
Previous Article
Graphtheoretic conditions for zeroeigenvalue Turing instability in general chemical reaction networks
 MBE Home
 This Issue

Next Article
Modelling seasonal HFMD with the recessive infection in Shandong, China
The impact of an imperfect vaccine and pap cytology screening on the transmission of human papillomavirus and occurrence of associated cervical dysplasia and cancer
1.  Department of Applied Mathematics and Sciences, Khalifa University of Science, Technology and Research, PO Box 127788, Abu Dhabi, United Arab Emirates 
2.  Mathematical Institute, University of Oxford, 2429 St Giles', Oxford OX1 3LB, United Kingdom 
3.  Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada 
4.  Merck Research Laboratories, UG1C60, PO Box 1000, North Wales, PA 194541099 
5.  Community Health Sciences, University of Manitoba, Winnipeg, Manitoba, Canada 
References:
[1] 
M. Llamazares and R. J. Smith, Evaluating human papillomavirus vaccination programs in Canada: Should provincial healthcare pay for voluntary adult vaccination?, BMC Public Health, 8 (2008), 112. doi: 10.1186/147124588114. 
[2] 
M. Alarydah and R. J. Smith, An agestructured model of human papillomavirus vaccination, Mathematics and Computers in Simulation, 82 (2011), 629652. doi: 10.1016/j.matcom.2011.10.006. 
[3] 
F. Brauer, Backward bifurcations in simple vaccination models, J. Math. Anal. Appl., 298 (2004), 418431. doi: 10.1016/j.jmaa.2004.05.045. 
[4] 
M. Brisson, N. Van de Velde and M. C. Boily, Different populationlevel vaccination effectiveness for HPV types 16, 18, 6 and 11, Sex. Transm. Infect., 87 (2011), 4143. doi: 10.1136/sti.2010.044412. 
[5] 
V. Brown and K. A. J. White, The HPV vaccination strategy: Could male vaccination have a significant impact?, Comput. Math. Methods. Med., 11 (2010), 223237. doi: 10.1080/17486700903486613. 
[6] 
Canadian Cancer Society's Steering Committee, "Cancer Statistics 2009," (2009). Available from: http://www.cancer.ca. 
[7] 
J. Carr, "Applications of Centre Manifold Theory," SpringerVerlag, New York, 1981. 
[8] 
C. CastilloChavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Engrg., 1 (2004), 361404. doi: 10.3934/mbe.2004.1.361. 
[9] 
B. Crawford and C. M. Kribs Zaleta, The impact of vaccination and coinfection on HPV and cervical cancer, Discrete Contin. Dyn. Syst. Ser. B., 12 (2009), 279304. doi: 10.3934/dcdsb.2009.12.279. 
[10] 
L. A. Denny and J. T. C. Wright, Human papillomavirus testing and screening, Best Practice & Research Clinical Obstetrics and Gynaecology, 19 (2005), 501515. doi: 10.1016/j.bpobgyn.2005.02.004. 
[11] 
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365382. doi: 10.1007/BF00178324. 
[12] 
J. Dushoff, H. Wenzhang and C. CastilloChavez, Backward bifurcations and catastrophe in simple models of fatal diseases, J. Math. Biol., 36 (1998), 227248. doi: 10.1007/s002850050099. 
[13] 
E. H. Elbasha and A. P. Galvani, Vaccination against multiple HPV types, Math. Biosci., 197 (2005), 88117. doi: 10.1016/j.mbs.2005.05.004. 
[14] 
E. H. Elbasha and A. B. Gumel, Theoretical assesment of public health impact of imperfect prophylactic HIV1 vaccines with therapeutic benefits, Bull. Math. Biol., 68 (2006), 577614. 
[15] 
E. H. Elbasha, E. J.Dasbach and R. P. Insinga, Model for assessing human papillomavirus vaccination strategies, Emerg. Infect. Dis., 13 (2007), 2841. doi: 10.3201/eid1301.060438. 
[16] 
E. H. Elbasha, Global stability of equilibria in a twosex HPV vaccination model, Bull. Math. Biol., 70 (2008), 894909. doi: 10.1007/s1153800792830. 
[17] 
E. H. Elbasha, E. J. Dasbach and R. P. Insinga, A multitype HPV transmission model, Bull. Math. Biol., 70 (2008), 21262176. doi: 10.1007/s115380089338x. 
[18] 
J. Ferlay, H. R. Shin, F. Bray, D. Forman, C. Mathers and D. M. Parkin, Estimates of worldwide burden of cancer in 2008: GLOBOCAN 2008, Int. J. Cancer., 127 (2010), 28932917. doi: 10.1002/ijc.25516. 
[19] 
E. L. Franco, S. M. Mahmud, J. Tota, A. Ferenczy and F. Coutle, The expected impact of HPV vaccination on the accuracy of cervical cancer screening: The need for a paradigm change, Arch. Med. Res., 40 (2009), 478485. doi: 10.1016/j.arcmed.2009.06.003. 
[20] 
E. L. Franco, E. DuarteFranco and A. Ferenczy, Cervical cancer: Epidemiology, prevention and the role of human papillomavirus infection, CMAJ., 164 (2001), 10171025. 
[21] 
S. M. Garba, A. B. Gumel and M. R. Abu Bakar, Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215 (2008), 1125. doi: 10.1016/j.mbs.2008.05.002. 
[22] 
, The GlaxoSmithKline Vaccine HPV007 Study Group,, Sustained efficacy and immunogenicity of the human papillomavirus (HPV)16/17 ASO4adjuvanted vaccine: Analysis of a randomised placebocontrolled trial up to 6.4 years, (). 
[23] 
S. J. Goldie et al., Projected clinical benefits and costeffectiveness of a human papillomavirus 16/18 vaccine, Journal of the National Cancer Institute, 96 (2004), 604615. 
[24] 
O. P. Günther et al., Protecting the next generation: What is the role of the duration of Human Papillomavirus vaccinerelated immunity?, J. Infect. Dis., 197 (2008), 16531661. 
[25] 
B. T. Hansen et al., Factors associated with nonattendance, opportunistic attendance and reminded attendance to cervical screening in an organized screening program: A crosssectional study of 12,058 Norwegian women, BMC Public Health, 11 (2011), 113. 
[26] 
Health Canada, "Cervical Cancer Screening Activities in Canada," (2012). Available from: http://www.phacaspc.gc.ca. 
[27] 
H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599653. doi: 10.1137/S0036144500371907. 
[28] 
J. Hughes, G. Garnett and L. Koutsky, The theoretical population level impact of a prophylactic human papillomavirus vaccine, Epidemiology, 13 (2002), 631639. 
[29] 
"International Agency for Research on Cancer" Working Group., Human papillomaviruses, IARC Monographs on the Evaluation of the Carcinogenic Risks to Humans, (1995). Lyon, France. 
[30] 
O. Klungsøyr, M. Nygård, G. Skare, T. Eriksen and J. F Nygård, Validity of selfreported Pap smear history in Norwegian women, J. Med. Screen, 16 (2009), 9197. doi: 10.1258/jms.2009.008087. 
[31] 
L. Koutsky, Epidemiology of genital human papillomavirus infection, American Journal of Medicine, 102 (1997), 38. 
[32] 
C. KribsZaleta and J. VelascoHernandez, A simple vaccination model with multiple endemic states, Math Biosci., 164 (2000), 183201. doi: 10.1016/S00255564(00)000031. 
[33] 
V. Lakshmikantham, S. Leela and A. A. Martynyuk, "Stability Analysis of Nonlinear Systems," Marcel Dekker, Inc., New York and Basel, 1989. 
[34] 
J. P. LaSalle, "The Stability of Dynamical Systems," Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976. 
[35] 
D. C. McCrory and D. B. Matchar, Evaluation of Cervical Cytology. Evidence Report/Technology Assessment No. 5;, AHCPR Pub; No 99E 010 1999. 
[36] 
Z. Mukandavire, A. B. Gumel, W. Garira and J. M. Tchuenche, Mathematical analysis of a model for HIVmalaria coinfection, Math. Biosci. Engrg., 6 (2009), 333362. doi: 10.3934/mbe.2009.6.333. 
[37] 
N. Munoz, F. X. Bosch, S. de Sanjose et al., Epidemiologic classification of human papillomavirus types associated with cervical cancer, N. Engl. J. Med., 348 (2003), 518527. 
[38] 
N. Munoz et al., Against which human papillomavirus types shall we vaccinate and screen? The international perspective, International Journal of Cancer, 111 (2004), 278285. 
[39] 
E. R. Myers et al., Mathematical model for the natural history of human papillomavirus infection and cervical carcinogenesis, Am. J. Epidemiol., 151 (2000), 11581171. 
[40] 
S. L. Kulasingam and E. R. Myers, Potential health and economic impact of adding a human papillomavirus vaccine to screening programs, JAMA., 290 (2003), 781789. doi: 10.1001/jama.290.6.781. 
[41] 
J. M. Palefsky, Human papillomavirusrelated disease in men: Not just a women's issue, Journal of Adolescent Health, 46 (2010), S12S19. doi: 10.1016/j.jadohealth.2010.01.010. 
[42] 
C. N. Podder and A. B. Gumel, Transmission dynamics of a twosex model for Herpes Simplex Virus type 2, Can. Appl. Math. Quarterly, 17 (2009), 339386. 
[43] 
Public Health Agency of Canada, "Cervical Cancer Screening in Canada," (2013). Available from: http://www.phacaspc.gc.ca/publicat/ccsicdccuac/pdf/chap_3_e.pdf. 
[44] 
Public Health Agency of Canada, "Human Papillomavirus. HPV Purple Paper (bds)," (2010). Available from: http://www.phacaspc.gc.ca. 
[45] 
P. Sasieni and A. Castanon, Call and recall cervical screening programme: Screening interval and age limits, Curr. Diagn. Pathol., 12 (2006), 114126. 
[46] 
D. Saslow et al., American cancer society, American society for colposcopy and cervical pathology, and American society for clinical pathology screening guidelines for the prevention and early detection of cervical cancer, Am. J. Clin. Pathol., 137 (2012), 516542. 
[47] 
M. Schiffman and P. E. Castle, When to test women for human papillomavirus, BMJ., 332 (2006), 6162. doi: 10.1136/bmj.332.7533.61. 
[48] 
O. Sharomi, C. N. Podder, A. B. Gumel, E. H. Elbasha and J. Watmough, Role of incidence function in vaccineinduced backward bifurcation in some HIV models, Math. Biosci., 210 (2007), 436463. doi: 10.1016/j.mbs.2007.05.012. 
[49] 
O. Sharomi, C. N. Podder, A. B. Gumel and B. Song, Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment, Math. Biosci. Engrg., 5 (2008), 145174. doi: 10.3934/mbe.2008.5.145. 
[50] 
H. L. Smith and P. Waltman, "The Theory of the Chemostat," Cambridge University Press, 1995. doi: 10.1017/CBO9780511530043. 
[51] 
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 2948. doi: 10.1016/S00255564(02)001086. 
[52] 
N. Van de Velde, M. Brisson and M. C. Boily, Modeling human papillomavirus vaccine effectiveness: Quantifying the impact of parameter uncertainty, Am. J. Epidemiol., 165 (2007), 762775. 
[53] 
L. L. Villa et al., High sustained efficacy of a prophylactic quadrivalent human Papillomavirus types 6/11/16/18 viruslike particle vaccine through 5 years of followup, British Journal of Cancer, 95 (2006), 14591466. 
[54] 
J. M. M. Walboomers, Human papillomavirus is a necessary cause of invasive cervical cancer worldwide, J. Pathol., 189 (1999), 1219. doi: 10.1002/(SICI)10969896(199909)189:1<12::AIDPATH431>3.0.CO;2F. 
show all references
References:
[1] 
M. Llamazares and R. J. Smith, Evaluating human papillomavirus vaccination programs in Canada: Should provincial healthcare pay for voluntary adult vaccination?, BMC Public Health, 8 (2008), 112. doi: 10.1186/147124588114. 
[2] 
M. Alarydah and R. J. Smith, An agestructured model of human papillomavirus vaccination, Mathematics and Computers in Simulation, 82 (2011), 629652. doi: 10.1016/j.matcom.2011.10.006. 
[3] 
F. Brauer, Backward bifurcations in simple vaccination models, J. Math. Anal. Appl., 298 (2004), 418431. doi: 10.1016/j.jmaa.2004.05.045. 
[4] 
M. Brisson, N. Van de Velde and M. C. Boily, Different populationlevel vaccination effectiveness for HPV types 16, 18, 6 and 11, Sex. Transm. Infect., 87 (2011), 4143. doi: 10.1136/sti.2010.044412. 
[5] 
V. Brown and K. A. J. White, The HPV vaccination strategy: Could male vaccination have a significant impact?, Comput. Math. Methods. Med., 11 (2010), 223237. doi: 10.1080/17486700903486613. 
[6] 
Canadian Cancer Society's Steering Committee, "Cancer Statistics 2009," (2009). Available from: http://www.cancer.ca. 
[7] 
J. Carr, "Applications of Centre Manifold Theory," SpringerVerlag, New York, 1981. 
[8] 
C. CastilloChavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Engrg., 1 (2004), 361404. doi: 10.3934/mbe.2004.1.361. 
[9] 
B. Crawford and C. M. Kribs Zaleta, The impact of vaccination and coinfection on HPV and cervical cancer, Discrete Contin. Dyn. Syst. Ser. B., 12 (2009), 279304. doi: 10.3934/dcdsb.2009.12.279. 
[10] 
L. A. Denny and J. T. C. Wright, Human papillomavirus testing and screening, Best Practice & Research Clinical Obstetrics and Gynaecology, 19 (2005), 501515. doi: 10.1016/j.bpobgyn.2005.02.004. 
[11] 
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365382. doi: 10.1007/BF00178324. 
[12] 
J. Dushoff, H. Wenzhang and C. CastilloChavez, Backward bifurcations and catastrophe in simple models of fatal diseases, J. Math. Biol., 36 (1998), 227248. doi: 10.1007/s002850050099. 
[13] 
E. H. Elbasha and A. P. Galvani, Vaccination against multiple HPV types, Math. Biosci., 197 (2005), 88117. doi: 10.1016/j.mbs.2005.05.004. 
[14] 
E. H. Elbasha and A. B. Gumel, Theoretical assesment of public health impact of imperfect prophylactic HIV1 vaccines with therapeutic benefits, Bull. Math. Biol., 68 (2006), 577614. 
[15] 
E. H. Elbasha, E. J.Dasbach and R. P. Insinga, Model for assessing human papillomavirus vaccination strategies, Emerg. Infect. Dis., 13 (2007), 2841. doi: 10.3201/eid1301.060438. 
[16] 
E. H. Elbasha, Global stability of equilibria in a twosex HPV vaccination model, Bull. Math. Biol., 70 (2008), 894909. doi: 10.1007/s1153800792830. 
[17] 
E. H. Elbasha, E. J. Dasbach and R. P. Insinga, A multitype HPV transmission model, Bull. Math. Biol., 70 (2008), 21262176. doi: 10.1007/s115380089338x. 
[18] 
J. Ferlay, H. R. Shin, F. Bray, D. Forman, C. Mathers and D. M. Parkin, Estimates of worldwide burden of cancer in 2008: GLOBOCAN 2008, Int. J. Cancer., 127 (2010), 28932917. doi: 10.1002/ijc.25516. 
[19] 
E. L. Franco, S. M. Mahmud, J. Tota, A. Ferenczy and F. Coutle, The expected impact of HPV vaccination on the accuracy of cervical cancer screening: The need for a paradigm change, Arch. Med. Res., 40 (2009), 478485. doi: 10.1016/j.arcmed.2009.06.003. 
[20] 
E. L. Franco, E. DuarteFranco and A. Ferenczy, Cervical cancer: Epidemiology, prevention and the role of human papillomavirus infection, CMAJ., 164 (2001), 10171025. 
[21] 
S. M. Garba, A. B. Gumel and M. R. Abu Bakar, Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215 (2008), 1125. doi: 10.1016/j.mbs.2008.05.002. 
[22] 
, The GlaxoSmithKline Vaccine HPV007 Study Group,, Sustained efficacy and immunogenicity of the human papillomavirus (HPV)16/17 ASO4adjuvanted vaccine: Analysis of a randomised placebocontrolled trial up to 6.4 years, (). 
[23] 
S. J. Goldie et al., Projected clinical benefits and costeffectiveness of a human papillomavirus 16/18 vaccine, Journal of the National Cancer Institute, 96 (2004), 604615. 
[24] 
O. P. Günther et al., Protecting the next generation: What is the role of the duration of Human Papillomavirus vaccinerelated immunity?, J. Infect. Dis., 197 (2008), 16531661. 
[25] 
B. T. Hansen et al., Factors associated with nonattendance, opportunistic attendance and reminded attendance to cervical screening in an organized screening program: A crosssectional study of 12,058 Norwegian women, BMC Public Health, 11 (2011), 113. 
[26] 
Health Canada, "Cervical Cancer Screening Activities in Canada," (2012). Available from: http://www.phacaspc.gc.ca. 
[27] 
H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599653. doi: 10.1137/S0036144500371907. 
[28] 
J. Hughes, G. Garnett and L. Koutsky, The theoretical population level impact of a prophylactic human papillomavirus vaccine, Epidemiology, 13 (2002), 631639. 
[29] 
"International Agency for Research on Cancer" Working Group., Human papillomaviruses, IARC Monographs on the Evaluation of the Carcinogenic Risks to Humans, (1995). Lyon, France. 
[30] 
O. Klungsøyr, M. Nygård, G. Skare, T. Eriksen and J. F Nygård, Validity of selfreported Pap smear history in Norwegian women, J. Med. Screen, 16 (2009), 9197. doi: 10.1258/jms.2009.008087. 
[31] 
L. Koutsky, Epidemiology of genital human papillomavirus infection, American Journal of Medicine, 102 (1997), 38. 
[32] 
C. KribsZaleta and J. VelascoHernandez, A simple vaccination model with multiple endemic states, Math Biosci., 164 (2000), 183201. doi: 10.1016/S00255564(00)000031. 
[33] 
V. Lakshmikantham, S. Leela and A. A. Martynyuk, "Stability Analysis of Nonlinear Systems," Marcel Dekker, Inc., New York and Basel, 1989. 
[34] 
J. P. LaSalle, "The Stability of Dynamical Systems," Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976. 
[35] 
D. C. McCrory and D. B. Matchar, Evaluation of Cervical Cytology. Evidence Report/Technology Assessment No. 5;, AHCPR Pub; No 99E 010 1999. 
[36] 
Z. Mukandavire, A. B. Gumel, W. Garira and J. M. Tchuenche, Mathematical analysis of a model for HIVmalaria coinfection, Math. Biosci. Engrg., 6 (2009), 333362. doi: 10.3934/mbe.2009.6.333. 
[37] 
N. Munoz, F. X. Bosch, S. de Sanjose et al., Epidemiologic classification of human papillomavirus types associated with cervical cancer, N. Engl. J. Med., 348 (2003), 518527. 
[38] 
N. Munoz et al., Against which human papillomavirus types shall we vaccinate and screen? The international perspective, International Journal of Cancer, 111 (2004), 278285. 
[39] 
E. R. Myers et al., Mathematical model for the natural history of human papillomavirus infection and cervical carcinogenesis, Am. J. Epidemiol., 151 (2000), 11581171. 
[40] 
S. L. Kulasingam and E. R. Myers, Potential health and economic impact of adding a human papillomavirus vaccine to screening programs, JAMA., 290 (2003), 781789. doi: 10.1001/jama.290.6.781. 
[41] 
J. M. Palefsky, Human papillomavirusrelated disease in men: Not just a women's issue, Journal of Adolescent Health, 46 (2010), S12S19. doi: 10.1016/j.jadohealth.2010.01.010. 
[42] 
C. N. Podder and A. B. Gumel, Transmission dynamics of a twosex model for Herpes Simplex Virus type 2, Can. Appl. Math. Quarterly, 17 (2009), 339386. 
[43] 
Public Health Agency of Canada, "Cervical Cancer Screening in Canada," (2013). Available from: http://www.phacaspc.gc.ca/publicat/ccsicdccuac/pdf/chap_3_e.pdf. 
[44] 
Public Health Agency of Canada, "Human Papillomavirus. HPV Purple Paper (bds)," (2010). Available from: http://www.phacaspc.gc.ca. 
[45] 
P. Sasieni and A. Castanon, Call and recall cervical screening programme: Screening interval and age limits, Curr. Diagn. Pathol., 12 (2006), 114126. 
[46] 
D. Saslow et al., American cancer society, American society for colposcopy and cervical pathology, and American society for clinical pathology screening guidelines for the prevention and early detection of cervical cancer, Am. J. Clin. Pathol., 137 (2012), 516542. 
[47] 
M. Schiffman and P. E. Castle, When to test women for human papillomavirus, BMJ., 332 (2006), 6162. doi: 10.1136/bmj.332.7533.61. 
[48] 
O. Sharomi, C. N. Podder, A. B. Gumel, E. H. Elbasha and J. Watmough, Role of incidence function in vaccineinduced backward bifurcation in some HIV models, Math. Biosci., 210 (2007), 436463. doi: 10.1016/j.mbs.2007.05.012. 
[49] 
O. Sharomi, C. N. Podder, A. B. Gumel and B. Song, Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment, Math. Biosci. Engrg., 5 (2008), 145174. doi: 10.3934/mbe.2008.5.145. 
[50] 
H. L. Smith and P. Waltman, "The Theory of the Chemostat," Cambridge University Press, 1995. doi: 10.1017/CBO9780511530043. 
[51] 
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 2948. doi: 10.1016/S00255564(02)001086. 
[52] 
N. Van de Velde, M. Brisson and M. C. Boily, Modeling human papillomavirus vaccine effectiveness: Quantifying the impact of parameter uncertainty, Am. J. Epidemiol., 165 (2007), 762775. 
[53] 
L. L. Villa et al., High sustained efficacy of a prophylactic quadrivalent human Papillomavirus types 6/11/16/18 viruslike particle vaccine through 5 years of followup, British Journal of Cancer, 95 (2006), 14591466. 
[54] 
J. M. M. Walboomers, Human papillomavirus is a necessary cause of invasive cervical cancer worldwide, J. Pathol., 189 (1999), 1219. doi: 10.1002/(SICI)10969896(199909)189:1<12::AIDPATH431>3.0.CO;2F. 
[1] 
Britnee Crawford, Christopher M. KribsZaleta. The impact of vaccination and coinfection on HPV and cervical cancer. Discrete and Continuous Dynamical Systems  B, 2009, 12 (2) : 279304. doi: 10.3934/dcdsb.2009.12.279 
[2] 
Najat Ziyadi. A malefemale mathematical model of human papillomavirus (HPV) in African American population. Mathematical Biosciences & Engineering, 2017, 14 (1) : 339358. doi: 10.3934/mbe.2017022 
[3] 
Tufail Malik, Abba Gumel, Elamin H. Elbasha. Qualitative analysis of an age and sexstructured vaccination model for human papillomavirus. Discrete and Continuous Dynamical Systems  B, 2013, 18 (8) : 21512174. doi: 10.3934/dcdsb.2013.18.2151 
[4] 
Linda J. S. Allen, P. van den Driessche. Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences & Engineering, 2006, 3 (3) : 445458. doi: 10.3934/mbe.2006.3.445 
[5] 
Erica M. Rutter, Yang Kuang. Global dynamics of a model of joint hormone treatment with dendritic cell vaccine for prostate cancer. Discrete and Continuous Dynamical Systems  B, 2017, 22 (3) : 10011021. doi: 10.3934/dcdsb.2017050 
[6] 
Renhao Cui. Asymptotic profiles of the endemic equilibrium of a reactiondiffusionadvection SIS epidemic model with saturated incidence rate. Discrete and Continuous Dynamical Systems  B, 2021, 26 (6) : 29973022. doi: 10.3934/dcdsb.2020217 
[7] 
Chengxia Lei, Xinhui Zhou. Concentration phenomenon of the endemic equilibrium of a reactiondiffusionadvection SIS epidemic model with spontaneous infection. Discrete and Continuous Dynamical Systems  B, 2022, 27 (6) : 30773100. doi: 10.3934/dcdsb.2021174 
[8] 
Benoît Merlet, Morgan Pierre. Convergence to equilibrium for the backward Euler scheme and applications. Communications on Pure and Applied Analysis, 2010, 9 (3) : 685702. doi: 10.3934/cpaa.2010.9.685 
[9] 
Xiaomei Feng, Zhidong Teng, Kai Wang, Fengqin Zhang. Backward bifurcation and global stability in an epidemic model with treatment and vaccination. Discrete and Continuous Dynamical Systems  B, 2014, 19 (4) : 9991025. doi: 10.3934/dcdsb.2014.19.999 
[10] 
Sumei Li, Yicang Zhou. Backward bifurcation of an HTLVI model with immune response. Discrete and Continuous Dynamical Systems  B, 2016, 21 (3) : 863881. doi: 10.3934/dcdsb.2016.21.863 
[11] 
Muntaser Safan, Klaus Dietz. On the eradicability of infections with partially protective vaccination in models with backward bifurcation. Mathematical Biosciences & Engineering, 2009, 6 (2) : 395407. doi: 10.3934/mbe.2009.6.395 
[12] 
Maurizio Grasselli, Morgan Pierre. Convergence to equilibrium of solutions of the backward Euler scheme for asymptotically autonomous secondorder gradientlike systems. Communications on Pure and Applied Analysis, 2012, 11 (6) : 23932416. doi: 10.3934/cpaa.2012.11.2393 
[13] 
Benjamin H. Singer, Denise E. Kirschner. Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection. Mathematical Biosciences & Engineering, 2004, 1 (1) : 8193. doi: 10.3934/mbe.2004.1.81 
[14] 
Hongying Shu, Lin Wang. Global stability and backward bifurcation of a general viral infection model with virusdriven proliferation of target cells. Discrete and Continuous Dynamical Systems  B, 2014, 19 (6) : 17491768. doi: 10.3934/dcdsb.2014.19.1749 
[15] 
Svetlana BunimovichMendrazitsky, Yakov Goltser. Use of quasinormal form to examine stability of tumorfree equilibrium in a mathematical model of bcg treatment of bladder cancer. Mathematical Biosciences & Engineering, 2011, 8 (2) : 529547. doi: 10.3934/mbe.2011.8.529 
[16] 
Folashade B. Agusto, Abba B. Gumel. Theoretical assessment of avian influenza vaccine. Discrete and Continuous Dynamical Systems  B, 2010, 13 (1) : 125. doi: 10.3934/dcdsb.2010.13.1 
[17] 
Kerioui Nadjah, Abdelouahab Mohammed Salah. Stability and Hopf bifurcation of the coexistence equilibrium for a differentialalgebraic biological economic system with predator harvesting. Electronic Research Archive, 2021, 29 (1) : 16411660. doi: 10.3934/era.2020084 
[18] 
G.A. Ngwa. Modelling the dynamics of endemic malaria in growing populations. Discrete and Continuous Dynamical Systems  B, 2004, 4 (4) : 11731202. doi: 10.3934/dcdsb.2004.4.1173 
[19] 
Renato Soeiro, Abdelrahim Mousa, Tânia R. Oliveira, Alberto A. Pinto. Dynamics of human decisions. Journal of Dynamics and Games, 2014, 1 (1) : 121151. doi: 10.3934/jdg.2014.1.121 
[20] 
Erika Asano, Louis J. Gross, Suzanne Lenhart, Leslie A. Real. Optimal control of vaccine distribution in a rabies metapopulation model. Mathematical Biosciences & Engineering, 2008, 5 (2) : 219238. doi: 10.3934/mbe.2008.5.219 
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]