SIR model with general distribution function in the infectious period

Marcelo F.C. Gomes and Sebastián Gonçalves

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 15, 3133-3142

Abstract: The Susceptible-Infected-Removed or SIR model, as it was formulated by Kermack and McKendrick, is the key model for epidemic dynamics. Most applications of such a basic scheme use a constant rate for the removal term. However, that assumption corresponds to the rather unrealistic exponential distribution of infectious times. On the other hand, recent approaches, like numerical simulations, frequently assume a fixed and uniform duration for the infectious state—which is unrealistic too. The extreme assumptions in those different schemes are a hurdle that can frustrate any intention of drawing comparison between results from them. In the present contribution we study the delay equations for the SIR model, comparing the solutions for many typical cases with the simulation counterpart and with the standard SIR model. Using delay equations, where each infected individual is removed at a specific time after being infected, the dynamics for the infected and susceptible agree almost exactly with the numerical implementation. Even in the general case of distributed infective periods, the agreement is excellent.

Keywords: Epidemics dynamics; SIR model; Numerical simulations; Differential equations (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437109002969
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:15:p:3133-3142

DOI: 10.1016/j.physa.2009.04.015

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().