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Dynamics of a networked connectivity model of epidemics

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  • A networked connectivity model of waterborne disease epidemics on a site of $n$ communities is studied. Existence and local stability analysis for both the disease-free equilibrium and the endemic equilibrium are studied. Using an appropriate Lyapunov function and Lasalle invariance principle, global asymptotic stability of the disease-free equilibrium point is established. Existence of a transcritical bifurcation at the disease outbreak is also proved. This work extends previous research in networked connectivity models of epidemics.
    Mathematics Subject Classification: Primary: 37B25, 92D30; Secondary: 92D25.


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  • [1]

    F. Albertini and D. D'Alessandro, Asymptotic stability of continuous-time systems with saturation nonlinearities, Systems & Control Letters, 29 (1996), 175-180.doi: 10.1016/S0167-6911(96)00052-7.


    A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics, 9. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994.doi: 10.1137/1.9781611971262.


    C. Castillo-Chavez, Z. Feng and W. Huang, On the computation of $R_0$ and its role on global stability, Math. Appr. for Emerg. and Reemerg. Infect. Dis, 125 (2002), 229-250.


    H. Freedman, S. Ruan and M. Tang, Uniform persistence and flows near a closed positively invariant set, J. Dynamics & Diff. Equations, 6 (1994), 583-600.doi: 10.1007/BF02218848.


    M. Gatto, L. Mari, E. Bertuzzo, R. Casagrandi, L. Righetto, I. Rodriguez-Iturbe and A. Rinaldo, Generalized reproduction numbers and the prediction of patterns in waterborne disease, Proceed. Nat. Acad. of Scienc., 109 (2012), 19703-19708.doi: 10.1073/pnas.1217567109.


    Z. Hu, Z. Teng and L. Zhang, Stability and bifurcation analysis in a discrete SIR epidemic model, Mathematics & Computers in Simulation, 97 (2014), 80-93.doi: 10.1016/j.matcom.2013.08.008.


    J. P. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976.doi: 10.1137/1.9781611970432.


    M. Li, J. Graef, L. Wang and J. Karsai, Global dynamics of a SEIR model with varying total population size, Mathematical Biosciences, 160 (1999), 191-213.doi: 10.1016/S0025-5564(99)00030-9.


    J. Rebaza, Dynamics of prey threshold harvesting and refuge, Computational & Applied Mathematics, 236 (2012), 1743-1752.doi: 10.1016/j.cam.2011.10.005.


    E. Seneta, Nonnegative Matrices and Markov Chains, Springer-Verlag, New York, 1981.doi: 10.1007/0-387-32792-4.


    Z. Shuai and P. van den Driessche, Global stability of infectious disease models using Lyapunov functions, SIAM J. of Applied Mathematics, 73 (2013), 1513-1532.doi: 10.1137/120876642.


    J. R. Silvester, Determinants of block matrices, Mathematical Gazette, 84 (2000), 460-467.doi: 10.2307/3620776.


    H. L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, Cambridge, 1995.doi: 10.1017/CBO9780511530043.


    J. P. Tian, S. Liao and J. Wang, Analyzing the infection dynamics and control strategies of cholera, Discr. Cont. Dynam. Syst. 2013, Dynamical Systems, Differential Equations and Applications. 9th AIMS Conference. Suppl., (2013), 747-757.


    C. Torres Codeço, Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir, BMC Infectious Diseases, 1 (2001), 1-14.doi: 10.1186/1471-2334-1-1.

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