Reducing vaccination level to eradicate a disease by means of a mixed control with isolation

The present study has investigated mixed control strategy to reduce the required level of vaccination to eradicate a disease. It is well known that despite the advances on the development of new vaccines and control strategies to eradicate diseases, many diseases such as measles, tuberculosis and flu are still persistent. Any effort made to bring some light in this issue should be considered and developed. Here, we present a dynamic analysis of the SIR model to develop a simple but efficient strategy of control based on the simultaneously application of vaccination and isolation. We show how to significantly decrease the required level of vaccination to eradicate a disease. We have also found that a growth in population decreases the effects of isolation in the required time to eradicate a disease. Finally, we noticed that the effect of isolation for both fixed size population or variable population is more significant for lower levels of vaccination, which is particularly interesting in real life situations, where the high levels of vaccination are not undertaken. Numerical simulations are provided to show the effectiveness of the proposed technique.