (i.e., in the absence of vaccination action).
This is due to the fact that the estimation errors converge faster to zero as the observer gain increases (see Figures 10, 11 and 12), and then the switching time t 1 happens earlier and the vaccination action consequences are reached more rapidly.
Multivariate analysis identified three independent significant factors for initiation of vaccination (action and intention): perceived cancer as terrifying disease, school should provide more information on cancer prevention, and comments from relatives and friends having received the vaccine.
