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Volumn 3, Issue 3, 2006, Pages 445-458

Stochastic epidemic models with a backward bifurcation

Author keywords

Bistability; Continuous time Markov chain; Epidemic model; Stochastic differential equations; Vaccination

Indexed keywords


EID: 33846964182     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2006.3.445     Document Type: Article
Times cited : (34)

References (24)
  • 1
    • 1042298863 scopus 로고    scopus 로고
    • J. Arino, C. C. McCluskey, and P. van den Driessche, GLOBAL RESULTS FOR AN EPIDEMIC MODEL WITH VACCINATION THAT EXHIBITS BACKWARD BIFURCATION. SIAM J Appl Math 64 (2003) 260-76.
    • J. Arino, C. C. McCluskey, and P. van den Driessche, GLOBAL RESULTS FOR AN EPIDEMIC MODEL WITH VACCINATION THAT EXHIBITS BACKWARD BIFURCATION. SIAM J Appl Math 64 (2003) 260-76.
  • 2
    • 0029055539 scopus 로고
    • A CORE GROUP MODEL FOR DISEASE TRANSMISSION. Math
    • K. P. Hadeler and C. Castillo-Chavez, A CORE GROUP MODEL FOR DISEASE TRANSMISSION. Math Biosci 128 (1995) 41-55.
    • (1995) Biosci , vol.128 , pp. 41-55
    • Hadeler, K.P.1    Castillo-Chavez, C.2
  • 3
    • 0030882301 scopus 로고    scopus 로고
    • BACKWARD BIFURCATION IN EPIDEMIC CONTROL. Math
    • K. P. Hadeler and P. van den Driessche, BACKWARD BIFURCATION IN EPIDEMIC CONTROL. Math Biosci 146 (1997) 15-35.
    • (1997) Biosci , vol.146 , pp. 15-35
    • Hadeler, K.P.1    van den Driessche, P.2
  • 4
    • 85039223382 scopus 로고    scopus 로고
    • E. J. Allen, STOCHASTIC DIFFERENTIAL EQUATIONS AND PERSISTENCE TIME FOR TWO INTERACTING POPULATIONS. Dyn Cont Discrete and Impulsive Systems 5 (1999) 271-81.
    • E. J. Allen, STOCHASTIC DIFFERENTIAL EQUATIONS AND PERSISTENCE TIME FOR TWO INTERACTING POPULATIONS. Dyn Cont Discrete and Impulsive Systems 5 (1999) 271-81.
  • 5
    • 3042695162 scopus 로고    scopus 로고
    • N. Kirupaharan and L. J. S. Allen, COEXISTENCE OF MULTIPLE PATHOGEN STRAINS IN STOCHASTIC EPIDEMIC MODELS WITH DENSITY-DEPENDENT MORTALITY. Bull Math Biol 66 (2004) 841-64.
    • N. Kirupaharan and L. J. S. Allen, COEXISTENCE OF MULTIPLE PATHOGEN STRAINS IN STOCHASTIC EPIDEMIC MODELS WITH DENSITY-DEPENDENT MORTALITY. Bull Math Biol 66 (2004) 841-64.
  • 6
    • 85039212925 scopus 로고    scopus 로고
    • L. J. S. Allen, AN INTRODUCTION TO STOCHASTIC PROCESSES WITH APPLICATIONS TO BIOLOGY. Prentice Hall, Upper Saddle River, N. J., 2003.
    • L. J. S. Allen, AN INTRODUCTION TO STOCHASTIC PROCESSES WITH APPLICATIONS TO BIOLOGY. Prentice Hall, Upper Saddle River, N. J., 2003.
  • 7
    • 85039218991 scopus 로고    scopus 로고
    • N. T. J. Bailey, THE MATHEMATICAL THEORY OF INFECTIOUS DISEASES AND ITS APPLICATIONS. Griffin, London, 1975.
    • N. T. J. Bailey, THE MATHEMATICAL THEORY OF INFECTIOUS DISEASES AND ITS APPLICATIONS. Griffin, London, 1975.
  • 8
    • 85039187907 scopus 로고    scopus 로고
    • F. A. Ball, A NOTE ON THE TOTAL SIZE DISTRIBUTION OF EPIDEMIC MODELS. J Appl Prob 23 (1986) 832-36.
    • F. A. Ball, A NOTE ON THE TOTAL SIZE DISTRIBUTION OF EPIDEMIC MODELS. J Appl Prob 23 (1986) 832-36.
  • 9
    • 85039220485 scopus 로고    scopus 로고
    • D. J. Daley and J. Gani, EPIDEMIC MODELLING: AN INTRODUCTION. Cambridge Studies in Mathematical Biology, 15. Cambridge Univ. Press, Cambridge, 1999.
    • D. J. Daley and J. Gani, EPIDEMIC MODELLING: AN INTRODUCTION. Cambridge Studies in Mathematical Biology, Vol. 15. Cambridge Univ. Press, Cambridge, 1999.
  • 10
    • 85039216101 scopus 로고    scopus 로고
    • J. -P. Gabriel, C. Lefèvre, and P. Picard (Eds.), STOCHASTIC PROCESSES IN EPIDEMIC THEORY. Lecture Notes in Biomathematics 86. Springer-Verlag, New York, Berlin, Heidelberg, 1990.
    • J. -P. Gabriel, C. Lefèvre, and P. Picard (Eds.), STOCHASTIC PROCESSES IN EPIDEMIC THEORY. Lecture Notes in Biomathematics 86. Springer-Verlag, New York, Berlin, Heidelberg, 1990.
  • 11
    • 0027305851 scopus 로고
    • THE STOCHASTIC SI EPIDEMIC MODEL WITH RECRUITMENT AND DEATHS I. COMPARISON WITH THE CLOSED SIS MODEL. Math
    • J. Jacquez and C. P. Simon, THE STOCHASTIC SI EPIDEMIC MODEL WITH RECRUITMENT AND DEATHS I. COMPARISON WITH THE CLOSED SIS MODEL. Math Biosci 117 (1993) 77-125.
    • (1993) Biosci , vol.117 , pp. 77-125
    • Jacquez, J.1    Simon, C.P.2
  • 12
    • 85039190407 scopus 로고    scopus 로고
    • C. J. Mode and C. K. Sleeman, STOCHASTIC PROCESSES IN EPIDEMIOLOGY. HIV/AIDS, OTHER INFECTIOUS DISEASES AND COMPUTERS. World Scientific, Singapore, New Jersey, 2000.
    • C. J. Mode and C. K. Sleeman, STOCHASTIC PROCESSES IN EPIDEMIOLOGY. HIV/AIDS, OTHER INFECTIOUS DISEASES AND COMPUTERS. World Scientific, Singapore, New Jersey, 2000.
  • 13
    • 85039237407 scopus 로고    scopus 로고
    • D. Mollison (Ed.), EPIDEMIC MODELS: THEIR STRUCTURE AND RELATION TO DATA. Cambridge Univ. Press, Cambridge, 1995.
    • D. Mollison (Ed.), EPIDEMIC MODELS: THEIR STRUCTURE AND RELATION TO DATA. Cambridge Univ. Press, Cambridge, 1995.
  • 14
    • 2542509066 scopus 로고    scopus 로고
    • ON THE QUASI-STATIONARY DISTRIBUTION OF THE STOCHASTIC LOGISTIC EPIDEMIC
    • I. Nasell, ON THE QUASI-STATIONARY DISTRIBUTION OF THE STOCHASTIC LOGISTIC EPIDEMIC. Math Biosci 156 (1999) 21-40.
    • (1999) Math. Biosc. , vol.156 , pp. 21-40
    • Nasell, I.1
  • 15
    • 16244363078 scopus 로고    scopus 로고
    • I. Nasell, A NEW LOOK AT CRITICAL COMMUNITY SIZE FOR CHILDHOOD INFECTIONS. Theor Pop Biol 67 (2005) 203-16.
    • I. Nasell, A NEW LOOK AT CRITICAL COMMUNITY SIZE FOR CHILDHOOD INFECTIONS. Theor Pop Biol 67 (2005) 203-16.
  • 16
    • 17744385524 scopus 로고    scopus 로고
    • M. E. Alexander, C. Bowman, S. M. Moghadas, R. Summers, A. B. Gumel, and B. M. Sahai, A VACCINATION MODEL FOR TRANSMISSION DYNAMICS OF INFLUENZA. SIAM J Appl. Dyn Sys 3 (2004) 503-24.
    • M. E. Alexander, C. Bowman, S. M. Moghadas, R. Summers, A. B. Gumel, and B. M. Sahai, A VACCINATION MODEL FOR TRANSMISSION DYNAMICS OF INFLUENZA. SIAM J Appl. Dyn Sys 3 (2004) 503-24.
  • 17
    • 0026335575 scopus 로고
    • ASSESSING THE VARIABILITY OF STOCHASTIC EPIDEMICS. Math
    • V. Isham, ASSESSING THE VARIABILITY OF STOCHASTIC EPIDEMICS. Math Biosci 107 (1991) 209-24.
    • (1991) Biosci , vol.107 , pp. 209-224
    • Isham, V.1
  • 18
    • 0347063875 scopus 로고    scopus 로고
    • A. L. Lloyd, ESTIMATING VARIABILITY IN MODELS FOR RECURRENT EPIDEMICS: ASSESSING THE USE OF MOMENT CLOSURE TECHNIQUES. Theor Pop Biol 65 (2004) 49-65.
    • A. L. Lloyd, ESTIMATING VARIABILITY IN MODELS FOR RECURRENT EPIDEMICS: ASSESSING THE USE OF MOMENT CLOSURE TECHNIQUES. Theor Pop Biol 65 (2004) 49-65.
  • 19
    • 85039208278 scopus 로고    scopus 로고
    • J. M. Ortega, MATRIX THEORY A SECOND COURSE. Plenum Press, New York, 1987.
    • J. M. Ortega, MATRIX THEORY A SECOND COURSE. Plenum Press, New York, 1987.
  • 20
    • 85039179808 scopus 로고    scopus 로고
    • T. C. Gard, INTRODUCTION TO STOCHASTIC DIFFERENTIAL EQUATIONS. Marcel Dekker, Inc., New York and Basel, 1988.
    • T. C. Gard, INTRODUCTION TO STOCHASTIC DIFFERENTIAL EQUATIONS. Marcel Dekker, Inc., New York and Basel, 1988.
  • 21
    • 85039188125 scopus 로고    scopus 로고
    • P. E. Kloeden and E. Platen, NUMERICAL SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS. Springer-Verlag, New York, 1992.
    • P. E. Kloeden and E. Platen, NUMERICAL SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS. Springer-Verlag, New York, 1992.
  • 22
    • 85039222430 scopus 로고    scopus 로고
    • T. G. Kurtz, LIMIT THEOREMS FOR SEQUENCES OF JUMP MARKOV PROCESSES APPROXIMATING ORDINARY DIFFERENTIAL PROCESSES. J Appl Prob 8 (1971) 344-56.
    • T. G. Kurtz, LIMIT THEOREMS FOR SEQUENCES OF JUMP MARKOV PROCESSES APPROXIMATING ORDINARY DIFFERENTIAL PROCESSES. J Appl Prob 8 (1971) 344-56.
  • 23
    • 0042531779 scopus 로고    scopus 로고
    • S. M. Henson, A. A. King, R. F. Costantino, J. M. Gushing, B. Dennis, and R. A. Desharnais, EXPLAINING AND PREDICTING PATTERNS IN STOCHASTIC POPULATION SYSTEMS. Proc Roy Soc Lond B 270 (2003) 1549-53.
    • S. M. Henson, A. A. King, R. F. Costantino, J. M. Gushing, B. Dennis, and R. A. Desharnais, EXPLAINING AND PREDICTING PATTERNS IN STOCHASTIC POPULATION SYSTEMS. Proc Roy Soc Lond B 270 (2003) 1549-53.
  • 24
    • 3042626993 scopus 로고    scopus 로고
    • S. M. Henson, J. R. Reilly, S. L. Robertson, M. C. Shu, E. W. D. Rozier, and J. M. Cushing, PREDICTING IRREGULARITIES IN POPULATION CYCLES. SIAM J Applied Dyn Sys 2 (2003) 238-53.
    • S. M. Henson, J. R. Reilly, S. L. Robertson, M. C. Shu, E. W. D. Rozier, and J. M. Cushing, PREDICTING IRREGULARITIES IN POPULATION CYCLES. SIAM J Applied Dyn Sys 2 (2003) 238-53.


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