A Markov Chain Approach to Calculate R0 in Stochastic Epidemic Models
✍ Scribed by CARLOS M. HERNÁNDEZ-SUÁREZ
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 157 KB
- Volume
- 215
- Category
- Article
- ISSN
- 0022-5193
No coin nor oath required. For personal study only.
✦ Synopsis
R
has been de"ned as &&The expected number of secondary infections originated by a &&typical'' infective individual when introduced into a population of susceptibles'', and it is perhaps the single most important parameter in epidemic models. A general framework to calculate R that can be applied to complicated stochastic epidemic models that may include demography, several strains, latent or carrier-like states, with or without density-dependent parameters is introduced. This framework helps us to understand the concept of a &&typical'' infective individual used in the deterministic de"nition of R . The method is illustrated with applications to several epidemic models, including some in which it has been found that the disease may persist even if R
(1. It is shown that although the probability of extinction is di$cult to calculate in these latter cases, it is possible to give general conditions on the parameters under which eventual extinction is certain.