English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A very large class of ODE epidemic models (2.2) discussed in this paperenjoys the property of admitting also an integral renewal formulation, withrespect to an "age of infection kernel" a(t) which has a matrix exponentialform (3.2). We observe first that a very short proof of this fact is availablewhen there is only one susceptible compartment, and when its associated "newinfections" matrix has rank one. In this case, a(t) normalized to have integral1, is precisely the probabilistic law which governs the time spent in all the"infectious states associated to the susceptible compartment", and thenormalization is precisely the basic replacement number. The Laplace transform(LT) of a(t) is a generalization of the basic replacement number, and itsstructure reflects the laws of the times spent in each infectious state.Subsequently, we show that these facts admit extensions to processes withseveral susceptible classes, provided that all of them have a new infectionsmatrix of rank one. These results reveal that the ODE epidemic modelshighlighted below have also interesting probabilistic properties.

Explicit mathematical epidemiology results on age renewal kernels and R0  formulas are often consequences of the rank one property of the next  generation matrix