Double asymmetric percolation drives a quadruple transition in sexual contact networks

Since 2007, ZIKV outbreaks have been occurring around the world. While ZIKV is mainly spread by mosquito vectors, transmission via sex activities enables the virus to spread in regions without mosquito vectors. Modeling the patterns of ZIKV outbreak in these regions remain challenging. We consider age as an asymmetric factor in transmitting ZIKV, in addition to gender as seen in previous literature, and modify the graph structure for better modeling of such patterns. We derived our results by both solving the underlying differential equations and simulation on population graph. Based on a double asymmetric percolation process on sexual contact networks. we discovered a quadruple ZIKV epidemic transition. Moreover, we explored the double asymmetric percolation on scale-free networks. Our work provides more insight into the ZIKV transmission dynamics through sexual contact networks, which may potentially provide better public health control and prevention means in a ZIKV outbreak.

[1]  G. Ergun Human Sexual Contact Network as a Bipartite Graph , 2001, cond-mat/0111323.

[2]  S. Sardi,et al.  Zika Virus Outbreak, Bahia, Brazil , 2015, Emerging infectious diseases.

[3]  P. Hayot,et al.  Zika virus in the female genital tract. , 2016, Lancet. Infectious Diseases (Print).

[4]  Stacy Tessler Lindau,et al.  Sex, health, and years of sexually active life gained due to good health: evidence from two US population based cross sectional surveys of ageing , 2010, BMJ : British Medical Journal.

[5]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.

[6]  R. Lanciotti,et al.  Zika virus outbreak on Yap Island, Federated States of Micronesia. , 2009, The New England journal of medicine.

[7]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[8]  D. Musso,et al.  Rapid spread of emerging Zika virus in the Pacific area. , 2014, Clinical microbiology and infection : the official publication of the European Society of Clinical Microbiology and Infectious Diseases.

[9]  Stefan Bornholdt,et al.  Handbook of Graphs and Networks: From the Genome to the Internet , 2003 .

[10]  Camilla Rodrigues,et al.  Therapeutic choices in rifampicin-resistant tuberculosis. , 2016, The Lancet. Infectious diseases.

[11]  G. Ippolito,et al.  Persistent detection of Zika virus RNA in semen for six months after symptom onset in a traveller returning from Haiti to Italy, February 2016 , 2016, Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin.

[12]  Brian D. Foy,et al.  Probable Non–Vector-borne Transmission of Zika Virus, Colorado, USA , 2011, Emerging infectious diseases.

[13]  M. Eric Gershwin,et al.  The Zika outbreak of the 21st century , 2016, Journal of Autoimmunity.

[14]  S. Strogatz Exploring complex networks , 2001, Nature.

[15]  Sebastian Funk,et al.  Transmission Dynamics of Zika Virus in Island Populations: A Modelling Analysis of the 2013–14 French Polynesia Outbreak , 2016, bioRxiv.

[16]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[17]  B. Althouse,et al.  Asymmetric percolation drives a double transition in sexual contact networks , 2017, Proceedings of the National Academy of Sciences.

[18]  Antoine Allard,et al.  General and exact approach to percolation on random graphs. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  M. Keeling,et al.  Modeling Infectious Diseases in Humans and Animals , 2007 .

[20]  John S Brownstein,et al.  Potential for Zika virus introduction and transmission in resource-limited countries in Africa and the Asia-Pacific region: a modelling study. , 2016, The Lancet. Infectious diseases.

[21]  Alessandro Vespignani,et al.  Absence of epidemic threshold in scale-free networks with degree correlations. , 2002, Physical review letters.

[22]  Maria Marfel,et al.  Zika Virus, French Polynesia, South Pacific, 2013 , 2014, Emerging Infectious Diseases.

[23]  V. Cao-Lormeau,et al.  Zika Virus, French Polynesia, South Pacific, 2013 , 2014, Emerging infectious diseases.

[24]  Gerardo Chowell,et al.  Prevention and Control of Zika as a Mosquito-Borne and Sexually Transmitted Disease: A Mathematical Modeling Analysis , 2016, Scientific Reports.

[25]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[26]  G. J. Rodgers,et al.  Growing random networks with fitness , 2001, cond-mat/0103423.