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Lecture

Branching Processes: Understanding R0 and Complement

In course

COM-417: Advanced probability and applications

In this course, various aspects of probability theory are considered. The first part covers the main theorems in the field (law of large numbers, central limit theorem), while the second part focuses on the theory of martingales and concentration inequalit ...

Description

This lecture delves into branching processes, focusing on the concept of R0 and its complement R. The instructor explains the Galton-Watson model and the effective reproduction number, emphasizing the impact of our behavior on controlling the spread of viruses.

Instructors (2)

Olivier Lévêque

Olivier Lévêque was born in Switzerland in 1971. He received the physics diploma from EPFL in 1995 and completed his PhD in mathematics at EPFL in 2001. Since then, he has been with the Laboratory of Information Theory at EPFL. He spent the academical year 2005-2006 at the Electrical Engineering Department of Stanford University, where he was appointed as lecturer. His research interests include stochastic analysis, random matrices, wireless communications and information theory.

Yanina Yurina Shkel

Official source

Related concepts (28)

Basic reproduction number

In epidemiology, the basic reproduction number, or basic reproductive number (sometimes called basic reproduction ratio or basic reproductive rate), denoted (pronounced R nought or R zero), of an infection is the expected number of cases directly generated by one case in a population where all individuals are susceptible to infection. The definition assumes that no other individuals are infected or immunized (naturally or through vaccination).

Computer virus

A computer virus is a type of malware that, when executed, replicates itself by modifying other computer programs and inserting its own code into those programs. If this replication succeeds, the affected areas are then said to be "infected" with a computer virus, a metaphor derived from biological viruses. Computer viruses generally require a host program. The virus writes its own code into the host program. When the program runs, the written virus program is executed first, causing infection and damage.

Reproduction

Reproduction (or procreation or breeding) is the biological process by which new individual organisms – "offspring" – are produced from their "parent" or parents. Reproduction is a fundamental feature of all known life; each individual organism exists as the result of reproduction. There are two forms of reproduction: asexual and sexual. In asexual reproduction, an organism can reproduce without the involvement of another organism. Asexual reproduction is not limited to single-celled organisms.

Virus

A virus is a submicroscopic infectious agent that replicates only inside the living cells of an organism. Viruses infect all life forms, from animals and plants to microorganisms, including bacteria and archaea. Since Dmitri Ivanovsky's 1892 article describing a non-bacterial pathogen infecting tobacco plants and the discovery of the tobacco mosaic virus by Martinus Beijerinck in 1898, more than 11,000 of the millions of virus species have been described in detail.

Macro virus

In computing terminology, a macro virus is a virus that is written in a macro language: a programming language which is embedded inside a software application (e.g., word processors and spreadsheet applications). Some applications, such as Microsoft Office, Excel, PowerPoint allow macro programs to be embedded in documents such that the macros are run automatically when the document is opened, and this provides a distinct mechanism by which malicious computer instructions can spread.

Related lectures (1)

Generation and Recombination