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On the Jacobi Stability of Two SIR Epidemic Patterns With Demography
Version 1
: Received: 28 April 2023 / Approved: 28 April 2023 / Online: 28 April 2023 (07:57:30 CEST)
A peer-reviewed article of this Preprint also exists.
Munteanu, F. On the Jacobi Stability of Two SIR Epidemic Patterns with Demography. Symmetry 2023, 15, 1110. Munteanu, F. On the Jacobi Stability of Two SIR Epidemic Patterns with Demography. Symmetry 2023, 15, 1110.
Abstract
In this work, we consider two SIR patterns with demography: the classical pattern and a modified pattern with a linear transmission coefficient of the infection. By reformulating of each first order differential systems as a system with two second-order differential equations, we investigate the nonlinear dynamics of the system from the Jacobi stability point of view by using the KCC geometric theory. We will study the intrinsic geometric properties of the systems by determining the geometric associated objects: the zero-connection curvature tensor, the nonlinear connection, the Berwald connection, and the five KCC invariants: the first invariant - the external force εi, the second invariant - the deviation curvature tensor Pji, the third invariant - the torsion tensor Pjki, the fourth invariant - the Riemann-Christoffel curvature tensor Pjkli, and the fifth invariant - the Douglas tensor Djkli. In order to obtain necessary and sufficient conditions for the Jacobi stability near the equilibrium points, the deviation curvature tensor will be determined at each equilibrium points. Furthermore, we will compare the Jacobi stability with the classical linear stability, inclusive by diagrams related to the values of parameters of the system.
Keywords
SIR pattern; KCC theory; the deviation curvature tensor; Jacobi stability
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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