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<p>Evolutionary games provide a very useful tool for analyzing how agents of population behave during the epidemic outbreak. Based on the fact that in the process of virus spreading, individuals may take different measures to inhibit virus spreading according to the environmental influences, we construct a two-stage evolutionary game process: the first stage is the choice of whether to vaccinate or not before the virus spreads, and the second stage is the process of virus spreading (SEIRD epidemic model). In the epidemic model, we analyze its basic reproduction number, the final epidemic size and the optimal control problem with efficacy of medicine as the control variable. At the level of the evolutionary game, we analyze the existence and stability of its equilibrium points and the effect of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {R}_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> on evolutionary stable strategies. Finally, a series of numerical experiments support the theoretical results obtained.</p>

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Stability Analysis of Two-Stage Evolutionary SEIRD Model

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • Xiu-Xiu Liu,
  • Elena Gubar,
  • Yin Li

摘要

Evolutionary games provide a very useful tool for analyzing how agents of population behave during the epidemic outbreak. Based on the fact that in the process of virus spreading, individuals may take different measures to inhibit virus spreading according to the environmental influences, we construct a two-stage evolutionary game process: the first stage is the choice of whether to vaccinate or not before the virus spreads, and the second stage is the process of virus spreading (SEIRD epidemic model). In the epidemic model, we analyze its basic reproduction number, the final epidemic size and the optimal control problem with efficacy of medicine as the control variable. At the level of the evolutionary game, we analyze the existence and stability of its equilibrium points and the effect of \(\mathcal {R}_{0}\) R 0 on evolutionary stable strategies. Finally, a series of numerical experiments support the theoretical results obtained.