Repository logo
 
Loading...
Thumbnail Image
Publication

On the Final Size of Epidemics with Seasonality

Use this identifier to reference this record.
Name:Description:Size:Format: 
Bacaer_MBM2009.pdf339.11 KBAdobe PDF Download

Advisor(s)

Abstract(s)

We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number ℛ0 or of the initial fraction of infected people. Moreover, large epidemics can happen even if ℛ0<1. But like in a constant environment, the final epidemic size tends to 0 when ℛ0<1 and the initial fraction of infected people tends to 0. When ℛ0>1, the final epidemic size is bigger than the fraction 1−1/ℛ0 of the initially nonimmune population. In summary, the basic reproduction number ℛ0 keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.

Description

Keywords

Basic reproduction number Seasonality Final epidemic size

Citation

Bacaër,N., Gomes,M.G.M. (2009)."On the Final Size of Epidemics with Seasonality". Bulletin of Mathematical Biology.[Epub ahead of print]

Research Projects

Organizational Units

Journal Issue

Publisher

Collections

CC License