Abstract
In this paper, we construct and formulate a new mathematical model for the spread of epidemic diseases with vaccination. The proposed model is composed of eight compartments, namely susceptible (S), exposed (E), infected (I), recovered (R), vaccinated (V ), quarantined (Q) and died (D). We prove the existence of a unique solution. Additionally, the region of the feasibility of the system and equilibrium points are presented. In order to indicate the level of viral invasion and demonstrate the ability of infection transmission, we calculate the basic reproduction number ( R 0 ) by the next generation matrix method. Furthermore, the sensitivity of the basic reproduction number ( R 0 ) concerning the fluctuations of the biological parameters of the presented model has been investigated. Finally, Numerical simulations are performed using MATLAB to illustrate and validate the efficiency of the proposed model and its accordance using real data for Chinese measles and Portugal's COVID-19 outbreaks.
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