Fig. 1

Schematic diagram of the model in which the population is divided into nine states: Susceptible \(S(t)\), Lockdown \(L(t)\), Exposed \(E(t)\), Infected \(I(t)\), Recovered \(R(t)\), Vaccinated \(V(t)\), Vaccinated exposed \({E}_{V}(t)\), Vaccinated infected \({I}_{V}(t)\) and Vaccinated Recovered \({R}_{V}\left(t\right)\)