Symbols | Description | Value | Reference |

$\beta $ | Exposed rate | 0.02 | [2] |

$\gamma $ | Infection rate | 0.29 | [3] |

$\omega $ | Recovered rate | 0.3 | Estimation |

$\varphi $ | Natural death rate | 0.00002 | [6] |

$\theta $ | Rate of losing immunity and move to S from R Compartment. | 0.00002 | Estimation |

$\alpha $ | Birth rate | 0.0004 | [6] |

A | Balancing cost factor | 1000 | Estimation |

B | The weight of the cost of vaccination | 200 | Estimation |

[0, t] | Vaccination period | [0, 12] months | [6] |

[0, u] | Vaccination rate | [0, 0.9] | [6] |

S | Initial Susceptible population | 3000 | [3] |

E | Initial Exposed, Infected, and Recovered Population | 10 | [11] |