Sub-Cenozoic geology of the British continental margin (lat 50°N to 57°N) and the reassembly of the North Atlantic late Paleozoic supercontinent

Discrete-Time Stochastic Epidemic Models and Their Statistical Inference

“…This model has received the most attention in the literature, and its analysis can be found in [2], [1] and [23]. Two type of transitions are possible for any individual, from susceptible to infected and from infected to removed individuals.…”

“…As pointed out in Subsection 4.2, a fundamental concept resulting from the mathematical theory of the general deterministic epidemic model is the relative removal-rate, see for instance [2] and [3]. This number is defined as τ = γ/β,whereγ and β represent the removal and infection rates, respectively, and it plays a crucial part in determining the probable occurrence of an epidemic outbreak.…”

“…The following result aims to the problem of finding approximate confident bands for the solution to (2). Before stating it, for each x ∈ E,l e tD (F)(x) denote the Jacobian matrix of…”

“…The relative removal-rate, see for instance [2] and [3], is defined as τ = γ/β,w h e r eγ and β represent the removal and infection rates, respectively. We note that…”

“…Furthermore, stochastic models based on Markovian counting processes and differential equations are mainly used to carry out the statistical analysis of the model parameters. The Mathematical Theory of Infectious Diseases by Bailey [2] represents a classical reference containing a presentation and analysis of these models. However a more recent book by Andersson and Britton [1] entitled Stochastic Epidemic Models and their Statistical Analysis is a more appropriate reference according to the point of view of this chapter.…”