SIR dynamics in random networks with communities

Journal of Mathematical Biology
Jinxian LiZhen Jin

Abstract

This paper investigates the effects of the community structure of a network on the spread of an epidemic. To this end, we first establish a susceptible-infected-recovered (SIR) model in a two-community network with an arbitrary joint degree distribution. The network is formulated as a probability generating function. We also obtain the sufficient conditions for disease outbreak and extinction, which involve the first-order and second-order moments of the degree distribution. As an example, we then study the effect of community structure on epidemic spread in a complex network with a Poisson joint degree distribution. The numerical solutions of the SIR model well agree with stochastic simulations based on the Monte Carlo method, confirming that the model is reliable and accurate. Finally, by strengthening the community structure in the simulation, i.e. fixing the total degree distribution and reducing the number ratio of the external edges, we can increase or decrease the final cumulative epidemic incidence depending on the transmissibility of the virus between humans and the community structure at that point. Why community structure can affect disease dynamics in a complicated way is also discussed. In any case, for large-scale...Continue Reading

References

Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M E J Newman
Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M E J Newman
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M E J Newman
Mar 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M E J Newman, M Girvan
Jun 29, 2006·Physical Review Letters·Thilo GrossBernd Blasius
Aug 2, 2007·Journal of Mathematical Biology·Erik Volz
Nov 17, 2007·Theoretical Population Biology·K T D Eames
Feb 19, 2008·Mathematical Biosciences·Frank Ball, Peter Neal
Mar 28, 2009·Journal of the Royal Society, Interface·Joel C Miller
Mar 28, 2009·Journal of the Royal Society, Interface·Robert E RowthornChristopher A Gilligan
Oct 2, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Joel C Miller
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·James P Gleeson
Dec 17, 2009·Mathematical Biosciences·Frank BallPieter Trapman
Mar 24, 2010·Journal of Mathematical Biology·Joel C Miller
Apr 14, 2010·PLoS Computational Biology·Marcel Salathé, James H Jones
Jun 12, 2010·Journal of the Royal Society, Interface·Thomas House, Matt J Keeling
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·James P GleesonAdam Hackett
Dec 15, 2010·Journal of Theoretical Biology·Thomas House, Matt J Keeling
Jan 19, 2012·Journal of Mathematical Biology·Junling MaFrederick H Willeboordse
May 5, 2012·Journal of Theoretical Biology·Bing WangKazuyuki Aihara
May 24, 2012·Journal of Mathematical Biology·Dean KochJunling Ma
Sep 13, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ilker Tunc, Leah B Shaw

❮ Previous
Next ❯

Citations

Sep 19, 2020·Physical Review. E·Liang FengCangqi Zhou
Mar 24, 2021·Chaos·Jin-Xuan Yang

❮ 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.