Stochastic amplification in epidemics

Stochastic amplification in epidemics.

The role of stochasticity and its interplay with nonlinearity are central current issues in studies of the complex population patterns observed in nature, including the pronounced oscillations of wildlife and infectious diseases. The dynamics of childhood diseases have provided influential case studies to develop and test mathematical models with practical application to epidemiology, but are a...

in stochastic SIS epidemics

Stochastic Epidemics in Growing Populations

Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that three different scenarios may occur: (i) an epidemic never takes off, (ii) an epidemic gets going and grows but at a slower rate than the community thus still ...

Stochastic Models for Epidemics

Early in 1987, the AIDS epidemic was still in its relatively early stages in the United Kingdom, although well underway in the United States. In preparation for a one-day Royal Statistical Society meeting on the statistical aspects of AIDS (Royal Statistical Society, 1988) later that year, an informal workshop was organised by David Cox to discuss the various mathematical modelling approaches t...

Stochastic dynamics of dengue epidemics.

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected...