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Kumar, G, Ramesh, K, Nisar, Kottakkaran. (1402). Dynamics of an SEIR epidemic model with saturated incidence rate including stochastic influence. سامانه مدیریت نشریات علمی, 12(2), 350-360. doi: 10.22034/cmde.2023.56544.2365
G Kumar; K Ramesh; Kottakkaran Sooppy Nisar. "Dynamics of an SEIR epidemic model with saturated incidence rate including stochastic influence". سامانه مدیریت نشریات علمی, 12, 2, 1402, 350-360. doi: 10.22034/cmde.2023.56544.2365
Kumar, G, Ramesh, K, Nisar, Kottakkaran. (1402). 'Dynamics of an SEIR epidemic model with saturated incidence rate including stochastic influence', سامانه مدیریت نشریات علمی, 12(2), pp. 350-360. doi: 10.22034/cmde.2023.56544.2365
Kumar, G, Ramesh, K, Nisar, Kottakkaran. Dynamics of an SEIR epidemic model with saturated incidence rate including stochastic influence. سامانه مدیریت نشریات علمی, 1402; 12(2): 350-360. doi: 10.22034/cmde.2023.56544.2365

Dynamics of an SEIR epidemic model with saturated incidence rate including stochastic influence

Computational Methods for Differential Equations
مقاله 11، دوره 12، شماره 2، خرداد 2024، صفحه 350-360    اصل مقاله (634.89 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.56544.2365
نویسندگان
G Kumar1؛ K Ramesh1؛ Kottakkaran Sooppy Nisar* 2
1Department of Mathematics, Anurag University, Venkatapur, Hyderabad-500088, Telangana, India.
2Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia.
چکیده
This paper aims to develop a stochastic perturbation into SEIR (Susceptible-Exposed-Infected-Removed) epidemic model including a saturated estimated incidence. A set of stochastic differential equations is used to study its behavior, with the assumption that each population’s exposure to environmental unpredictability is represented by noise terms. This kind of randomness is considerably more reasonable and realistic in the proposed model. The current study has been viewed as strengthening the body of literature because there is less research on the dynamics of this kind of model. We discussed the structure of all equilibriums’ existence and the dynamical behavior of all the steady states. The fundamental replication number for the proposed method was used to discuss the stability of every equilibrium point; if $R_0<1$, the infected free equilibrium is resilient, and if $R_0>1$, the endemic equilibrium is resilient. The system’s value is primarily described by its ambient stochasticity, which takes the form of Gaussian white noise. Additionally, the suggested model can offer helpful data for comprehending, forecasting, and controlling the spread of various epidemics globally. Numerical simulations are run for a hypothetical set of parameter values to back up our analytical conclusions. 
کلیدواژه‌ها
SEIR model؛ Basic reproduction number؛ Stochastic stability؛ White noise
مراجع
  • [1] JR. Artalejo and A. Gomez-Corral, A state-dependent Markov-modulated mechanism for generating events and stochastic models, Mathematical Methods in the Applied Sciences., 33 (2010), 1342-1349.
  • [2] A. Bahar and X. Mao, Stochastic delay Lotka–Volterra model, J. Math. Anal. Appl., 292 (2004), 364–380.
  • [3] X. Han, F. Li, and X. Meng, Dynamics analysis of a nonlinear stochastic SEIR epidemic system with varying population size, Entropy., 20 (2018), 376-20.
  • [4] S. Hariprasad, M. A. S. Srinivas, and N. Phanikumar, Three Species Epidemiological Model with Holling Type Functional Responses.International journal of mathematical models and methods in applied sciences, Int. J. Math. Models and Methods in App. Sci., 14 (2020), 62–75.
  • [5] S. Hariprasad, M. A. S. Srinivas, and N. Phanikumar,Mathematical Study of Plant-Herbivore-Carnivore System with Holling Type-II Functional Responses, J. Adv. Research in Dynamical and Control Systems., 11 (2019).
  • [6] C. Ji, D. Jiang, and X. Li, Qualitative analysis of a stochastic ratio-dependent predator–prey system, J. Comput. Appl. Math., 235 (2011), 1326–1341.
  • [7] C. Ji, D. Jiang, and N. Jiang, Analysis of a predator–prey model with modified Leslie-Gower and Holling-type II schemes with stochasticperturbation, J. Math. Anal. Appl., 359 (2009), 482–498.
  • [8] D. Jiang, N. Shi, and X. Li, Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl., 340 (2008), 588–597.
  • [9] K. Jothimani, N. Valliammal, and S. Alsaeed, Controllability Results of Hilfer Fractional Derivative Through Integral Contractors, Qual. Theory Dyn. Syst., 22 (2023), 137.
  • [10] W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics,” Proceedings of the Royal Society, A: Mathematical, Physical and Engineering Sciences, 115 (1927), 700–721.
  • [11] W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics: II. The problem of endemicity,” Proceedings of the Royal Society, A: Mathematical, Physical and Engineering Sciences, 138 (1932), 55–83.
  • [12] W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics. III. Further studies of the problem of endemicity, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 141 (1933), 94–122.
  • [13] A. Lahrouz and A. Settati, Necessary and sufficient condition for extinction and persistence of SIRS system with random perturbation, Appl. Math. Comput., 233 (2014), 10–19.
  • [14] Q. Liu, D. Jiang, T. Hayat, and A. Alsaedi, Dynamics of a stochastic tuberculosis model with antibiotic resistance, Chaos Solitons Fractals., 109 (2018), 223–230.
  • [15] Y. Li and H. Gao, Existence, uniqueness and global asymptotic stability of positive solutions of a predator–prey system with Holling IIfunctional response with random perturbation, Nonlinear Anal., 68 (2008), 1694–1705.
  • [16] M. Liu, C. Bai, and K. Wang, Asymptotic stability of a two-group stochastic SEIR model with infinite delays,Communications in Nonlinear Science and Numerical Simulation., 19 (2014), 3444–3453.
  • [17] X. Mao, S. Sabanis, and E. Renshaw, Asymptotic behaviour of the stochastic Lotka–Volterra model, J. Math. Anal. Appl., 287 (2003), 141–156.
  • [18] X. Mao, C.Yuan, and J. Zou, Stochastic differential delay equations of population dynamics, J. Math. Anal. Appl., 304 (2005), 296–320.
  • [19] J. Miekisz, J. Poleszczuk, M. Bodnar, and U. Forys, Stochastic models of gene expression with delayed degradation, Bulletin of Mathematical Biology., 73 (2011), 2231–2247.
  • [20] J. Ong, M. Chen, A. Cook, H. Lee, V. Lee, R. Lin , P.Tambyah, and L. Goh, Real-time epidemic monitoring and forecasting of H1N1-2009 using influenza-like illness from general practice and family doctor clinics in Singapore, PLoS ONE 2010 4 (2010), e10036.
  • [21] C. Ravichandran, K. Logeswari, and F.Jarad, New results on existence in the framework of Atangana–Baleanu derivative for fractional integrodifferential equations, Chaos, Solitons.Fractals., 125 (2019), 194–200.
  • [22] Li. Shangzhi and Guo. Shangjiang, Asymptotic behaviour of the stochastic Lotka–Volterra model, Mathematics and Computers in Simulation., 187 (2021), 308–336.
  • [23] K. Sooppy Nisar, K. Munusamy, and C. Ravichandran, Results on existence of solutions in nonlocal partial functional integrodifferential equations with finite delay in non-dense domain, Alexandria Engineering Journal., 73 (2023), 377–384.
  • [24] S. Takeuchi and Y. Kuroda, Predicting spread of new pandemic swine-origin influenza A (H1N1) in local mid-size city: evaluation of hospital bed shortage and effectiveness of vaccination, Nippon Eiseigaku Zasshi., 65 (2010), 48–52.
  • [25] F. Wei and R. Xue, Stability and extinction of SEIR epidemic models with generalized nonlinear incidence, Math. Comput. Simul., 170 (2020), 1–15.
  • [26] P. J. Witbooi, Stability of an SEIR epidemic model with independent stochastic perturbations, Physica A: Statistical Mechanics and its Applications., 392 (2013), 4928–4936.
  • [27] Q. Yang and X. Mao, Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbations, Nonlinear Anal., Real World Appl., 14 (2013), 1434–1456.
  • [28] X. Zhang and K. Wang, Stochastic SEIR model with jumps, Applied Mathematics and Computation., 239 (2014), 133–143.
  • [29] J. Zhang, Z. Jin, GQ. Sun, T. Zhou, and S. Ruan, Analysis of rabies in China: transmission dynamics and control, PLoS ONE., 7 (2011), e20891.
  • [30] X. Zhao and Z. Zeng, Stationary distribution and extinction of a stochastic ratio dependent predator prey system withstage structure for the predator, Physica A., 14 (2019), 1434–1456.
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