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Nyamoradi, Nemat, Allali, Karam, Ahmad, Bashir. (1405). Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity. سامانه مدیریت نشریات علمی, 14(2), 908-918. doi: 10.22034/cmde.2025.64267.2901
Nemat Nyamoradi; Karam Allali; Bashir Ahmad. "Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity". سامانه مدیریت نشریات علمی, 14, 2, 1405, 908-918. doi: 10.22034/cmde.2025.64267.2901
Nyamoradi, Nemat, Allali, Karam, Ahmad, Bashir. (1405). 'Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity', سامانه مدیریت نشریات علمی, 14(2), pp. 908-918. doi: 10.22034/cmde.2025.64267.2901
Nyamoradi, Nemat, Allali, Karam, Ahmad, Bashir. Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity. سامانه مدیریت نشریات علمی, 1405; 14(2): 908-918. doi: 10.22034/cmde.2025.64267.2901

Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity

Computational Methods for Differential Equations
مقاله 25، دوره 14، شماره 2، تیر 2026، صفحه 908-918    اصل مقاله (534.79 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.64267.2901
نویسندگان
Nemat Nyamoradi* 1؛ Karam Allali2؛ Bashir Ahmad3
1Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran.
2Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, PO Box 146, Mohammedia, Morocco.
3Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
چکیده
This paper studies the dynamics of a SAIR mathematical model that describes the interaction among susceptible, asymptomatic, symptomatic, and recovered individuals. Two general incidence functions describing the infection caused by the asymptomatic and symptomatic individuals are introduced. We also take into account a temporary immunity, that is, a proportion of the recovered individuals becomes susceptible again. The basic reproduction number $R_0$ depends on the general incidence functions. The local and global asymptotical stability for each equilibrium will depend on the basic reproduction number $R_0$. In precise terms, the disease-free equilibrium is locally and globally asymptotically stable when $R_0<1$, while   the endemic equilibrium is locally and globally asymptotic stable when $R_0>1$. The numerical simulation is performed for different incidence rate cases, such as bilinear, Beddington-DeAngelis, Crowley Martin, and non-monotonic incidence rate functions. The simulation results are found to agree with the theoretical endings.
کلیدواژه‌ها
SAIR mathematical model؛ Stability؛ Basic reproduction number؛ Periodic orbit
مراجع
  • [1] R. T. Alqahtani, Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis, Advances in Difference Equations, 2021(1) (2021), 1–16.
  • [2] L. J. S. Allen, Some discrete-time SI, SIR, and SIS epidemic models, Mathematical Biosciences, 124 (1994), 83–105.
  • [3] L. J. S. Allen, Y. Lou, and A. L. Nevai, Spatial patterns in a discrete-time SIS patch model, Journal of Mathematical Biology, 58 (2009), 339–375.
  • [4] S. Ansumali, S. Kaushal, A. Kumar, M. K. Prakash, and M. Vidyasagar, Modelling a pandemic with asymptomatic patients, impact of lockdown and herd immunity, with applications to SARS-CoV-2, Annual Reviews in Control, 50 (22020), 432–447.
  • [5] I. Barbˆalat, Syst`emes d’´quations diff´erentielles d’oscillations non Lin´eaires, Revue roumaine de math´ematiques pures et appliqu´ees, 4 (1959), 267–270.
  • [6] J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, Journal of Animal Ecology, 44 (1975), 331–341.
  • [7] M. Bisiacco, G. Pillonetto, and C. Cobelli, Closed-form expressions and nonparametric estimation of COVID-19 infection rate, Automatica, 140 (2022), 110265.
  • [8] O. N. Bjrnstad, B. F. Finkenstaedt, and B. T. Greenfell, Dynamics of measles epidemics: estimating scaling of transmission rates using a time series SIR model, Ecological Monographs, 72 (2002), 169–184.
  • [9] R. S. Cantrell and C. Cosner, On the dynamics of predator-prey models with the Beddington-DeAngelis functional response, Journal of Mathematical Analysis and Applications, 257 (2001), 206–222.
  • [10] P. H. Crowley and E. K. Martin, Functional responses and interference within and between year classes of a dragonfly population, Journal of the North American Benthological Society, 8 (1989), 211–221.
  • [11] R. Casagrandi, L. Bolzoni, S. A. Levin, and V. Andreasen, The SIRC model for influenza Mathematical Biosciences, 200 (2006), 152–169.
  • [12] M. Das and G. P. Samanta, Optimal control of fractional order COVID-19 epidemic spreading in Japan and India 2020, Biophysical Reviews and Letters, 15(04) (2020), 207–236.
  • [13] D. L. DeAngelis, R. A. Goldstein, and R. V. O’Neill, A model for tropic interaction, Ecology, 56 (1975), 881–892.
  • [14] K. Goel Nilam, A nonlinear SAIR epidemic model: Effect of awareness class, nonlinear incidences, saturated treatment and time delay Ricerche di Matematica, 2022 (2022), 1–35.
  • [15] M. Grunnill, An exploration of the role of asymptomatic infections in the epidemiology of dengue viruses through susceptible, asymptomatic, infected and recovered (SAIR) models, Journal of theoretical biology, 439 (2020), 106442.
  • [16] J. K. Hale, S. M. V. Lunel, and L. S. Verduyn, Introduction to functional differential equations, Springer, New York, 99 (1993).
  • [17] W. Hamer, The milroy lectures on epidemic disease in england the evidence of variability and persistence of type, Lancet 1, (1906), 733–739.
  • [18] K. Hattaf, N. Yousfi, and A. Tridane, Mathematical analysis of a virus dynamics model with general incidence rate and cure rate, Nonlinear Anal. (RWA), 13(4) (2012), 1866–1872.
  • [19] J. Jiao, Z. Liu, and S. Cai, Dynamics of an SEIR model with infectivity in incubation period and homesteadisolation on the susceptible, Applied Mathematics Letters, 107 (2020), 106442.
  • [20] W. Kermack and A. McKendrick, Contributions to the mathematical theory of epidemics-I, Proceedings of the Royal Society A, 115 (1927), 700–721.
  • [21] M. A. Khan, Y. Khan, and S. Islam, Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment, Physica A, 493 (2018), 210–227.
  • [22] O. Khyar and K. Allali, Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic, Nonlinear Dynamics, 102 (2020), 489-509.
  • [23] O. Khyar and K. Allali, Dynamic Analysis of a three-Strain COVID-19 SEIR epidemic model with general incidence rates, Advances in Nonlinear Dynamics, 2022 (2022), 49–59.
  • [24] X. Zhang, Z. Li, and L. Gao, Stability analysis of a SAIR epidemic model on scale-free community networks, Mathematical Biosciences and Engineering, 21(3) (2024), 4648–4668.
  • [25] X. Liu and L. Yang, Stability analysis of an SEIQV epidemic model with saturated incidence rate, Nonlinear Analysis: Real World Applications, 13 (2012), 2671–2679.
  • [26] X. Q. Liu, S. M. Zhong, B. D. Tian, and F. X. Zheng, Asymptotic properties of a stochastic predator-prey model with Crowley-Martin functional response, Journal of Applied Mathematics and Computing, 43 (2013), 479–490.
  • [27] L. H. A. Monteiro, An epidemiological model for SARS-CoV-2, Ecological Complexity, 43 (2020), 100836.
  • [28] N. Ozalp and E. Demirrci, A fractional order SEIR model with vertical transmission, Mathematical and Computer Modelling, 54(12) (2011), 1–6.
  • [29] I. Nesteruk, Detections and SIR simulations of the COVID-19 pandemic waves in Ukraine, Computational and Mathematical Biophysics, 9 (2021), 46–65.
  • [30] R. Ross, The prevention of malaria, New York: EP Dutton and Company, (1910).
  • [31] P. Samui, J. Mondal, B. Ahmad, and A. N. Chatterjee, Clinical effects of 2-DG drug restraining SARS-CoV-2 infection: A fractional order optimal control study, J. Biological Physics, 48 (2022), 415–438.
  • [32] T. Sitthiwirattham, A. Zeb, S. Chasreechai, Z. Eskandari, M. Tilioua, and S. Djilali, Analysis of a discrete mathematical COVID-19 model, Results in Physics, 28 (2021), 104668.
  • [33] P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endmic equlibria for compartmental models of diesease transmission, Mathematical Biosciences, 180 (2002), 29–48.
  • [34] S. Wiggins, Introduction to applied nonlinear dynamical systems and chaos, Springer, (2003).
  • [35] L. Ying and T. Xiaoqing, COVID-19: Is it safe now? Study of asymptomatic infection spread and quantity risk based on SAIR model, Chaos Solitons Fractals, 6 (2021), 100060.
  • [36] X. Zhou and J. Cui, Global stability of the viral dynamics with Crowley-Martin functional response, Bulletin of the Korean Mathematical Society, 48 (2011), 555–574.
  • [37] Y. Zhao and D. Jiang, The threshold of a stochastic SIRS epidemic model with saturated incidence, Applied Mathematics Letters, 34 (2014), 90–93.
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