Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics.
Bull Math Biol
; 84(1): 4, 2021 11 20.
Article
en En
| MEDLINE
| ID: mdl-34800180
ABSTRACT
Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here, we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour. We develop a system of ordinary differential equations that approximate the number of infected individuals in the QSD for arbitrary contact networks and parameter values. When the epidemic level is high, these QSD approximations coincide with the existing approximation methods. However, as we approach the epidemic threshold, the models deviate, with these models following the QSD and the existing methods approaching the all susceptible state. Through consistently approximating the QSD, the proposed methods provide a more robust link to the stochastic models.
Palabras clave
Texto completo:
1
Colección:
01-internacional
Banco de datos:
MEDLINE
Asunto principal:
Enfermedades Transmisibles
/
Epidemias
Tipo de estudio:
Prognostic_studies
Límite:
Humans
Idioma:
En
Revista:
Bull Math Biol
Año:
2021
Tipo del documento:
Article
País de afiliación:
Reino Unido