Warianty tytułu
Języki publikacji
Abstrakty
The aim of this paper is to study the existence and the asymptotic stability of solutions for an epidemiologically emerging reaction-diffusion model. We show that the model has two types of equilibrium points to resolve the proposed system for a fairly broad class of nonlinearity that describes the transmission of an infectious disease between individuals. The model is analyzed by using the basic reproductive number R0 . Finally, we present the numerical examples simulations that clarifies and confirms the results of the study throughout the paper.
Czasopismo
Rocznik
Tom
Strony
553--573
Opis fizyczny
Bibliogr. 35 poz., tab., wykr.
Twórcy
autor
- Department of Science and Technology, Larbi Tebessi University, Tebessa, Algeria , khalifa.bouaziz@univ-tebessa.dz
autor
- Laboratory of Mathematics, Informatics and Systems (LAMIS), Larbi Tebessi University, Tebessa, Algeria, redouane.douaifia@univ-tebessa.dz
autor
- Department of Mathematics and Computer, Larbi Tebessi University, Tebessa, Algeria, salem.abdelmalek@univ-tebessa.dz
Bibliografia
- [1] Z. U. A. Zafar, S. Zaib, M. T. Hussain, C. Tunç, and S. Javeed, Analysis and numerical simulation of tuberculosis model using different fractional derivatives, Chaos Solitons Fractals. 160 (2022), 112202, DOI: https://doi.org/10.1016/j.chaos.2022.112202.
- [2] Z. U. A. Zafar, L. Akinyemi, H. Rezazadeh, and M. Inc, Non-topological, topological and rogue wave Soliton solutions for Sharma Tasso Olver equation, J. Ocean Eng. Sci, (2022), DOI: https://doi.org/10.1016/j.joes.2022.04.028.
- [3] Z. U. A. Zafar, S. Younas, S. Zaib, and C. Tunç, An efficient numerical simulation and mathematical modeling for the prevention of tuberculosis, Int. J. Biomath. 15 (2022), no. 4, 2250015, DOI: https://doi.org/10.1142/S1793524522500152.
- [4] Z. U. A. Zafar, M. T. Hussain, M. Inc, D. Baleanu, B. Almohsen, A. S. Oke, et al., Fractional-order dynamics of human papillomavirus, Results Phys. 34 (2022), 105281, DOI: https://doi.org/10.1016/j.rinp.2022.105281.
- [5] L. Chengxia and X. Zhou, Concentration phenomenon of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with spontaneous infection, Discrete Contin. Dyn. Syst. Ser. B 27 (2022), no. 6, 3077–3100, DOI: https://doi.org/10.3934/dcdsb.2021174.
- [6] C. Shanshan, J. Shi, Z. Shuai, and Y. Wu, Asymptotic profiles of the steady states for an SIS epidemic patch model with asymmetric connectivity matrix, J. Math. Biol. 80 (2020), no. 7, 2327–2361, DOI: https://doi.org/10.1007/s00285-020-01497-8.
- [7] A. Touil and A. Youkana, Boundedness and asymptotic behavior of solutions for a diffusive epidemic model, Math. Methods Appl. Sci. 40 (2017), no. 4, 970–978, DOI: https://doi.org/10.1002/mma.4029.
- [8] R. Peng and X. Q. Zhao, A reaction-diffusion SIS epidemic model in a time-periodic environment, Nonlinearity 25 (2012), no. 5, 1451, DOI: https://doi.org/10.1088/0951-7715/25/5/1451.
- [9] Y. Tong and C. Lei, An SIS epidemic reaction-diffusion model with spontaneous infection in a spatially heterogeneous environment, Nonlinear Anal. Real World Appl. 41 (2018), 443–460, DOI: https://doi.org/10.1016/j.nonrwa.2017.11.002.
- [10] C. Castillo-Chavez, K. Cooke, W. Huang, and S. A. Levin, On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS), Journal of Mathematical Biology 27 (1989), 373–398, DOI: https://doi.org/10.1007/BF00290636.
- [11] M. de Jong, O. Diekmann, and H. Heesterbeek, How does transmission of infection depend on population size?, in: D. Mollison (ed.), Epidemic Models: Their Structure and Relation to Data, Cambridge University Press, Cambridge, UK, 1995, pp. 84–94.
- [12] L. J. S. Allen, B. M. Bolker, J. Lou, and A. L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model, Discrete Contin. Dyn. Syst. 21 (2008), no. 1, 1–20, DOI: https://doi.org/10.3934/dcds.2008.21.1.
- [13] R. Peng and S. Liu, Global stability of the steady states of an SIS epidemic reaction-diffusion model, Nonlinear Anal. 71 (2009), no. 1–2, 239–247, DOI: https://doi.org/10.1016/j.na.2008.10.043.
- [14] O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, On the de nition and computation of basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990), no. 3, 365–382, DOI: https://doi.org/10.1007/BF00178324.
- [15] Z. U. A. Zafar, C. Tunç, N. Ali, G. Zaman, and P. Thounthong, Dynamics of an arbitrary order model of toxoplasmosis ailment in human and cat inhabitants, J. Taibah Univ. Medical Sci. 15 (2021), no. 1, 882–896, DOI: https://doi.org/10.1080/16583655.2021.1990603.
- [16] Z. U. A. Zafar, N. Ali, and D. Baleanu, Dynamics and numerical investigations of a fractional-order model of toxoplasmosis in the population of human and cats, Chaos, Solitons & Fractals 151 (2021), 111261, DOI: https://doi.org/10.1016/j.chaos.2021.111261.
- [17] H. Wenzhang, M. Han, and K. Liu, Dynamics of an SIS reaction-diffusion epidemic model for disease transmission, Math. Biosci. Eng. 7 (2010), no. 1, 51–66, DOI: https://doi.org//10.3934/mbe.2010.7.51.
- [18] Y. Wan and X. Zou, Asymptotic profiles of steady states for a diffusive SIS epidemic model with mass action infection mechanism, J. Differ. Equ. 261 (2016), no. 8, 4424–4447, DOI: https://doi.org/10.1016/j.jde.2016.06.028.
- [19] S. Abdelmalek and S. Bendoukha, On the global asymptotic stability of solutions to a generalised Lengyel-Epstein system, Nonlinear Anal. Real World Appl. 35 (2017), 397–413, DOI: https://doi.org/10.1016/j.nonrwa.2016.11.007.
- [20] J. Piqueira, M. Castano, and L. Monteiro, Modeling the spreading of HIV in homosexual populations with heterogeneous preventive attitude, J. Biol. Systems 12 (2004), no. 4, 439–456, DOI: https://doi.org/10.1142/S0218339004001312.
- [21] K. Kim, Z. Lin, and Q. Zhang, An SIR epidemic model with free boundary, Nonlinear Anal. Real World Appl. 14 (2013), no. 5, 1992–2001, DOI: https://doi.org/10.1016/j.nonrwa.2013.02.003.
- [22] S. Al-Sheikh and F. Musali, Stability analysis of an HIV/AIDS epidemic model with screening, Int. Math. Forum 66 (2011), 3251–3273.
- [23] P. Driessche and J. Watmough, Reproduction number and sub-threshold endemic equilibria for compartmental models for disease transmission, Math. Biosci. 180 (2002), no. 1–2, 29–48, DOI: https://doi.org/10.1016/S0025-5564(02)00108-6.
- [24] D. Henry, Geometric theory of semi-linear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981.
- [25] S. L. Hollis, R. H. Martin, and M. Pierre, Global existence and boundedness in reaction-diffusion systems, SIAM J. Math. Anal. 18 (1987), no. 3, 744–761, DOI: https://doi.org/10.1137/0518057.
- [26] A. Pazy, Semigroups of linear operators and applications to partial differntial equations, Applied Mathematical Sciences, vol 44, Springer, New York, NY, USA, 1983.
- [27] Z. Du and R. Peng, A priori L∞ estimates for solutions of a class of reaction-diffusion systems, J. Math. Biol. 72 (2016), no. 6, 1429–1439, DOI: https://doi.org/10.1007/s00285-015-0914-z.
- [28] N. D. Alikakos, An application of the invariance principle to reaction-diffusion equations, J. Differ. Equ. 33 (1979), no. 2, 201–225, DOI: https://doi.org/10.1016/0022-0396(79)90088-3.
- [29] S. Abdelmalek and S. Bendoukha, Global asymptotic stability of a diffusive SIVR epidemic model with immigration, Electron J. Differ. Equ. 2016 (2016), no. 284, 1–14.
- [30] J. P. Tripathi, J. S. Tyagi, and S. Abbas, Dynamical analysis of a predator-prey interaction model with time delay and prey refuge, Nonauton. Dyn. Syst. 5 (2018), no. 1, 138–151, DOI: https://doi.org/10.1515/msds-2018-0011.
- [31] M. Martcheva, An introduction of mathematical epidemiology, Texts in Applied Mathematics, vol. 61, Springer, New York, 2015. https://link.springer.com/book/10.1007/978-1-4899-7612-3.
- [32] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic Publishers, Dordrecht, 1992.
- [33] H. Alain and K. Mokhtar, Estimations C1 pour des problèmes paraboliques semi-linéaires, Annales de la Faculté des sciences de Toulouse, Mathématiques 5 (1983), no. 3–4, 265–280.
- [34] R. P. Sigdel and C. C. McCluskey, Global stability for an SEI model of infectious disease with immigration, Appl. Math. Comput. 243 (2014), 684–689, DOI: https://doi.org/10.1016/j.amc.2014.06.020.
- [35] S. Henshaw and C. C. McCluskey, Global stability of a vaccination model with immigration, Electron. J. Differ. Equ. 2015 (2015), no. 92, 1–10.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-ade22b13-a8b2-4379-8f97-ba58dfe7bb04