Asymptotic stability of a two-group stochastic SEIR model with infinite delays

• A stochastic SEIR model with infinite delays is proposed.
• The stochastic model will also be stable if the noise is not large.
• Simulation figures support the analytical findings.

A two-group stochastic SEIR epidemic model with infinite delays is proposed and investigated. Sufficient conditions for asymptotic stability are established. Some simulation figures are introduced to support the results.