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Zhang, Tianran; Gou, Qingming (2014)
Publisher: Hindawi Publishing Corporation
Journal: The Scientific World Journal
Languages: English
Types: Article
Subjects: Research Article, Science (General), Q1-390, Article Subject
Based on Codeço's cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed c ∗ is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder's fixed point theorem is applied. The nonexistence of traveling wave solutions is proved by two-sided Laplace transform. However, to apply two-sided Laplace transform, the prior estimate of exponential decrease of traveling wave solutions is needed. For this aim, a new method is proposed, which can be applied to reaction-diffusion systems consisting of more than three equations.
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    • Capasso, V, Paveri-Fontana, SL. Mathematical model for the 1973 cholera epidemic in the European Mediterranean region. Revue d’Epidemiologie et de Sante Publique . 1979; 27 (2): 121-132
    • Codeço, CT. Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir. BMC Infectious Diseases . 2001; 1, article 1
    • Goh, KT, Teo, SH, Lam, S, Ling, MK. Person-to-person transmission of cholera in a psychiatric hospital. Journal of Infection . 1990; 20 (3): 193-200
    • Tien, JH, Earn, DJD. Multiple transmission pathways and disease dynamics in a waterborne pathogen model. Bulletin of Mathematical Biology . 2010; 72 (6): 1506-1533
    • Weil, AA, Khan, AI, Chowdhury, F. Clinical outcomes in household contacts of patients with cholera in Bangladesh. Clinical Infectious Diseases . 2009; 49 (10): 1473-1479
    • Andrews, JR, Basu, S. Transmission dynamics and control of cholera in Haiti: an epidemic model. The Lancet . 2011; 377 (9773): 1248-1255
    • Hartley, DM, Morris, JG, Smith, DL. Hyperinfectivity: a critical element in the ability of V. cholerae to cause epidemics?. PLoS Medicine . 2006; 3 (1): 63-69
    • Jensen, MA, Faruque, SM, Mekalanos, JJ, Levin, BR. Modeling the role of bacteriophage in the control of cholera outbreaks. Proceedings of the National Academy of Sciences of the United States of America . 2006; 103 (12): 4652-4657
    • Mukandavire, Z, Liao, S, Wang, J, Gaff, H, Smith, DL, Morris, JG. Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe. Proceedings of the National Academy of Sciences of the United States of America . 2011; 108 (21): 8767-8772
    • Sanches, RP, Ferreira, CP, Kraenkel, RA. The role of immunity and seasonality in cholera epidemics. Bulletin of Mathematical Biology . 2011; 73 (12): 2916-2931
    • Shuai, Z, van den Driessche, P. Global dynamics of cholera models with differential infectivity. Mathematical Biosciences . 2011; 234 (2): 118-126
    • Shuai, Z, Tien, JH, Driessche, PVV. Cholera Models with hyperinfectivity and temporary immunity. Bulletin of Mathematical Biology . 2012; 74 (10): 2423-2445
    • Tian, JP, Wang, J. Global stability for cholera epidemic models. Mathematical Biosciences . 2011; 232 (1): 31-41
    • Mutreja, A, Kim, DW, Thomson, NR. Evidence for several waves of global transmission in the seventh cholera pandemic. Nature . 2011; 477 (7365): 462-465
    • Emch, M, Feldacker, C, Islamand, MS, Ali, M. Global climate and infectious disease: the cholera paradigm. Science . 1996; 274 (5295): 2025-2031
    • Faruque, SM, Islam, MJ, Ahmad, QS. Self-limiting nature of seasonal cholera epidemics: role of host-mediated amplification of phage. Proceedings of the National Academy of Sciences of the United States of America . 2005; 102 (17): 6119-6124
    • Capasso, V, Kunisch, K. A reaction-diffiusion system arising in modelling man- environment diseases. Quarterly of Applied Mathematics . 1988; 46 (3): 431-450
    • Capasso, V, Maddalena, L. Convergence to equilibrium states for a reaction-diffusion system modelling the spatial spread of a class of bacterial and viral diseases. Journal of Mathematical Biology . 1981; 13 (2): 173-184
    • Capasso, V, Wilson, RE. Analysis of a reaction-diffusion system modeling man-environment-man epidemics. SIAM Journal on Applied Mathematics . 1997; 57 (2): 327-346
    • Aniţa, S, Capasso, V. Stabilization of a reaction-diffusion system modelling a class of spatially structured epidemic systems via feedback control. Nonlinear Analysis: Real World Applications . 2012; 13 (2): 725-735
    • Bertuzzo, E, Azaele, S, Maritan, A, Gatto, M, Rodriguez-Iturbe, I, Rinaldo, A. On the space-time evolution of a cholera epidemic. Water Resources Research . 2008; 44 (1)
    • Bertuzzo, E, Casagrandi, R, Gatto, M, Rodriguez-Iturbe, I, Rinaldo, A. On spatially explicit models of cholera epidemics. Journal of the Royal Society Interface . 2010; 7 (43): 321-333
    • Mari, L, Bertuzzo, E, Righetto, L. Modelling cholera epidemics: the role of waterways, human mobility and sanitation. Journal of the Royal Society Interface . 2012; 9 (67): 376-388
    • Diekmann, O. Thresholds and travelling waves for the geographical spread of infection. Journal of Mathematical Biology . 1978; 6 (2): 109-130
    • Lewis, M, Rencławowicz, J, van den Driessche, P. Traveling waves and spread rates for a west nile virus model. Bulletin of Mathematical Biology . 2006; 68 (1): 3-23
    • Radcliffe, J, Rass, L. The asymptotic speed of propagation of the deterministic non-reducible n-type epidemic. Journal of Mathematical Biology . 1986; 23 (3): 341-359
    • Zhao, X-Q, Wang, W. Fisher waves in an epidemic model. Discrete and Continuous Dynamical Systems B . 2004; 4 (4): 1117-1128
    • Xu, D, Zhao, X-Q. Bistable waves in an epidemic model. Journal of Dynamics and Differential Equations . 2004; 16 (3): 679-707
    • Jin, Y, Zhao, X-Q. Bistable waves for a class of cooperative reaction-diffiusion systems. Journal of Biological Dynamics . 2008; 2 (2): 196-207
    • Hsu, C-H, Yang, T-S. Existence, uniqueness, monotonicity and asymptotic behaviour of travelling waves for epidemic models. Nonlinearity . 2013; 26 (1): 121-139
    • Li, W-T, Lin, G, Ruan, S. Existence of travelling wave solutions in delayed reaction-diffusion systems with applications to diffusion-competition systems. Nonlinearity . 2006; 19 (6): 1253-1273
    • Wang, Z-C, Wu, J. Travelling waves of a diffiusive KermackCMcKendrick epidemic model with non-local delayed transmission. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences . 2010; 466 (2113): 237-261
    • Wang, Z-C, Li, W-T, Ruan, S. Traveling fronts in monostable equations with nonlocal delayed effects. Journal of Dynamics and Differential Equations . 2008; 20 (3): 573-607
    • Wang, Z-C, Li, W-T, Ruan, S. Entire solutions in bistable reaction-diffusion equations with nonlocal delayed nonlinearity. Transactions of the American Mathematical Society . 2009; 361 (4): 2047-2084
    • Carr, J, Chmaj, A. Uniqueness of travelling waves for nonlocal monostable equations. Proceedings of the American Mathematical Society . 2004; 132 (8): 2433-2439
    • Perko, L. Diffierential Equations and Dynamical Systems . 2001
    • Irving, RS. Integers, Polynomials, and Rings . 2004
    • Zeilder, E. Nonlinear Functional Analysis and Its Applications I . 1986
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