On extinction time of a generalized endemic chain-binomial model

• A classical chain binomial model not conferring immunity is generalized.
• The mean field equation of the Markov chain is found and stability of endemic equilibrium is studied.
• It was shown that the stochastic epidemic process and deterministic model stay close to each other for bounded time.
• It was shown that the extinction time of the infected individuals increases exponentially with the population size.

We considered a chain-binomial epidemic model not conferring immunity after infection. Mean field dynamics of the model has been analyzed and conditions for the existence of a stable endemic equilibrium are determined. The behavior of the chain-binomial process is probabilistically linked to the mean field equation. As a result of this link, we were able to show that the mean extinction time of the epidemic increases at least exponentially as the population size grows. We also present simulation results for the process to validate our analytical findings.