On the dynamics of a vaccination model with multiple transmission ways

Anderson, R.M. and May, R.M.(1990). Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford.Search in Google Scholar

Arino, J.C., McCluskey, C. and van den Driessche P. (2003).Search in Google Scholar

Global results for an epidemic model with vaccination that exhibits backward bifurcation, SIAM Journal on Applied Mathematics, 64(1): 260-276.10.1137/S0036139902413829Search in Google Scholar

Blayneh, K.W., Gumel, A.B., Lenhart, S. and Clayton, T. (2010).Search in Google Scholar

Backward bifurcation and optimal control in transmission dynamics of West Nile Virus, Bulletin of Mathematical Biology 72(4): 1006-1028.10.1007/s11538-009-9480-020054714Search in Google Scholar

Brauer, F. (2004). Backward bifurcations in simple vaccination models, Journal of Mathematical Analysis and Application 298(2): 418-431.10.1016/j.jmaa.2004.05.045Search in Google Scholar

Blower, S.M. and Dowlatabadi, H. (1994). Sensitivity and uncertainty analysis of complex models of disease transmission: An HIV model, as an example, International Statistical Review 62(2): 229-243.10.2307/1403510Search in Google Scholar

Buonomo, B. and Lacitignola, D. (2011). On the backward bifurcation of a vaccination model with nonlinear incidence, Nonlinear Analysis: Modelling and Control 16(1): 30-46.10.15388/NA.16.1.14113Search in Google Scholar

Buonomo, B. and Lacitignola, D. (2008). On the dynamics of an SEIR epidemic model with a convex incidence rate, Ricerche di Matematica 57(2): 261-281.10.1007/s11587-008-0039-4Search in Google Scholar

Buonomo, B. and Lacitignola, D. (2010). Analysis of a tuberculosis model with a case study in Uganda, Journal of Biological Dynamics 4(6): 571-593.10.1080/1751375090351844122881205Search in Google Scholar

Castillo-Chavez, C. and Song, B.(2004). Dynamical models of tubercolosis and their applications, Mathematical Biosciences and Engineering 1(2): 361-404.10.3934/mbe.2004.1.36120369977Search in Google Scholar

Capasso, V. and Paveri-Fontana, S.L. (1979). A mathematical model for the 1973 cholera epidemic in the European Mediterranean region, Revue D’Epid´emiologie de Sant´e Publique 27(2): 121-132.Search in Google Scholar

Chitnis, N., Cushing, J.M. and Hyman, J.M.(2006). Bifurcation analysis of a mathematical model for malaria transmission, SIAM Journal of Applied Mathematics 67(1): 24-45.10.1137/050638941Search in Google Scholar

Chitnis, N., Cushing, J.M. and Cushing, J.M. (2008). Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of Mathematical Biology 79(5): 1272-1296.10.1007/s11538-008-9299-018293044Search in Google Scholar

Codec¸o, C.T. (2001). Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir, BMC Infectious Diseases, 1:1.10.1186/1471-2334-1-1Search in Google Scholar

Dietz, K. and Schenzle, D.(1985). Mathematical models for infectious disease statistics, in A.C. Atkinson and S.E.10.1007/978-1-4613-8560-8_8Search in Google Scholar

Fienberg (Eds.), Centenary Volume of the International Statistical Institute, Springer-Verlag, Berlin, pp. 167-204.Search in Google Scholar

Feckan, M. (2001). Criteria on the nonexistence of invariant Lipschitz submanifolds for dynamical systems, Journal of Differential Equations 174(2): 392-419.10.1006/jdeq.2000.3943Search in Google Scholar

Gani, J., Yakowitz, S. and Blount, M. (1997). The spread and quarantine of HIV infection in a prison system, SIAMJournal on Applied Mathematics 57(6): 1510-1530.10.1137/S0036139995283237Search in Google Scholar

Gumel, A.B. and Moghadas, S.M. (2003). A qualitative study of a vaccination model with non-linear incidence, Applied Mathematics and Computation 143(2-3): 409-419.10.1016/S0096-3003(02)00372-7Search in Google Scholar

Hartley, D.M., Morris, J.G. and Smith, D.L. (2006).Search in Google Scholar

Hyperinfectivity: A critical element in the ability of V. cholerae to cause epidemics?, PLoS Medicine 3(1): 63-69.Search in Google Scholar

Hethcote, H.W. (2000). The mathematics of infectious diseases, SIAM Review 42(4):599-653.10.1137/S0036144500371907Search in Google Scholar

Korn, G.A. and Korn, T.M. (2000). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for References and Review, Dover Publications, Mineola, NY.Search in Google Scholar

Kribs-Zaleta, C.M. (1999). Structured models for heterosexual disease transmission, Mathematical Biosciences 160(1): 83-108.10.1016/S0025-5564(99)00026-7Search in Google Scholar

Kribs-Zaleta, C.M. and Martchevab, M. (2002). Vaccination strategies and backward bifurcation in an age-since-infection structured model, Mathematical Biosciences 177/178: 317-332.10.1016/S0025-5564(01)00099-2Search in Google Scholar

Kribs-Zaleta, C.M. and Velasco-Hernandez, J.X. (2000). A simple vaccination model with multiple endemic states, Mathematical Biosciences 164(2): 183-201.10.1016/S0025-5564(00)00003-1Search in Google Scholar

Li, G. and Zhen, J. (2005). Global stability of an SEI epidemic model with general contact rate, Chaos Solitons & Fractals 23(3): 997-1004.10.1016/S0960-0779(04)00355-8Search in Google Scholar

Liao, S. and Wang, J. (2011). Stability analysis and application of a mathematical cholera model, Mathematical Biosciences and Engineering 8(3):733-752.10.3934/mbe.2011.8.733Search in Google Scholar

Liu, X. and Wang, C. (2010). Bifurcation of a predator-prey model with disease in the prey, Nonlinear Dynamics 62(4):841-850.10.1007/s11071-010-9766-7Search in Google Scholar

Marino, S., Hogue, I., Ray, C.J. and Kirschner, D.E.(2008). A methodology for performing global uncertainty and sensitivity analysis in system biology, Journal of Theoretical Biology 254(1): 178-196.10.1016/j.jtbi.2008.04.011Search in Google Scholar

Moghadas, S.M. and Gumel, A.B. (2002). Global stability of a two-stage epidemic model with generalized non-linear incidence, Mathematics and Computers in Simulation 60(1-2): 107-118.10.1016/S0378-4754(02)00002-2Search in Google Scholar

Mukandavire, Z., Liao, S., Wang, J., Gaff, H., Smith, D.L. and Morris, J.G. (2011). 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 108(21): 8767-8772.10.1073/pnas.1019712108Search in Google Scholar

Samsuzzoha, M.D., Singh, M. and Lucy, D. (2012). A numerical study on an influenza epidemic model with vaccination and diffusion, Applied Mathematics and Computation 219(1): 122-141.10.1016/j.amc.2012.04.089Search in Google Scholar

Song, X., Jiang, Y. and Wei, H.(2009). Analysis of a saturation incidence SVEIRS epidemic model with pulse and two time delays, Applied Mathematics and Computation 214(2): 381-390.10.1016/j.amc.2009.04.005Search in Google Scholar

Szyma´nska, Z. (2013). Analysis of immunotherapy models in the context of cancer dynamics, International Journal of Applied Mathematics and Computer Science 13(3): 407-418.Search in Google Scholar

Sanchez, L.A. (2010). Existence of periodic orbits for high-dimensional autonomous systems, Journal of Mathematical Analysis and Applications 363(2): 409-418.10.1016/j.jmaa.2009.08.058Search in Google Scholar

Tien, J.H. and Earn, D.J.D. (2010). Multiple transmission pathways and disease dynamics in a waterborne pathogen model, Bulletin of Mathematical Biology 72(6): 1502-1533.10.1007/s11538-010-9507-6Search in Google Scholar

Van den Driessche, P. and Watmough, J.(2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences 180(1-2): 29-48.10.1016/S0025-5564(02)00108-6Search in Google Scholar

Van den Driessche, P. and Watmough, J. (2000). A simple SIS epidemic model with a backward bifurcation, Journal of Mathematical Biology 40(6): 525-540.10.1007/s002850000032Search in Google Scholar

Vynnycky, E., Trindall, A. and Mangtani, P.(2007). Estimates of the reproduction numbers of Spanish influenza using morbidity data, International Journal of Epidemiology 36(4): 881-889.10.1093/ije/dym071Search in Google Scholar

Yildirim, A. and Cherruault, Y.(2009). Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method, Kybernetes 38(9): 1566-1575.10.1108/03684920910991540Search in Google Scholar

Yu, H.G., Zhong, S.M., Agarwal, R.P. and Xiong L.L. (2010). Species permanence and dynamical behaviour analysis of an impulsively controlled ecological system with distributed time delay, Computers and Mathematics with Applications 59(2): 3824-3835.10.1016/j.camwa.2010.04.018Search in Google Scholar

Zhang, X. and Liu, X. (2009). Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment, Nonlinear Analysis: Real World Applications 10(2): 565-575.10.1016/j.nonrwa.2007.10.011Search in Google Scholar

Zhang, J. and Ma, Z. (2003). Global dynamics of an SEIR epidemic model with saturating contact rate, Mathematical Biosciences 185(1): 15-32. 10.1016/S0025-5564(03)00087-7Search in Google Scholar