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Analysis of stochastic delayed SIRS model with exponential birth and saturated incidence rate

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  • Ali, Ishtiaq
  • Ullah Khan, Sami

Abstract

In this paper, we investigate numerically a stochastic delayed SIRS model with exponential structure and saturated incidence. A Legendre collocation method which convert the given model to a nonlinear algebraic system of equations is applied for the approximate solution. The general dynamics of the model is analyzed for relatively small noise and it is shown that large noise will cause the eradication, which will control the spreading of the disease further. Stability of the endemic equilibrium with delay is analyzed with imposing some conditions on the intensity of the noise for both stochastic and deterministic SIRS models. Some numerical test are performed to justify the mathematical conclusions.

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  • Ali, Ishtiaq & Ullah Khan, Sami, 2020. "Analysis of stochastic delayed SIRS model with exponential birth and saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920304069
    DOI: 10.1016/j.chaos.2020.110008
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    References listed on IDEAS

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    1. Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
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    3. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    4. Zhang, Tailei & Teng, Zhidong, 2008. "Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1456-1468.
    5. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
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    Cited by:

    1. Gao, Yin & Jia, Lifen, 2021. "Stability in mean for uncertain delay differential equations based on new Lipschitz conditions," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    2. Barraza, Néstor Ruben & Pena, Gabriel & Moreno, Verónica, 2020. "A non-homogeneous Markov early epidemic growth dynamics model. Application to the SARS-CoV-2 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Ishtiaq Ali & Sami Ullah Khan, 2022. "Asymptotic Behavior of Three Connected Stochastic Delay Neoclassical Growth Systems Using Spectral Technique," Mathematics, MDPI, vol. 10(19), pages 1-15, October.
    4. Turkyilmazoglu, Mustafa, 2022. "A restricted epidemic SIR model with elementary solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    5. Ishtiaq Ali & Sami Ullah Khan, 2023. "A Dynamic Competition Analysis of Stochastic Fractional Differential Equation Arising in Finance via Pseudospectral Method," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    6. Azhar Iqbal Kashif Butt & Saira Batool & Muhammad Imran & Muneerah Al Nuwairan, 2023. "Design and Analysis of a New COVID-19 Model with Comparative Study of Control Strategies," Mathematics, MDPI, vol. 11(9), pages 1-29, April.

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