Teorik Makale
BibTex RIS Kaynak Göster

ATTAINABLE SETS OF INTEGRAL CONSTRAINED SEIR CONTROL SYSTEM WITH NONLINEAR INCIDENCE

Yıl 2023, Sayı: 054, 322 - 337, 30.09.2023
https://doi.org/10.59313/jsr-a.1312173

Öz

In this survey, we consider the dynamics of a contagious disease spread by employing a nonlinear dynamical control system of differential equations. It considers treatment and vaccination as key control parameters to discern their influence on disease control. The study, approximate the attainable sets of a given control system and presents visual results, while also discussing potential biological applications of their findings.

Kaynakça

  • [1] Kermack W.O., Mckendric A.G. (1927). Contributions to the mathematical theory of epidemics, part i, Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 115 (772), 700-721.
  • [2] Hethcote H.W. (2000). The mathematics of infectious diseases, SIAM Review, 42(4), 599–653.
  • [3] Hoppensteadt F.C. (1982). Mathematical methods in population biology, Cambridge University Press, Cambridge.
  • [4] Anderson R.M. (1982). Population dynamics of infectious diseases: Theory and applications, Chapman and Hall, London.
  • [5] Grassly N.C., Fraser C. (2008). Mathematical models of infectious disease transmission, Nature Reviews Microbiology 6, 477-487. doi:10.1038/nrmicro1845.
  • [6] Keeling M.J., Danon L. (2009). Mathematical modelling of infectious diseases, Br Med Bull, 92(1), 33-42. doi: 10.1093/bmb/ldp038.
  • [7] Biswas M.H.A., Paiva L.T., Pinho M. (2014). A SEIR model for control of infectious diseases with constraints, Mathematical Biosciences and Engineering, 11(4), 761-784. doi:10.3934/mbe.2014.11.761.
  • [8] Neilan R.M., Lenhart S. (2010). An Introduction to Optimal Control with an Application in Disease Modeling, Modeling Paradigms and Analysis of Disease Trasmission Models, 49, 67-82.
  • [9] Gaff H., Schaffer E. (2009). Optimal control applied to vaccination and treatment strategies for various epidemiological models, Math. Bio. Sci. Eng. (MBE), 6, 469-492.
  • [10] Guseinov Kh. G., Ozer O., Akyar E. (2004). On the continuity properties of the attainable sets of control systems with integral constraints on control, Nonl. Anal.: Theo., Meth. App. 56, 433–449.
  • [11] Guseinov Kh. G., Ozer O., Akyar E., Ushakov V.N. (2007). The approximation of reachable sets of control systems with integral constraint on controls, Non. Diff. Equat. Appl. 14, 57–73.
  • [12] Guseinov Kh.G., Nazlipinar A.S. (2007). On the continuity property of Lp balls and an application, J.Math. Anal. Appl., 335, 1347-1359.
  • [13] Guseinov Kh.G., Nazlipinar A.S. (2008). On the continuity properties of attainable sets of nonlinear control systems with integral constraint on controls, Abstr. Appl. Anal., p.14.
  • [14] Guseinov KH.G. (2009). Approximation of the attainable sets of the nonlinear control systems with integral constraints on control, Nonlinear Analysis, TMA, 71, 622-645.
  • [15] Guseinov Kh.G., Nazlipinar A.S. (2011). An algorithm for approximate calculation of the attainable sets of the nonlinear control systems with integral constraint on controls, Comp. Math. Appl., 62(4), 1887-1895.
  • [16] Krasovskii N.N., Subbotin A.I. (1988). Game-theoretical control problems, Springer, NewYork.
  • [17] Krasovskii N.N. (1968). Theory of control of motion: Linear systems, Nauka, Moscow.
  • [18] Nazlipinar A.S., Basturk B. (2020). Attainable set of a SIR epidemiological model with constraints on vaccination and treatment stocks, Tbilisi Mathematical Journal 13(1), pp. 11-22.
  • [19] Hethcote H.W. (1989). Three Basic Epidemiological Models, In Levin SA, Hallam TG, Gross LJ (eds.). Applied Mathematical Ecology. Biomathematics. Vol. 18. Berlin: Springer. pp. 119–144. doi:10.1007/978-3-642-61317-3_5. ISBN 3-540-19465-7.
  • [20] Padua RN, Tulang A.B. (2010). A Density–Dependent Epidemiological Model for the Spread of Infectious Diseases, Liceo Journal of Higher Education Research. 6 (2). doi:10.7828/ljher.v6i2.62.
Yıl 2023, Sayı: 054, 322 - 337, 30.09.2023
https://doi.org/10.59313/jsr-a.1312173

Öz

Kaynakça

  • [1] Kermack W.O., Mckendric A.G. (1927). Contributions to the mathematical theory of epidemics, part i, Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 115 (772), 700-721.
  • [2] Hethcote H.W. (2000). The mathematics of infectious diseases, SIAM Review, 42(4), 599–653.
  • [3] Hoppensteadt F.C. (1982). Mathematical methods in population biology, Cambridge University Press, Cambridge.
  • [4] Anderson R.M. (1982). Population dynamics of infectious diseases: Theory and applications, Chapman and Hall, London.
  • [5] Grassly N.C., Fraser C. (2008). Mathematical models of infectious disease transmission, Nature Reviews Microbiology 6, 477-487. doi:10.1038/nrmicro1845.
  • [6] Keeling M.J., Danon L. (2009). Mathematical modelling of infectious diseases, Br Med Bull, 92(1), 33-42. doi: 10.1093/bmb/ldp038.
  • [7] Biswas M.H.A., Paiva L.T., Pinho M. (2014). A SEIR model for control of infectious diseases with constraints, Mathematical Biosciences and Engineering, 11(4), 761-784. doi:10.3934/mbe.2014.11.761.
  • [8] Neilan R.M., Lenhart S. (2010). An Introduction to Optimal Control with an Application in Disease Modeling, Modeling Paradigms and Analysis of Disease Trasmission Models, 49, 67-82.
  • [9] Gaff H., Schaffer E. (2009). Optimal control applied to vaccination and treatment strategies for various epidemiological models, Math. Bio. Sci. Eng. (MBE), 6, 469-492.
  • [10] Guseinov Kh. G., Ozer O., Akyar E. (2004). On the continuity properties of the attainable sets of control systems with integral constraints on control, Nonl. Anal.: Theo., Meth. App. 56, 433–449.
  • [11] Guseinov Kh. G., Ozer O., Akyar E., Ushakov V.N. (2007). The approximation of reachable sets of control systems with integral constraint on controls, Non. Diff. Equat. Appl. 14, 57–73.
  • [12] Guseinov Kh.G., Nazlipinar A.S. (2007). On the continuity property of Lp balls and an application, J.Math. Anal. Appl., 335, 1347-1359.
  • [13] Guseinov Kh.G., Nazlipinar A.S. (2008). On the continuity properties of attainable sets of nonlinear control systems with integral constraint on controls, Abstr. Appl. Anal., p.14.
  • [14] Guseinov KH.G. (2009). Approximation of the attainable sets of the nonlinear control systems with integral constraints on control, Nonlinear Analysis, TMA, 71, 622-645.
  • [15] Guseinov Kh.G., Nazlipinar A.S. (2011). An algorithm for approximate calculation of the attainable sets of the nonlinear control systems with integral constraint on controls, Comp. Math. Appl., 62(4), 1887-1895.
  • [16] Krasovskii N.N., Subbotin A.I. (1988). Game-theoretical control problems, Springer, NewYork.
  • [17] Krasovskii N.N. (1968). Theory of control of motion: Linear systems, Nauka, Moscow.
  • [18] Nazlipinar A.S., Basturk B. (2020). Attainable set of a SIR epidemiological model with constraints on vaccination and treatment stocks, Tbilisi Mathematical Journal 13(1), pp. 11-22.
  • [19] Hethcote H.W. (1989). Three Basic Epidemiological Models, In Levin SA, Hallam TG, Gross LJ (eds.). Applied Mathematical Ecology. Biomathematics. Vol. 18. Berlin: Springer. pp. 119–144. doi:10.1007/978-3-642-61317-3_5. ISBN 3-540-19465-7.
  • [20] Padua RN, Tulang A.B. (2010). A Density–Dependent Epidemiological Model for the Spread of Infectious Diseases, Liceo Journal of Higher Education Research. 6 (2). doi:10.7828/ljher.v6i2.62.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Biyolojik Matematik, Uygulamalarda Dinamik Sistemler, Varyasyon Hesabı, Sistem Teorisinin Matematiksel Yönleri ve Kontrol Teorisi
Bölüm Research Articles
Yazarlar

Ali Serdar Nazlıpınar 0000-0002-5114-208X

Farıdeh Mohammadımehr 0000-0003-0122-7920

Yayımlanma Tarihi 30 Eylül 2023
Gönderilme Tarihi 9 Haziran 2023
Yayımlandığı Sayı Yıl 2023 Sayı: 054

Kaynak Göster

IEEE A. S. Nazlıpınar ve F. Mohammadımehr, “ATTAINABLE SETS OF INTEGRAL CONSTRAINED SEIR CONTROL SYSTEM WITH NONLINEAR INCIDENCE”, JSR-A, sy. 054, ss. 322–337, Eylül 2023, doi: 10.59313/jsr-a.1312173.