Dynamical behavior of the SEIARM-COVID-19 related models

In this study, the analytical, integrability, and dynamical properties of an epidemic COVID-19 model called SEIARM, a six-dimensional coupled nonlinear system of ordinary differential equations from the mathematical point of view, are investigated by the artificial Hamiltonian method based on Lie symmetry groups. By constraining some constraint relations for the model parameters using this method, Lie symmetries, first integrals, and analytical solutions of the model are studied. By examining key factors like how many people are susceptible, infected, or recovered, we unveil hidden patterns and “constraints” within the model. These “constraints” show us how the virus might spread under different conditions, especially when a crucial number called $\Psi$ is between 0 and 1, providing valuable insights into the potential spread of COVID-19 and the effectiveness of control measures. The analytical solutions and their graphical representations for some real values of model parameters obtained from China during the pandemic period are also provided.