Generalization of Pairwise Models to non-Markovian Epidemics on Networks

Physical Review Letters
Istvan Z KissZsolt Vizi

Abstract

In this Letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations, which shows excellent agreement with results based on stochastic simulations. Furthermore, we analytically compute a new R_{0}-like threshold quantity and an analytical relation between this and the final epidemic size. Additionally, we show that the pairwise model and the analytic results can be generalized to an arbitrary distribution of the infectious times, using integro-differential equations, and this leads to a general expression for the final epidemic size. By showing the rigorous link between non-Markovian dynamics and pairwise delay differential equations, we provide the framework for a more systematic understanding of non-Markovian dynamics.

References

May 27, 1999·Proceedings. Biological Sciences·M J Keeling
Apr 6, 2001·Physical Review Letters·R Pastor-Satorras, A Vespignani
Mar 12, 2002·Proceedings. Biological Sciences·Matt J Keeling, Bryan T Grenfell
Sep 25, 2002·Proceedings of the National Academy of Sciences of the United States of America·Ken T D Eames, Matt J Keeling
Jul 10, 2003·American Journal of Epidemiology·Martin Eichner, Klaus Dietz
Jun 29, 2006·Physical Review Letters·Thilo GrossBernd Blasius
Oct 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Eben Kenah, James M Robins
Nov 20, 2008·Proceedings of the National Academy of Sciences of the United States of America·R Dean MalmgrenLuís A N Amaral
Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Till HoffmannRenaud Lambiotte
Mar 26, 2013·Physical Review Letters·Laurent Hébert-DufresneBenjamin M Althouse
Jul 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E CatorP Van Mieghem
Oct 11, 2014·BMC Medicine·Gerardo Chowell, Hiroshi Nishiura
Nov 7, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Marian BoguñáM Ángeles Serrano
Mar 31, 2015·Physical Review Letters·Antoine MoinetRomualdo Pastor-Satorras

❮ Previous
Next ❯

Citations

Apr 15, 2017·Journal of Mathematical Biology·Robert R WilkinsonKieran J Sharkey
Jun 13, 2017·Nature Communications·Xun Li, Xiang Li
Jan 20, 2018·Physical Review. E·Hanshuang ChenZhonghuai Hou
May 20, 2020·Nature Communications·Zhao-Hua LinYing-Cheng Lai
Jan 14, 2017·Physical Review. E·Hengcong LiuZonghua Liu
Sep 28, 2017·Physical Review. E·Chuang MaYing-Cheng Lai
May 16, 2018·Scientific Reports·Hengcong LiuZonghua Liu
May 22, 2019·Physical Review. E·V P Shkilev
Feb 9, 2017·Reports on Progress in Physics·Wei WangLidia A Braunstein
Nov 7, 2019·Proceedings of the National Academy of Sciences of the United States of America·Jiajun Zhang, Tianshou Zhou
Jul 8, 2017·Journal of Mathematical Biology·Neil SherborneIstvan Z Kiss
Jun 2, 2018·Journal of Biological Dynamics·Wenjun JingJuping Zhang
Mar 7, 2018·Proceedings. Mathematical, Physical, and Engineering Sciences·G RöstI Z Kiss
May 16, 2018·Physical Review. E·N SherborneI Z Kiss
May 1, 2019·Journal of Mathematical Biology·Stefan RuschelLai-Sang Young
Apr 8, 2017·Physical Review Letters·Michele StarniniMarián Boguñá
Oct 31, 2020·PloS One·Gerrit GroßmannVerena Wolf
Jan 21, 2021·Physical Review. E·Hanshuang ChenGinestra Bianconi
Apr 18, 2021·Physical Review. E·Chao-Ran CaiPetter Holme

❮ 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.

Related Papers

Proceedings of the National Academy of Sciences of the United States of America
W J Trjitzinsky
Mathematical Modelling of Natural Phenomena
Prapanporn RattanaIstvan Z Kiss
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
S Scarpetta, D Saad
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
E CatorP Van Mieghem
© 2021 Meta ULC. All rights reserved