Tian, Canrong; Zhang, Qunying; Zhang, Lai Global stability in a networked SIR epidemic model. (English) Zbl 1444.92125 Appl. Math. Lett. 107, Article ID 106444, 5 p. (2020). Summary: A graph Laplacian reaction-diffusion system is introduced to a networked SIR epidemic model. By the means of Lyapunov function, we show that the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than 1, while the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is lower than 1. We extend the stability theory of SIR models with classical Laplacian diffusion to models with graph Laplacian. Cited in 15 Documents MSC: 92D30 Epidemiology 35B35 Stability in context of PDEs 35Q92 PDEs in connection with biology, chemistry and other natural sciences Keywords:network; endemic equilibrium; disease-free equilibrium; Lyapunov function PDFBibTeX XMLCite \textit{C. Tian} et al., Appl. Math. Lett. 107, Article ID 106444, 5 p. (2020; Zbl 1444.92125) Full Text: DOI References: [1] Pastor-Satorras, R.; Castellano, C.; Van Mieghem, P.; Vespignani, A., Epidemic processes in complex networks, Rev. Modern Phys., 87, 925-986 (2015) [2] Bauer, F.; Horn, P.; Lin, Y.; Lippner, G.; Mangoubi, D.; Yau, S. T., Li-Yau inequality on graphs, J. Differential Geom., 99, 359-405 (2015) · Zbl 1323.35189 [3] Chung, Y.; Lee, Y.; Chung, S., Extinction and positivity of the solutions of the heat equations with absorption on networks, J. Math. Anal. Appl., 380, 642-652 (2011) · Zbl 1219.35024 [4] Grigoryan, A.; Lin, Y.; Yang, Y., Yamabe type equations on graphs, J. Differential Equations, 261, 4924-4943 (2016) · Zbl 1351.35038 [5] Grigoryan, A.; Lin, Y.; Yang, Y., Kazdan-Warner equation on graph, Calc. Var. Partial Differential Equations, 55, 92 (2016) · Zbl 1366.58006 [6] Li, M.; Shuai, Z., Global-stability problem for coupled systems of differential equations on networks, J. Differential Equations, 248, 1-20 (2010) · Zbl 1190.34063 [7] Zhang, H.; Small, M.; Fu, X.; Sun, G.; Wang, B., Modeling the influence of information on the coevolution of contact networks and the dynamics of infectious diseases, Physica D, 241, 1512-1517 (2012) · Zbl 1401.92209 [8] Tian, C.; Ruan, S., Pattern formation and synchronism in an allelopathic plankton model with delay in a network, SIAM J. Appl. Dyn. Syst., 18, 531-557 (2019) · Zbl 1416.34071 [9] Hall, J. K., Ordinary Differential Equations (1980), Krieger: Krieger Malabar FL This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.