Analytical investigation of fractional SEIRVQD measles mathematical model

In this paper, we construct and formulate a new mathematical model for the spread of epidemic diseases with vaccination especially for Chinese measles. This model including susceptible (S), exposed (E), infected (I), recovered (R), vaccinated (V), quarantined (Q) and died individuals (D) is been studied by applying Caputo fractional derivatives (CFD). We introduce the feasibility region and prove positively invariant property for this region. Then we prove the existence of a unique solution of our fractional measles model. Furthermore, the equilibrium points of the model are presented and the stability analysis of the model is proved based on Lyapunov and Ulam-Hyer criteria. The basic reproduction number (R_۰) is calculated by the next generation matrix method in order to demonstrate the level of measles virus invasion. Moreover, numerical simulations including data fitting are performed for different fractional orders to illustrate and validate the efficiency of the proposed model.

کلیدواژه ها:

Epidemic model ، fractional SEIRVQD model ، transmission simulation ، Differential equation ، Ulam-Hyer stability ، measles ، Lyapunov stability