A numerical study on an influenza epidemic model with vaccination and diffusion

Applied Mathematics and Computation

Volumn 219, Issue 1, 2012, Pages 122-141

  Samsuzzoha, Md ^a   Singh, Manmohan ^a   Lucy, David ^a  

^a SWINBURNE UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Diffusion; Epidemic model; Infectious diseases; Influenza; Routh Hurwitz stability conditions; Splitting method; Transmission coefficient; Vaccination

Indexed keywords

EPIDEMIC MODELS; INFECTIOUS DISEASE; INFLUENZA; SPLITTING METHOD; STABILITY CONDITION; TRANSMISSION COEFFICIENTS; VACCINATION;

DIFFUSION; VACCINES;

DISEASE CONTROL;

EID: 84864282127     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.04.089     Document Type: Conference Paper

References (49)

1. M.E. Alexander, C. Bowman, A.B. Gumel, S.M. Moghadas, B.M. Sahai, and R. Summers A vaccination model for transmission dynamics of influenza SIAM J. Appl. Dynam. Syst. 3 2004 503 524
2. R.M. Anderson, and R.M. May Vaccination against rubella and measles; quantitative investigations of different policies Hyg. Camb. 90 1983 259 325
3. R.M. Anderson, and R.M. May Age-related changes in the rate of disease transmission: implication for the design of vaccination programmes Hyg. Camb. 94 1985 365 436
4. R.M. Anderson, and R.M. May Infectious Diseases of Humans 1992 OUP Oxford
5. J. Arino, F. Brauer, P. van den Driessche, J. Watmough, and J. Wu A model for influenza with vaccination and antiviral treatment J. Theor. Biol. 253 2008 118 130
6. S.M. Blower, and H. Dowlatabadi Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example Int. Statist. Rev. 62 1994 229 243
7. G. Chowell, C.E. Ammon, N.W. Hengartner, and J.M. Hyman Estimating the reproduction number from the initial phase of the Spanish flu pandemic waves in Geneva, Switzerland Math. Biosci. Eng. 4 3 2007 457 470
8. G. Chowell, C. Castillo-Chavez, P.W. Fenimore, C. Kribs-Zaleta, L. Arriola, and J.M. Hyman Implications of an uncertainty and sensitivity analysis for SARS's basic reproductive number for general public health measures Emerg. Infect. Dis. 10 2004
9. G. Chowell, M.A. Miller, and C. Viboud Seasonal influenza in the United States, France, and Australia: transmission and prospects for control Epidemiol Infect. 136 6 2008 852 864
10. B.J. Coburn, B.G. Wagner, and S. Blower Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1) BMC Med. 7 2009 1 8
11. K.L. Cooke, and P. Van den Driesche Analysis of an SEIRS epidemic model with two delays J. Math. Biol. 35 1996 240 260
12. Y. Deguchi, and Y. Tagasugi Efficacy of influenza vaccine in the elderly: reduction in risk of mortality and morbidity during an influenza A (H3N2) epidemic for the elderly in nursing homes Int. J. Clin. Lab. Res. 30 2000 1 4
13. O. Diekmann, and J.A.P. Heesterbeek Mathematical Models in Population Biology and Epidemiology 2000 Springer Verlag New York
14. K. Dietz, and D. Schenzle Mathematical models for infectious disease statistics A.C. Atkinson, S.E. Fienberg, Centenary Volume of the International Statistical Institute 1985 Springer-Verlag Berlin
15. W.R. Dowdle, S.R. Mostow, M.T. Coleman, H.S. Kaye, and S.C. Schoenbaum Inactivated influenza vaccines. 2. Laboratory indices of protection Postgrad. Med. J. 49 1973 159 163
16. J. Dushoff, J.B. Plotkin, S.A. Levin, and D.J.D. Earn Dynamical resonance can account for seasonality of influenza epidemics Proc. Nat. Acad. Sci. USA 101 2004 16915 16916
17. D.J.D. Earn, J. Dushoff, and S.A. Levin Ecology and evolution of the flu Trends Ecol. Evol. 17 2002 334 340
18. A. Easton, M. Singh, and G. Cui Solutions of two species reaction-diffusion systems Can. Appl. Math. Quart. 5 1997 359 373
19. A.P. Galvani, T.C. Reluga, and G.B. Chapman Long-standing influenza vaccination policy is in accord with individual self-interest but not with the utilitarian optimum Proc. Nat. Acad. Sci. USA 104 2007 5692 5697
20. D. Greenhalgh, and R. Das An SIR epidemic model with a contact rate depending on population density O. Arino, O. Axelrod, M. Kimmel, M. Langlais, Mathematical Population Dynamics: Analysis of Heterogeneity 1995 Wuerz Publishing Winnipeg
21. J. Giesecke Modern Infectious Disease Epidemiology second ed. 2002 Arnold London
22. H.W. Hethcote The mathematics of infectious diseases SIAM Rev. 42 2000 599 653
23. A. Hoare, D.G. Regan, and D.P. Wilson Sampling and sensitivity analyses tools (SaSAT) for computational modelling Theor. Biol. Med. Model. 5 4 2008 10.1186/1742-4682-5-4
24. R.L. Iman, and W.J. Conover Small sample sensitivity analysis techniques for computer models, with an application to risk assessment Commun. Statist. Theor. Methods A9 1980 1749 1874
25. ED. Kilbouorne Influenza 1987 Plenum New York
26. J. Lin, V. Andreasen, and S.A. Levin Dynamics of influenza A drift: the linear three-strain model J. Math. Biosci. 162 1999 33 51
27. A. Klimov, L. Simonsen, K. Fukuda, and N. Cox Surveillance and impact of influenza in the United States Vaccine 17 1999 842 846
28. I.M. Longini The generalized discrete-time epidemic model with immunity: a synthesis Math. Biosci. 82 1 1986 19 41
29. I.M. Longini, E. Halloran, and L.R. Elvehack An optimization model for influenza A epidemics Math. Biosci. 38 1978 141 157
30. I.M. Longini, M.E. Ackerman, A. Nizam, and Y. Yang Containing pandemic influenza with antiviral agents Am. J. Epidemiol. 159 2004 623 633
31. E. Massad, N.M. Bruattini, B.A.F. Coutinho, and F.L. Lopez The 1918 influenza A epidemic in the city of São Paulo, Brazil Med. Hypotheses 68 2007 442 445
32. R.M. May Stability and Complexity in Model Ecosystems second ed. 1974 Princeton University Press Princeton and Oxford
33. M.D. McKay, W.J. Conover, and R.J. Beckman A comparison of three methods for selecting values of input variables in the analysis of output from a computer code Technometrics 21 1979 239 246
34. C.E. Mills, J.M. Robins, and M. Lipsitch Transmissibility of 1918 pandemic influenza Nature 432 7019 2004 904 906
35. Z. Qiu, and Z. Feng Transmission dynamics of an influenza model with vaccination and antiviral treatment Bull. Math. Biol. 72 1 2009 1 33
36. L.A. Rvachev, and I.M. Longini A mathematical model for the global spread of influenza Math. Biosci. 75 1 1985 3 22
37. M.A. Sanchez, and S.M. Blower Uncertainty and sensitivity analysis of the basic reproductive rate: tuberculosis as an example Am. J. Epidemiol. 145 1997 1127 1137
38. M. Samsuzzoha, M. Singh, and D. Lucy Numerical study of an influenza epidemic model with diffusion Appl. Math. Comput. 217 2010 3461 3479
39. N. Sapoukhina, Y. Tyutyunov, and A. Arditi The role of prey-taxis in biological control Am. Nat. 162 2003 61 76
40. M. Singh, A. Easton, and I. Kozlova A numerical study of the spruce-budworm reaction-diffusion equation with hostile boundaries Nat. Res. Model. 13 2000 535 549
41. M. Singh, A. Easton, G. Cui, and I. Kozlova A numerical study of the two-dimensional spruce-budworm reaction-diffusion equation with density dependent diffusion Nat. Res. Model. 11 1998 143 154
42. J.M. Tchuenche, S.A. Khamis, F.B. Agusto, and S.C. Mpeshe Optimal control and sensitivity analysis of an influenza model with treatment and vaccination Acta Biotheor. 2010 10.1007/s10441-010-9095-8
43. P. Van den Driesche, and J. Watmough Reproduction numbers and sub-threhold endemic equilibria for the compartmental models of disease transmission Math. Biosci. 180 2005 29 48
44. R. Vardavas, R. Breban, and S. Blower Can influenza epidemics be prevented by voluntary vaccination? PLoS Comput. Biol. 3 2007 e85
45. C. Viboud, P.Y. Boelle, F. Carrat, A.J. Valleron, and A. Flahault Prediction of the spread of influenza epidemics by the method of analogues Am. J. Epidemiol. 158 2003 996 1006
46. C. Viboud, P.Y. Boelle, K. Pakdaman, F. Carrat, A.J. Valleron, and A. Flahault Influenza epidemics in the United States, France, and Australia, 1972-1997 Emerg. Infect. Dis. 10 2004 32 39
47. W. Wang Global behavior of an SEIRS epidemic model with time delays Appl. Math. Lett. 15 2002 423 428
48. R.J. Webby, and R.G. Webster Are we ready for pandemic influenza? Science 302 2003 1519 1522
49. N.N. Yanenko The Method of Fractional Steps 1971 Springer-Verlag New York