Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models

Thresholds for disease extinction provide essential information for control, eradication or management of diseases. Through relations between branching process theory and the corresponding deterministic model, it is shown that the deterministic and stochastic thresholds are in agreement for discrete-time and continuous-time infectious disease models with multiple infectious groups. Branching process theory can be applied in conjunction with the deterministic model to give additional information about disease extinction. These relations are illustrated, analytically and numerically, in two settings, a general stage-structured model and a vector-host model applied to West Nile virus in mosquitoes and birds.

► Deterministic thresholds for disease extinction are linked to stochastic thresholds.
► Stochastic thresholds provide additional information about disease extinction.
► The threshold calculations are illustrated in stage-structured and vector-host models.