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# Collection Thematic Month Week 3: Mathematical Modeling and Statistical Analysis of Infectious Disease Outbreaks / Mois thématique Semaine 3 : Modélisation mathématique et analyses statistique des épidémies de maladies infectieuses

Organizer(s) Britton, Tom ; Forien, Raphaël ; Hubert, Florence ; Pardoux, Etienne
Date(s) 2/17/20 - 2/21/20
00:00:00 / 00:00:00
2 7

## Near-criticality in mathematical models of epidemics

In an epidemic model, the basic reproduction number $R_{0}$ is a function of the parameters (such as infection rate) measuring disease infectivity. In a large population, if $R_{0}> 1$, then the disease can spread and infect much of the population (supercritical epidemic); if $R_{0}< 1$, then the disease will die out quickly (subcritical epidemic), with only few individuals infected. For many epidemics, the dynamics are such that $R_{0}$ can cross the threshold from supercritical to subcritical (for instance, due to control measures such as vaccination) or from subcritical to supercritical (for instance, due to a virus mutation making it easier for it to infect hosts). Therefore, near-criticality can be thought of as a paradigm for disease emergence and eradication, and understanding near-critical phenomena is a key epidemiological challenge. In this talk, we explore near-criticality in the context of some simple models of SIS (susceptible-infective-susceptible) epidemics in large homogeneous populations.

### Citation data

• DOI 10.24350/CIRM.V.19612703
• Cite this video Luczak Malwina (2/20/20). Near-criticality in mathematical models of epidemics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19612703
• URL https://dx.doi.org/10.24350/CIRM.V.19612703

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