Dynamics and simulations of stochastic COVID-19 epidemic model using Legendre spectral collocation method

The aim of this study is to investigate the dynamics of epidemic transmission of COVID-19 SEIR stochastic model with generalized saturated incidence rate. We assume that the random perturbations depends on white noises, which implies that it is directly proportional to the steady states. The existen...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 2; pp. 4220 - 4236
Main Authors Ali, Ishtiaq, Khan, Sami Ullah
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
legendre spectral method
reproduction ratio
stability analysis
stochastic covid-19 model
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Summary:The aim of this study is to investigate the dynamics of epidemic transmission of COVID-19 SEIR stochastic model with generalized saturated incidence rate. We assume that the random perturbations depends on white noises, which implies that it is directly proportional to the steady states. The existence and uniqueness of the positive solution along with the stability analysis is provided under disease-free and endemic equilibrium conditions for asymptotically stable transmission dynamics of the model. An epidemiological metric based on the ratio of basic reproduction is used to describe the transmission of an infectious disease using different parameters values involve in the proposed model. A higher order scheme based on Legendre spectral collocation method is used for the numerical simulations. For the better understanding of the proposed scheme, a comparison is made with the deterministic counterpart. In order to confirm the theoretical analysis, we provide a number of numerical examples.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023210