메뉴 건너뛰기




Volumn 215, Issue 2, 2009, Pages 653-669

The explicit series solution of SIR and SIS epidemic models

Author keywords

Epidemiology; Homotopy analysis method; Series solution; SIR; SIS

Indexed keywords

ANALYTIC APPROACH; ANALYTIC TECHNIQUE; CONVERGENT SERIES; COUPLED NONLINEAR DIFFERENTIAL EQUATIONS; EPIDEMIC MODELS; HOMOTOPY ANALYSIS METHOD; HOMOTOPY ANALYSIS METHODS; NONLINEAR PROBLEMS; ONE PARAMETER FAMILY; PHYSICAL MEANINGS; SERIES SOLUTION; SERIES SOLUTIONS; SIR; SIS; SIS MODEL;

EID: 68949150809     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.05.051     Document Type: Article
Times cited : (97)

References (28)
  • 1
    • 0000998185 scopus 로고
    • Contribution to the mathematical theory of epidemics
    • Kermack W.O., and McKendrick A.G. Contribution to the mathematical theory of epidemics. Proc. Roy. Soc. A115 (1927) 700-721
    • (1927) Proc. Roy. Soc. , vol.A115 , pp. 700-721
    • Kermack, W.O.1    McKendrick, A.G.2
  • 2
    • 0025159677 scopus 로고
    • On the definition and computation of the basic reproductive ratio in models for infectious diseases in heterogeneous population
    • Diekmann O., Heesterbeek J.A.P., and Metz J.A.J. On the definition and computation of the basic reproductive ratio in models for infectious diseases in heterogeneous population. J. Math. Biol. 28 (1990) 365-382
    • (1990) J. Math. Biol. , vol.28 , pp. 365-382
    • Diekmann, O.1    Heesterbeek, J.A.P.2    Metz, J.A.J.3
  • 3
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 42 (2000) 599-653
    • (2000) SIAM Rev. , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 4
    • 0030824540 scopus 로고    scopus 로고
    • Models for the simple epidemic
    • West R.W., and Thompson J.R. Models for the simple epidemic. Math. Biosci. 141 (1997) 29-39
    • (1997) Math. Biosci. , vol.141 , pp. 29-39
    • West, R.W.1    Thompson, J.R.2
  • 6
    • 0038330387 scopus 로고    scopus 로고
    • Stability analysis for differential infectivity epidemic models
    • Zhien Ma., Liu J., and Li J. Stability analysis for differential infectivity epidemic models. Nonlinear Anal.-Real. 4 (2003) 841-856
    • (2003) Nonlinear Anal.-Real. , vol.4 , pp. 841-856
    • Zhien, Ma.1    Liu, J.2    Li, J.3
  • 7
    • 28844448156 scopus 로고    scopus 로고
    • Global stability and periodicity on SIS epidemic models with backward bifurcation
    • Jing H., and Zhu D. Global stability and periodicity on SIS epidemic models with backward bifurcation. Int. J. Comput. Math. 50 (2005) 1271-1290
    • (2005) Int. J. Comput. Math. , vol.50 , pp. 1271-1290
    • Jing, H.1    Zhu, D.2
  • 8
    • 31244431623 scopus 로고    scopus 로고
    • Lyapunov functions and global stability for SIR, SIRS and SIS epidemiological models
    • Korobeinikov A., and Wake G.C. Lyapunov functions and global stability for SIR, SIRS and SIS epidemiological models. Appl. Math. Lett. 15 (2002) 955-960
    • (2002) Appl. Math. Lett. , vol.15 , pp. 955-960
    • Korobeinikov, A.1    Wake, G.C.2
  • 9
    • 5244379790 scopus 로고
    • Fluctuations in a dynamic, intermediate-run IS-LM model applications of the Poincar-Bendixon theorem
    • Garry J.S. Fluctuations in a dynamic, intermediate-run IS-LM model applications of the Poincar-Bendixon theorem. J. Econom. Theory 15 (1982) 369-375
    • (1982) J. Econom. Theory , vol.15 , pp. 369-375
    • Garry, J.S.1
  • 10
    • 0141615743 scopus 로고    scopus 로고
    • Stability of periodic solutions for an SIS model with pulse vaccination
    • Yicang Z., and Liu H. Stability of periodic solutions for an SIS model with pulse vaccination. Math. Comput. Model. 38 (2003) 299-308
    • (2003) Math. Comput. Model. , vol.38 , pp. 299-308
    • Yicang, Z.1    Liu, H.2
  • 11
    • 33847331138 scopus 로고    scopus 로고
    • How mathematical models have helped to improve understanding the epidemiology of infection
    • Pietro G.C. How mathematical models have helped to improve understanding the epidemiology of infection. Early Hum. Dev. 83 (2007) 141-148
    • (2007) Early Hum. Dev. , vol.83 , pp. 141-148
    • Pietro, G.C.1
  • 12
    • 68949110738 scopus 로고
    • Qualitative analysis of an epidemic model with directed disprsion
    • D.B. Meade, Qualitative analysis of an epidemic model with directed disprsion, IMA preprint series, 1992.
    • (1992) IMA preprint series
    • Meade, D.B.1
  • 17
    • 0141961626 scopus 로고    scopus 로고
    • On the homotopy analysis method for nonlinear problems
    • Liao S.J. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147 2 (2004) 499-513
    • (2004) Appl. Math. Comput. , vol.147 , Issue.2 , pp. 499-513
    • Liao, S.J.1
  • 18
    • 0000615571 scopus 로고
    • A kind of approximate solution technique which does not depend upon small parameters: a special example
    • Liao S.J. A kind of approximate solution technique which does not depend upon small parameters: a special example. Int. J. Non-Linear Mech. 30 (1995) 371-380
    • (1995) Int. J. Non-Linear Mech. , vol.30 , pp. 371-380
    • Liao, S.J.1
  • 19
    • 34848900880 scopus 로고    scopus 로고
    • A general approach to obtain series solutions of nonlinear differential equations, Stud
    • Liao S.J., and Tan Y. A general approach to obtain series solutions of nonlinear differential equations, Stud. Appl. Math. 119 (2007) 297-354
    • (2007) Appl. Math. , vol.119 , pp. 297-354
    • Liao, S.J.1    Tan, Y.2
  • 20
    • 33744970924 scopus 로고    scopus 로고
    • An exact and explicit solution for the valuation of American put option
    • Zhu S.P. An exact and explicit solution for the valuation of American put option. Quant. Finan. 3 (2006) 229-242
    • (2006) Quant. Finan. , vol.3 , pp. 229-242
    • Zhu, S.P.1
  • 22
    • 33845907123 scopus 로고    scopus 로고
    • The application of the homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation
    • Abbasbandy S. The application of the homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation. Phys. Lett. A 361 (2007) 478-483
    • (2007) Phys. Lett. A , vol.361 , pp. 478-483
    • Abbasbandy, S.1
  • 23
    • 34047186947 scopus 로고    scopus 로고
    • Series solution to Thomas-Fermi equation
    • Khan H., and Xu H. Series solution to Thomas-Fermi equation. Phys. Lett. A 365 (2007) 111-115
    • (2007) Phys. Lett. A , vol.365 , pp. 111-115
    • Khan, H.1    Xu, H.2
  • 24
    • 33847658380 scopus 로고    scopus 로고
    • Homotopy analysis method for heat radiation equations
    • Abbasbandy S. Homotopy analysis method for heat radiation equations. Int. Commun. Heat Mass Transfer 34 (2007) 380-387
    • (2007) Int. Commun. Heat Mass Transfer , vol.34 , pp. 380-387
    • Abbasbandy, S.1
  • 25
    • 0141927321 scopus 로고    scopus 로고
    • On the explicit analytic solutions of an Oldroyd 6-constant fluid
    • Hayat T., Khan M., and Ayub M. On the explicit analytic solutions of an Oldroyd 6-constant fluid. Int. J. Eng. Sci. 42 (2004) 123-135
    • (2004) Int. J. Eng. Sci. , vol.42 , pp. 123-135
    • Hayat, T.1    Khan, M.2    Ayub, M.3
  • 26
    • 33747196070 scopus 로고    scopus 로고
    • MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel
    • Abbas Z., Sajid M., and Hayat T. MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel. Theor. Comput. Fluid Dyn. 20 (2006) 229-238
    • (2006) Theor. Comput. Fluid Dyn. , vol.20 , pp. 229-238
    • Abbas, Z.1    Sajid, M.2    Hayat, T.3
  • 27
    • 33646378690 scopus 로고    scopus 로고
    • Application of the homotopy analysis method to solving nonlinear evolution equations
    • Shi Y.R., Xu X.J., Wu Z.X., et al. Application of the homotopy analysis method to solving nonlinear evolution equations. Acta Phys. Sin. 55 (2006) 1555-1560
    • (2006) Acta Phys. Sin. , vol.55 , pp. 1555-1560
    • Shi, Y.R.1    Xu, X.J.2    Wu, Z.X.3
  • 28
    • 33845432502 scopus 로고    scopus 로고
    • On analytic solution for thin film flow of a forth grade fluid down a vertical cylinder
    • Hayat T., and Sajid M. On analytic solution for thin film flow of a forth grade fluid down a vertical cylinder. Phys. Lett. A 361 (2007) 316-322
    • (2007) Phys. Lett. A , vol.361 , pp. 316-322
    • Hayat, T.1    Sajid, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.