Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes

Infectious Disease Modelling

Volumn 2, Issue 1, 2017, Pages 35-55

  Miller, Joel C ^a,b  

^a MONASH UNIVERSITY   (Australia)

^b INSTITUTE FOR DISEASE MODELING   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BASIC REPRODUCTION NUMBER; CONFIGURATION MODEL NETWORK; EBOLAVIRUS; HUMAN; MASS ACTION MODEL; MATHEMATICAL MODEL; MOSQUITO; NONHUMAN; SEXUAL TRANSMISSION; SIMULATION; VIRUS CARRIER; VIRUS TRANSMISSION; ZIKA VIRUS;

EID: 85027885615     PISSN: 24680427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.idm.2016.12.003     Document Type: Article

References (41)

1. Allard, A., Althouse, B.M., Hébert-Dufresne, L., Scarpino, S.V., The risk of sustained sexual transmission of Zika is underestimated. bioRxiv, 2016, 090324.
2. Ball, F., Neal, P., Network epidemic models with two levels of mixing. Mathematical Biosciences 212:1 (2008), 69–87.
3. Baron, R.C., McCormick, J.B., Zubeir, O.A., Ebola virus disease in southern Sudan: Hospital dissemination and intrafamilial spread. Bulletin of the World Health Organization, 61(6), 1983, 997.
4. Christie, A., Davies-Wayne, G.J., Cordier-Lasalle, T., Blackley, D.J., Scott Laney, A., Williams, D.E., et al. Possible sexual transmission of Ebola virus—Liberia. MMWR. Morbidity and mortality weekly report 64:17 (2015), 479–481.
5. Deen, G.F., Knust, B., Broutet, N., Sesay, F.R., Formenty, P., Ross, C., et al. Ebola RNA persistence in semen of ebola virus disease survivorspreliminary report. New England Journal of Medicine, 2015.
6. Decreusefond, L., Dhersin, J.-S., Moyal, P., Tran, V.C., Large graph limit for an SIR process in random network with heterogeneous connectivity. The Annals of Applied Probability 22:2 (2012), 541–575.
7. Diekmann, O., Heesterbeek, H., Britton, T., Mathematical tools for understanding infectious disease dynamics. 2012, Princeton University Press.
8. 0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology 28 (1990), 365–382.
9. Diekmann, O., Heesterbeek, J.A.P., Roberts, M.G., The construction of next-generation matrices for compartmental epidemic models. Journal of the Royal Society Interface, 2009 rsif20090386.
10. Duffy, M.R., Chen, T.-H., Thane Hancock, W., Powers, A.M., Kool, J.L., Lanciotti, Robert S., et al. Zika virus outbreak on Yap Island, federated states of Micronesia. New England Journal of Medicine 360:24 (2009), 2536–2543.
11. Emond, R.T., Evans, B., Bowen, E.T., Lloyd, G., A case of Ebola virus infection. Br Med J 2:6086 (1977), 541–544.
12. Feld, S.L., Why your friends have more friends than you do. American Journal of Sociology 96:6 (1991), 1464–1477.
13. Fennell, Peter G., Melnik, S., Gleeson, J.P., The limitations of discrete-time approaches to continuous-time contagion dynamics. 2016 arXiv preprint arXiv:1603.01132.
14. Foy, B.D., Kobylinski, K.C., Chilson Foy, J.L., Blitvich, B.J., da Rosa, A.T., Haddow, A.D., et al. Probable non-vector-borne transmission of Zika virus, Colorado, USA. Emerging Infectious Diseases 17:5 (2011), 880–882.
15. Gao, D., Lou, Y., He, D., Porco, T.C., Kuang, Y., Chowell, G., et al. Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: A mathematical modeling analysis. Scientific Reports, 2016.
16. Heymann, D.L., Weisfeld, J.S., Webb, P.A., Johnson, K.M., Cairns, T., Berquist, H., Ebola hemorrhagic fever: Tandala, Zaire, 1977–1978. Journal of Infectious Diseases 142:3 (1980), 372–376.
17. Janson, S., Luczak, M., Windridge, P., Law of large numbers for the SIR epidemic on a random graph with given degrees. Random Structures & Algorithms 45:4 (2014), 724–761.
18. Kermack, W.O., McKendrick, A.G., A contribution to the mathematical theory of epidemics. Royal Society of London Proceedings Series A 115 (August 1927), 700–721.
19. Kiss, Istvan Z., Miller, Joel C., Simon, P.L., Mathematics of epidemics on networks: From exact to approximate models. 2017, Springer ISBN 978-3-319-50806-1, (Forthcoming) http://www.springer.com/us/book/9783319508047.
20. Kurtz, T.G., Limit theorems for sequences of jump markov processes approximating ordinary differential processes. Journal of Applied Probability 8:2 (1971), 344–356.
21. Lessler, J., Chaisson, L.H., Kucirka, L.M., Bi, Q., Grantz, K., Salje, H., et al. Assessing the global threat from Zika virus. Science, 353(6300), 2016.
22. Leung, K.Y., Dangerous connections: The spread of infectious diseases on dynamic networks., 2016, Utrecht University PhD thesis.
23. 0. Journal of mathematical biology 71:1 (2015), 1–56.
24. Ludwig, D., Final size distributions for epidemics. Mathematical Biosciences 23 (1975), 33–46.
25. Mackay, Ian M., Arden, K.E., Ebola virus in the semen of convalescent men. The Lancet Infectious Diseases 15:2 (2015), 149–150.
26. Mate, S.E., Kugelman, J.R., Nyenswah, T.G., Ladner, J.T., Wiley, M.R., Cordier-Lassalle, Athalia Christie, T., et al. Molecular evidence of sexual transmission of Ebola virus. New England Journal of Medicine 373:25 (2015), 2448–2454.
27. McElroy, A.K., Akondy, R.S., Davis, C.W., Ellebedy, A.H., Mehta, A.K., Kraft, C.S., et al. Human ebola virus infection results in substantial immune activation. Proceedings of the National Academy of Sciences 112:15 (2015), 4719–4724.
28. Miller, J.C., A note on a paper by Erik Volz: SIR dynamics in random networks. Journal of Mathematical Biology 62:3 (2011), 349–358.
29. Miller, J.C., A note on the derivation of epidemic final sizes. Bulletin of Mathematical Biology 74:9 (2012), 2125–2141.
30. Miller, J.C., Epidemics on networks with large initial conditions or changing structure. PLoS ONE, 9(7), 2014, e101421.
31. Miller, J.C., Kiss, I.Z., Epidemic spread in networks: Existing methods and current challenges. Mathematical modelling of natural phenomena 9:02 (2014), 4–42.
32. Miller, J.C., Volz, E.M., Incorporating disease and population structure into models of SIR disease in contact networks. PLoS ONE, 8(8), 2013, e69162.
33. Miller, Joel C., Slim, Anja C., Volz, E.M., Edge-based compartmental modelling for infectious disease spread. Journal of the Royal Society Interface 9:70 (2012), 890–906.
34. Moreno, Y., Gómez, J.B., Pacheco, A.F., Epidemic incidence in correlated complex networks. Physical Review E, 68(3)(035103), 2003.
35. Musso, D., Roche, C., Robin, E., Nhan, T., Teissier, A., Cao-Lormeau, V.-M., et al. Potential sexual transmission of Zika virus. Emerg Infect Dis 21:2 (2015), 359–361.
36. Newman, Mark E.J., Spread of epidemic disease on networks. Physical Review E, 66(1)(016128), 2002.
37. Newman, Mark E.J., The structure and function of complex networks. SIAM Review 45:2 (2003), 167–256.
38. Nicastri, E., Castilletti, C., Liuzzi, G., Iannetta, M., Capobianchi, M.R., Ippolito, G., Persistent detection of Zika virus RNA in semen for six months after symptom onset in a traveller returning from Haiti to Italy, february 2016. Eurosurveillance, 21(32), 2016.
39. Oliveira Melo, A.S., Malinger, G., Ximenes, R., Szejnfeld, P.O., Alves Sampaio, S., de Filippis, A.M.B., Zika virus intrauterine infection causes fetal brain abnormality and microcephaly: Tip of the iceberg?. Ultrasound in Obstetrics & Gynecology 47:1 (2016), 6–7.
40. Pellis, L., Ferguson, N.M., Fraser, C., The relationship between real-time and discrete-generation models of epidemic spread. Mathematical biosciences 216:1 (2008), 63–70.
41. Ventura, C.V., Maia, M., Bravo-Filho, V., Góis, A.L., Belfort, R., Zika virus in Brazil and macular atrophy in a child with microcephaly. The Lancet, 387(10015), 2016, 228.