On the Jacobi Stability of Two SIR Epidemic Patterns with Demography

In the present work, two SIR patterns with demography will be considered: classical pattern and a modified linear coefficient of infection transmission. By reformulating each first-order differential systems as system second-order equations, we examine nonlinear dynamics from Jacobi stability perspective through Kosambi–Cartan–Chern (KCC) geometric theory. The intrinsic properties studied by determining associated objects, i.e., zero-connection curvature tensor, connection, Berwald five KCC invariants: external force εi—the first invariant; deviation tensor Pji—the second torsion Pjki—the third Riemann–Christoffel Pjkli—the fourth Douglas Djkli—the fifth invariant. order to obtain necessary sufficient conditions for near equilibrium point, determined at point. Furthermore, compare stability, inclusive diagrams related values parameters system.