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<p>In the present study, we used a deterministic model to simulate the propagation of an epidemic by dividing the population into five sub classes: susceptible, vaccinated, exposed, infectious, and recovered. The fuzzy SVEIR model has been used to examine two equilibria mathematically: endemic equilibrium and disease-free equilibrium. Fuzzy analysis has been done by taking into account the infection rate, disease-related death rate, and recovery rate as membership functions of fuzzy numbers. In order to determine the stability of the disease, stability analyses for endemic equilibrium and equilibrium in the absence of disease were done with respect to the reproduction number. The system is locally asymptotically stable at the disease-free equilibrium point if the fundamental reproduction number is smaller than 1, else it is unstable. LaSalle’s invariance principle enables us to determine that the model is globally asymptotically stable when the reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_0&lt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Additionally, we examine the sensitivity of the parameters, offer suggestions for illness prevention, and clarify the viability of the model, using the Euler approach, numerical stimulation is discovered for various <i>h</i> values.</p>

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Dynamical Analysis of Fuzzy Measels SVEIR Model

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • H. A. Bhavithra,
  • S. Sindu Devi,
  • K. Kannan

摘要

In the present study, we used a deterministic model to simulate the propagation of an epidemic by dividing the population into five sub classes: susceptible, vaccinated, exposed, infectious, and recovered. The fuzzy SVEIR model has been used to examine two equilibria mathematically: endemic equilibrium and disease-free equilibrium. Fuzzy analysis has been done by taking into account the infection rate, disease-related death rate, and recovery rate as membership functions of fuzzy numbers. In order to determine the stability of the disease, stability analyses for endemic equilibrium and equilibrium in the absence of disease were done with respect to the reproduction number. The system is locally asymptotically stable at the disease-free equilibrium point if the fundamental reproduction number is smaller than 1, else it is unstable. LaSalle’s invariance principle enables us to determine that the model is globally asymptotically stable when the reproduction number \(R_0<1\) R 0 < 1 . Additionally, we examine the sensitivity of the parameters, offer suggestions for illness prevention, and clarify the viability of the model, using the Euler approach, numerical stimulation is discovered for various h values.