A Vaccination Strategy Based on a State Feedback Control Law for Linearizing SEIR Epidemic Models - Biomedical Engineering Systems and Technologies - page 186

be seen from such figures. Such a property is satisfied although all constraints of the
assumption (b) of Theorem 3 are not fulfilled by the system parameters and the cho-
sen control parameters. However, such a result is coherent since such constraints are
sufficient but not necessary to prove the positivity of the system. The switched off
time instant for the vaccination is t ≈ 0 s .

f

1000

900

R(t)

800

700

600

500

400

S(t)

300

E(t)

200

100

I(t)

0

0 5 10 15 20 25 30

Time (days)

Fig. 2. Time evolution of the individual populations with the vaccination control action

14000

12000

10000

8000

6000

4000

2000

0

0 5 10 15 20 25 30

Time (days)

Fig. 3. Time evolution of the vaccination function

The time evolution of the respective partial populations under the application of the
developed control strategy is similar to that obtained under the use of other vaccina-
tion strategies proposed in [1]. The main novelty of the current research is the use of a
systematic method to design a vaccination strategy based on a control technique for
input-output linearization of the SEIR epidemic model by exact state feedback.

5 Conclusions

A vaccination control strategy based on feedback input-output linearization tech-
niques has been proposed to fight against the propagation of epidemic diseases. A
SEIR model with known parameters is used to describe the propagation of the dis-
ease. The stability and the positivity properties of the closed-loop system as well
as the eradication of the epidemics have been proved. Such a strategy has a main
drawback, namely, the control law needs the knowledge of the true values of the