Evaluating different epidemiological models with the identical basic reproduction number ℛ0

Abstract

Epidemiological models with the identical basic reproduction number $ \mathcal {R}_0 $ may behave differently on both short time scale and long time scale. In this paper, we compare the predicted final sizes for several deterministic epidemic models and estimate the probabilities of a minor/major outbreak for continuous-time Markov chain (CTMC) models, all epidemic models have the identical $ \mathcal {R}_0 $ . It is proved that the final size predicted by the epidemic model with homogeneous mixing is larger than with heterogeneous mixing. For CTMC models with heterogeneous mixing, the probabilities of a minor outbreak initiated by superspreaders and non-superspreaders are calculated and compared. For both deterministic modelling and stochastic modelling, numerical simulations are performed to support the mathematical analysis.

Keywords

• deterministic modelling
• continuous-time markov chain models
• final epidemic size
• probability of a minor outbreak
• stochastic simulation algorithm