Simple Approximations for Epidemics with Exponential and Fixed Infectious Periods

Bulletin of Mathematical Biology
A C Fowler, T Déirdre Hollingsworth

Abstract

Analytical approximations have generated many insights into the dynamics of epidemics, but there is only one well-known approximation which describes the dynamics of the whole epidemic. In addition, most of the well-known approximations for different aspects of the dynamics are for the classic susceptible-infected-recovered model, in which the infectious period is exponentially distributed. Whilst this assumption is useful, it is somewhat unrealistic. Equally reasonable assumptions are that the infectious period is finite and fixed or that there is a distribution of infectious periods centred round a nonzero mean. We investigate the effect of these different assumptions on the dynamics of the epidemic by deriving approximations to the whole epidemic curve. We show how the well-known sech-squared approximation for the infective population in 'weak' epidemics (where the basic reproduction rate R₀ ≈ 1) can be extended to the case of an arbitrary distribution of infectious periods having finite second moment, including as examples fixed and gamma-distributed infectious periods. Further, we show how to approximate the time course of a 'strong' epidemic, where R₀ ≫ 1, demonstrating the importance of estimating the infectious period d...Continue Reading

References

Sep 1, 1990·Fertility and Sterility·R M WahJ A Hill
Oct 1, 1980·Theoretical Population Biology·Z Grossman
Jul 15, 2005·PLoS Medicine·Helen J WearingMatt J Keeling
Feb 15, 1944·Proceedings of the National Academy of Sciences of the United States of America·E B Wilson, J Worcester
Sep 1, 1942·Proceedings of the National Academy of Sciences of the United States of America·E B Wilson, M H Burke
Jun 24, 2006·Bulletin of Mathematical Biology·Junling Ma, David J D Earn
May 4, 2007·Proceedings. Biological Sciences·J Wallinga, M Lipsitch
Oct 2, 2009·Journal of the Royal Society, Interface·Andrew J K ConlanBryan T Grenfell
Jan 7, 2011·Bulletin of Mathematical Biology·Viggo Andreasen

❮ Previous
Next ❯

Citations

Jun 1, 2021·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Thomas CrellenT Déirdre Hollingsworth
Sep 1, 2021·Bulletin of Mathematical Biology·A C Fowler

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.