Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 3, 921 - 934, 02.06.2020
https://doi.org/10.15672/hujms.624042

Öz

Kaynakça

  • [1] S. Agrawal and S. Nadel, Acute bacterial meningitis in infants and children epidemi- ology and management, Pediatr Drugs, 13 (6), 385–400, 2011.
  • [2] O.M. Akpa and B.A. Oyejola, Modeling the transmission dynamics of HIV/AIDS epidemics: an introduction and a review, J. Infect. Dev. Ctries. 4 (10), 597–608, 2010.
  • [3] B.M. Althouse and S.V. Scarpino, Asymptomatic transmission and the resurgence of Bordetella pertussis, BMC Medicine, 13, 146, 2015.
  • [4] E.J. Anderson and S.G. Weber, Rotavirus infection in adults, Lancet Infect. Dis. 4, 91–99, 2004.
  • [5] R.M. Anderson and R.M. May, Infectious Diseases of Humans, Dynamics and Con- trol, Oxford University Press, Oxford, 1991.
  • [6] P. Balmer, C. Burman, L. Serra and L. J. York, Impact of meningococcal vaccina- tion on carriage and disease transmission: A review of the literature, Hum. Vaccin. Immunother, 14 (5), 1118–1130, 2018.
  • [7] S. Bunimovich-Mendrazitsky and L. Stone, Modeling polio as a disease of develop- ment, J. Theor. Biol. 237 (3), 302–315, 2005.
  • [8] Centers for Disease Control and Prevention, https://www.cdc.gov/meningitis/bacterial.html
  • [9] M. Ceyhan, M. Celik, E.T. Demir, V. Gurbuz, A.E. Aycan and S. Unal Acquisition of meningococcal serogroup W − 135 carriage in turkish hajj pilgrims who had received the quadrivalent meningococcal polysaccharide vaccine, Clin. Vaccine Immunol. 20 (1), 66–68, 2012.
  • [10] S. Chávez-Bueno and, G.H. Jr. McCracken, Bacterial meningitis in children, Pediatr Clin. N. Am. 52, 795–810, 2005.
  • [11] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180, 29–48, 2002.
  • [12] D.J.D. Earn, P. Rohani, B.M. Bolker and B.T. Grenfell, A simple model for complex dynamical transitions in epidemics, Science, 87, 667–670, 2000.
  • [13] T. Harko, S.N.F. Lobo and M.K. Mak, Exact analytical solutions of the Susceptible- Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates, Appl. Math. Comput. 236, 184–194, 2014.
  • [14] O. Hoffman and R.J. Weber, Pathophysiology and treatment of bacterial meningitis, Ther. Adv. Neurol. Disord. 2(6), 1–7, 2009.
  • [15] T.J. Irving, K.B. Bltuss, C. Colijn and C. L. Trotter, Modelling meningococcal menin- gitis in the African meningitis belt, Epidemiol. Infect. 140 (05), 89–905, 2011.
  • [16] D.S. Jones and B.D. Sleeman, Differential Equations and Mathematical Biology, Chapman and Hall/CRC, London, 2003.
  • [17] D. Kalajdzievska and M.Y. Li, Modeling the effects of carriers on transmission dy- namics of infectious diseases, Math. Biosci. Eng. 8, 3, 2011.
  • [18] W.O. Kermack and A.G. McKendrick, Contribution to mathematical theory of epi- demics, Soc. Lond. A Mat. 115, 700–721, 1927.
  • [19] Y.A. Kuznetsov and C. Piccardi, Bifurcation analysis of periodic SEIR and SIR epi- demic models, J. Math. Biol. 32, 109–121, 1994.
  • [20] C. Ma, S. Yan, Q. Su, L. Hao, S. Tang, Z. An, Y. He, G. Fan, L. Rodewald and H. Wang, Measles transmission among adults with spread to children during an outbreak: Implications for measles elimination in China, 2014, Vaccine, 34 (51), 6539–6544, 2016.
  • [21] MATLAB, version 9.14.0.813654 (R2018a), The MathWorks Inc., Massachusetts, 2018.
  • [22] A.M. Molesworth, L.E. Cuevas, S.J. Connor, A.P. Morse and M.C. Thomson, Envi- ronmental risk and meningitis epidemics in Africa, Emerg. Infect. Dis. 9 (10), 1287– 1293, 2003.
  • [23] J. Müller and C. Kuttler, Methods and Models in Mathematical Biology, Springer- Verlag, Berlin, Heidelberg, 2015.
  • [24] J.D. Murray, Mathematical Biology, Springer-Verlag, New York, 1993.
  • [25] L.F. Olsen and W.M. Schaffer, Chaos versus noisy periodicity: alternative hypotheses for childhood epidemics, Science, 249, 499–504, 1990.
  • [26] A.M. Oordt-Speets, R. Bolijn, R.C. van Hoorn, A. Bhavsar and M. Kyaw, Global etiology of bacterial meningitis: A systematic review and meta-analysis, PLoS One, 13 (6), e0198772, 2018.
  • [27] Y. Özsürekci, Turkiye’de menenjite neden olan bakteriel ajanlar ve meningokal sero- gruplarin seroprevelansi (Unpublished doctoral dissertation), Hacettepe University Faculty of Medicine, 2013.
  • [28] K. Rock, S. Brand, J. Moir and M.J. Keeling, Dynamics of infectious diseases, Rep. Prog. Phys. 77, 026602, 2014.
  • [29] D. Schenzle, An age-structured model of pre- and post-vaccination measles transmis- sion, Math. Med. Biol. 1, 169–191, 1984.
  • [30] R. Tekin, E.C. Dinleyici, M. Ceyhan, A. Karbuz, N. Salman, M. Sutcu, Z.Kurugol, Y. Balliel, M.Celik, M. Hacimustafaoglu, N. Kuyucu, M.Kondolot, G. Sensoy, O.Metin, S.S. Kara, M. Dinleyici, O.Kilic, C. Bayhan, V. Gurbuz, E. Aycan, A. Memedova, A. Karli and S. Celebi, The prevalence, serogroup distribution and risk factors of meningococcal carriage in adolescents and young adults in Turkey, Hum. Vaccin. Im- munother. 13(5), 1182–1189, 2017.

Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes

Yıl 2020, Cilt: 49 Sayı: 3, 921 - 934, 02.06.2020
https://doi.org/10.15672/hujms.624042

Öz

Infectious diseases are a serious problem for public health and spark the interest in interdisciplinary studies. In this paper, we present two mathematical models describing a possible scenario for infectious diseases. The first model considers the dynamics of the disease among adults and emphasizes the role of carriers in the SIR model and the second model assumes that the disease is transmitted to children by adults. We state the equilibria for each model and study the local stability of the equilibria. Furthermore, we perform simulations using a parameter set that explains the spread of a specific infectious disease (meningococcal disease) and interpret the possible cases of transmission via simulations.

Kaynakça

  • [1] S. Agrawal and S. Nadel, Acute bacterial meningitis in infants and children epidemi- ology and management, Pediatr Drugs, 13 (6), 385–400, 2011.
  • [2] O.M. Akpa and B.A. Oyejola, Modeling the transmission dynamics of HIV/AIDS epidemics: an introduction and a review, J. Infect. Dev. Ctries. 4 (10), 597–608, 2010.
  • [3] B.M. Althouse and S.V. Scarpino, Asymptomatic transmission and the resurgence of Bordetella pertussis, BMC Medicine, 13, 146, 2015.
  • [4] E.J. Anderson and S.G. Weber, Rotavirus infection in adults, Lancet Infect. Dis. 4, 91–99, 2004.
  • [5] R.M. Anderson and R.M. May, Infectious Diseases of Humans, Dynamics and Con- trol, Oxford University Press, Oxford, 1991.
  • [6] P. Balmer, C. Burman, L. Serra and L. J. York, Impact of meningococcal vaccina- tion on carriage and disease transmission: A review of the literature, Hum. Vaccin. Immunother, 14 (5), 1118–1130, 2018.
  • [7] S. Bunimovich-Mendrazitsky and L. Stone, Modeling polio as a disease of develop- ment, J. Theor. Biol. 237 (3), 302–315, 2005.
  • [8] Centers for Disease Control and Prevention, https://www.cdc.gov/meningitis/bacterial.html
  • [9] M. Ceyhan, M. Celik, E.T. Demir, V. Gurbuz, A.E. Aycan and S. Unal Acquisition of meningococcal serogroup W − 135 carriage in turkish hajj pilgrims who had received the quadrivalent meningococcal polysaccharide vaccine, Clin. Vaccine Immunol. 20 (1), 66–68, 2012.
  • [10] S. Chávez-Bueno and, G.H. Jr. McCracken, Bacterial meningitis in children, Pediatr Clin. N. Am. 52, 795–810, 2005.
  • [11] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180, 29–48, 2002.
  • [12] D.J.D. Earn, P. Rohani, B.M. Bolker and B.T. Grenfell, A simple model for complex dynamical transitions in epidemics, Science, 87, 667–670, 2000.
  • [13] T. Harko, S.N.F. Lobo and M.K. Mak, Exact analytical solutions of the Susceptible- Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates, Appl. Math. Comput. 236, 184–194, 2014.
  • [14] O. Hoffman and R.J. Weber, Pathophysiology and treatment of bacterial meningitis, Ther. Adv. Neurol. Disord. 2(6), 1–7, 2009.
  • [15] T.J. Irving, K.B. Bltuss, C. Colijn and C. L. Trotter, Modelling meningococcal menin- gitis in the African meningitis belt, Epidemiol. Infect. 140 (05), 89–905, 2011.
  • [16] D.S. Jones and B.D. Sleeman, Differential Equations and Mathematical Biology, Chapman and Hall/CRC, London, 2003.
  • [17] D. Kalajdzievska and M.Y. Li, Modeling the effects of carriers on transmission dy- namics of infectious diseases, Math. Biosci. Eng. 8, 3, 2011.
  • [18] W.O. Kermack and A.G. McKendrick, Contribution to mathematical theory of epi- demics, Soc. Lond. A Mat. 115, 700–721, 1927.
  • [19] Y.A. Kuznetsov and C. Piccardi, Bifurcation analysis of periodic SEIR and SIR epi- demic models, J. Math. Biol. 32, 109–121, 1994.
  • [20] C. Ma, S. Yan, Q. Su, L. Hao, S. Tang, Z. An, Y. He, G. Fan, L. Rodewald and H. Wang, Measles transmission among adults with spread to children during an outbreak: Implications for measles elimination in China, 2014, Vaccine, 34 (51), 6539–6544, 2016.
  • [21] MATLAB, version 9.14.0.813654 (R2018a), The MathWorks Inc., Massachusetts, 2018.
  • [22] A.M. Molesworth, L.E. Cuevas, S.J. Connor, A.P. Morse and M.C. Thomson, Envi- ronmental risk and meningitis epidemics in Africa, Emerg. Infect. Dis. 9 (10), 1287– 1293, 2003.
  • [23] J. Müller and C. Kuttler, Methods and Models in Mathematical Biology, Springer- Verlag, Berlin, Heidelberg, 2015.
  • [24] J.D. Murray, Mathematical Biology, Springer-Verlag, New York, 1993.
  • [25] L.F. Olsen and W.M. Schaffer, Chaos versus noisy periodicity: alternative hypotheses for childhood epidemics, Science, 249, 499–504, 1990.
  • [26] A.M. Oordt-Speets, R. Bolijn, R.C. van Hoorn, A. Bhavsar and M. Kyaw, Global etiology of bacterial meningitis: A systematic review and meta-analysis, PLoS One, 13 (6), e0198772, 2018.
  • [27] Y. Özsürekci, Turkiye’de menenjite neden olan bakteriel ajanlar ve meningokal sero- gruplarin seroprevelansi (Unpublished doctoral dissertation), Hacettepe University Faculty of Medicine, 2013.
  • [28] K. Rock, S. Brand, J. Moir and M.J. Keeling, Dynamics of infectious diseases, Rep. Prog. Phys. 77, 026602, 2014.
  • [29] D. Schenzle, An age-structured model of pre- and post-vaccination measles transmis- sion, Math. Med. Biol. 1, 169–191, 1984.
  • [30] R. Tekin, E.C. Dinleyici, M. Ceyhan, A. Karbuz, N. Salman, M. Sutcu, Z.Kurugol, Y. Balliel, M.Celik, M. Hacimustafaoglu, N. Kuyucu, M.Kondolot, G. Sensoy, O.Metin, S.S. Kara, M. Dinleyici, O.Kilic, C. Bayhan, V. Gurbuz, E. Aycan, A. Memedova, A. Karli and S. Celebi, The prevalence, serogroup distribution and risk factors of meningococcal carriage in adolescents and young adults in Turkey, Hum. Vaccin. Im- munother. 13(5), 1182–1189, 2017.
Toplam 30 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Meltem Gölgeli 0000-0002-3671-6225

Fatihcan M. Atay Bu kişi benim 0000-0001-6277-6830

Yayımlanma Tarihi 2 Haziran 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 3

Kaynak Göster

APA Gölgeli, M., & Atay, F. M. (2020). Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes. Hacettepe Journal of Mathematics and Statistics, 49(3), 921-934. https://doi.org/10.15672/hujms.624042
AMA Gölgeli M, Atay FM. Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes. Hacettepe Journal of Mathematics and Statistics. Haziran 2020;49(3):921-934. doi:10.15672/hujms.624042
Chicago Gölgeli, Meltem, ve Fatihcan M. Atay. “Analysis of an Epidemic Model for Transmitted Diseases in a Group of Adults and an Extension to Two Age Classes”. Hacettepe Journal of Mathematics and Statistics 49, sy. 3 (Haziran 2020): 921-34. https://doi.org/10.15672/hujms.624042.
EndNote Gölgeli M, Atay FM (01 Haziran 2020) Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes. Hacettepe Journal of Mathematics and Statistics 49 3 921–934.
IEEE M. Gölgeli ve F. M. Atay, “Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 3, ss. 921–934, 2020, doi: 10.15672/hujms.624042.
ISNAD Gölgeli, Meltem - Atay, Fatihcan M. “Analysis of an Epidemic Model for Transmitted Diseases in a Group of Adults and an Extension to Two Age Classes”. Hacettepe Journal of Mathematics and Statistics 49/3 (Haziran 2020), 921-934. https://doi.org/10.15672/hujms.624042.
JAMA Gölgeli M, Atay FM. Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes. Hacettepe Journal of Mathematics and Statistics. 2020;49:921–934.
MLA Gölgeli, Meltem ve Fatihcan M. Atay. “Analysis of an Epidemic Model for Transmitted Diseases in a Group of Adults and an Extension to Two Age Classes”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 3, 2020, ss. 921-34, doi:10.15672/hujms.624042.
Vancouver Gölgeli M, Atay FM. Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes. Hacettepe Journal of Mathematics and Statistics. 2020;49(3):921-34.