On exact integrability of a Covid-19 model: SIRV

In this study, the integrability conditions and the exact analytical solutions of the initial-value problem defined for the prominent SIRV model used for the pandemic Covid-19 are investigated by using the partial Hamiltonian approach based on the theory of Lie groups. Two different cases are considered with respect to the model parameters. In addition, the integrability properties and the associated approximate and exact analytical solutions to the SIRV model are analyzed and investigated by considering two different phase spaces. Furthermore, the graphical representations of susceptible, infected, recovered, and vaccinated population fractions evolving with time for subcases are introduced and discussed.