On the early epidemic dynamics for pairwise models

Journal of Theoretical Biology

Volumn 352, Issue , 2014, Pages 71-81

  Llensa, Carlos ^a   Juher, David ^a   Saldaña, Joan ^a  

^a UNIVERSITY OF GIRONA   (Spain)

Author keywords

Basic reproduction number; Initial epidemic growth rate; Pairwise epidemic models; SEIR model

Indexed keywords

EPIDEMIC; GROWTH RATE; HOMOGENEOUS MEDIUM; NUMERICAL MODEL; THEORETICAL STUDY;

ARTICLE; ATTITUDE TO HEALTH; BASIC REPRODUCTION NUMBER; CORRELATION ANALYSIS; DISEASE DURATION; DISEASE PREDISPOSITION; DISEASE TRANSMISSION; EPIDEMIC; GROWTH RATE; HUMAN; MATHEMATICS; NEIGHBORHOOD; PAIRWISE MODEL; POPULATION DYNAMICS; PREDICTION; PRIORITY JOURNAL; STATISTICAL MODEL; SUSCEPTIBLE EXPOSED INFECTIOUS RECOVERED MODEL; SUSCEPTIBLE INFECTED SUSCEPTIBLE MODEL; SUSCEPTIBLE INFECTIOUS RECOVERED MODEL; SUSCEPTIBLE POPULATION; VIRUS LATENCY; BIOLOGICAL MODEL; EPIDEMIOLOGY;

DISEASE SUSCEPTIBILITY; EPIDEMIOLOGIC STUDIES; HUMANS; MODELS, BIOLOGICAL;

EID: 84896446953     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2014.02.037     Document Type: Article

References (47)

1. Anderson R.M., May R.M. Infectious Diseases of Humans: Dynamics and Control 1991, Oxford University Press, USA.
2. Bansal S., Grenfell B.T., Meyers L.A. When individual behaviour matters. homogeneous and networks models in epidemiology. J. R. Soc. Interface 2007, 4:879-891.
3. Bauch C.T. The spread of infectious diseases in spatially structured populations: an invasory pair approximation. Math. Biosci. 2005, 198:217-237.
4. Catanzaro M., Boguñá M., Pastor-Satorras R. Generation of uncorrelated random scale-free networks. Phy. Rev. E 2005, 71:027103.
5. Chowell G., Nishiura H., Bettencourt L.M.A. Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. J. R. Soc. Interface 2007, 4:15-166.
6. Diekmann O., Heesterbeek J.A.P., Britton T. Mathematical Tools for Understanding Infectious Diseases Dynamics 2013, Princeton University Press, Princeton.
7. Do A.-L., Gross T. Contact processes and moment closure on adaptive networks. Adaptive Networks: Theory Models and Applications 2009, 191-208. Springer, New York. T. Gross, H. Sayama (Eds.).
8. Eames K.T.D., Keeling M.J. Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases. Proc. Natl. Acad. Sci. USA 2002, 99:13330-13335.
9. Ferguson N. Capturing human behaviour. Nature 2007, 446:733.
10. Garcia-Domingo J.L., Saldaña J. Extinction threshold for spatial forest dynamics with height structure. J. Theor. Biol. 2011, 276:138-149.
11. Gillespie D.T. Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 2007, 58:35-55.
12. Gross T. Interplay of network state and topology in epidemic dynamics. Handbook of Biological Networks 2009, 417-436. World Scientific, Singapore. S. Boccaletti, V. Latora, Y. Moreno (Eds.).
13. Gross T., DiLima C.J.D., Blasius B. Epidemic dynamics on an adaptive network. Phys. Rev. Lett. 2006, 96:208701.
14. Harada Y., Iwasa Y. Lattice population dynamics for plants with dispersing seeds and vegetative propagation. Res. Popul. Ecol. 1994, 36:237-249.
15. House T., Keeling M.J. Insights from unifying modern approximations to infections on networks. J. R. Soc. Interface 2011, 8:67-73.
16. Harada Y., Ezoe H., Iwasa Y., Matsuda H., Sato K. Population persistence and spatially limited social interaction. Theor. Popul. Biol. 1995, 48:65-91.
17. Juher D., Ripoll J., Saldaña J. Outbreak analysis of an SIS epidemic model with rewiring. J. Math. Biol. 2013, 67:411-432.
18. Keeling M.J. The effects of local spatial structure on epidemiological invasions. Proc. R. Soc. Lond. B 1999, 266:859-867.
19. Keeling M.J., Rand D.A., Morris A.J. Correlation models for childhood epidemics. Proc. R. Soc. Lond. B 1997, 264:1149-1156.
20. Kimura D., Hayakawa Y. Coevolutionary networks with homophily and heterophily. Phys. Rev. E 2008, 78:016103.
21. Lindquist J., Ma J., van den Driessche P., Willeboordse F.H. Effective degree network disease models. J. Math. Biol. 2011, 62:143-164.
22. Lipsitch M., et al. Transmission dynamics and control of severe acute respiratory syndrome. Science 2003, 300:1966-1970.
23. Lloyd A.L. Sensitivity of model-based epidemiological parameter estimation to model assumptions. Mathematical and Statistical Estimation Approaches 2009, 123-141. Springer, New York. Chowell (Ed.).
24. Lloyd-Smith J.O., Schreiber S.J., Kopp P.E., Getz W.M. Superspreading and the effect of individual variation on disease emergence. Nature 2005, 438:355-359.
25. McCarthy M., Haddow L.J., Furner V., Mindel A. Contact tracing for sexually transmitted infections in New South Wales, Australia. Sexual Health 2007, 4:21-25.
26. Marceau V., Noël P.A., Hébert-dufresne L., Allard A., Dubé L.J. Adaptive networks. coevolution of disease and topology. Phys. Rev. E 2010, 82:036116.
27. Meyers L.A., Pourbohloul B., Newman M.E.J., Skowronski D.M., Brunham R.C. Network theory and SARS. predicting outbreak diversity. J. Theor. Biol. 2005, 232:71-81.
28. Nishiura H., Chowell G., Safan M., Castillo-Chavez C. Pros and cons of estimating the reproduction number from early epidemic growth rate of influenza A (H1N1) 2009. Theor. Biol. Med. Model. 2010, 7.
29. Nowak M., Lloyd A.L., et al. Viral dynamics of primary viremia and antiretroviral therapy in simian immunodeficiency virus infection. J. Virol. 1997, 71:7518-7525.
30. Rand D.A. Correlation equations and pair approximation for spatial ecologies. Advanced Ecological Theory 1999, 100-142. Blackwell Science, London. J. McGlade (Ed.).
31. Riley S., et al. Transmission dynamics of the etiological agent of SARS in Hong Kong. impact of public health interventions. Science 2003, 300:1961-1966.
32. Risau-Gusman S., Zanette D.H. Contact switching as a control strategy for epidemic outbreaks. J. Theor. Biol. 2009, 257:52-60.
33. Roberts M.G., Heesterbeek J.A.P. Model-consistent estimation of the basic reproduction number from the incidence of an emerging infection. J. Math. Biol. 2007, 55:803-816.
34. Schwartz I.B., Shaw L.B. Rewiring for adaptation. Physics 2010, 3:17.
35. Schwarzkopf Y., Rákos A., Mukamel D. Epidemic spreading in evolving networks. Phys. Rev. E 2010, 82:036112.
36. Shil P., Gurav Y.K., Chadha M.S., Mishra A.C. Transmission dynamics of novel influenza A/H1N1 2009 outbreak in a residential school in India. Curr. Sci. 2011, 100:1127-1183.
37. Stack J.C., Bansal S., Kumar V.S.A., Grenfell B. Inferring population-level contact heterogeneity from common epidemic data. J. R. Soc. Interface 2012, 10:20120578.
38. Svensson A. A note on generation times in epidemic models. Math. Biosci. 2007, 208:300-311.
39. Taylor M., Simon P.L., Green D.M., House T., Kiss I.Z. From Markovian to pairwise epidemic models and the performance of moment closure approximations. J. Math. Biol. 2012, 64:1021-1042.
40. Trapman P. Reproduction numbers for epidemics on networks using pair approximation. Math. Biosci. 2007, 210:464-489.
41. Volz E. SIR dynamics in random networks with heterogeneous connectivity. J. Math. Biol. 2008, 56:293-310.
42. Volz E., Frost S.D., Rothenberg R., Meyers L.A. Epidemiological bridging by injection drug use drives an early HIV epidemic. Epidemics 2010, 2:155-164.
43. Volz E., Meyers L.A. Susceptible-infected-recovered epidemics in dynamic contact networks. Proc. R. Soc. B 2007, 274:2925-2933.
44. Wallinga J., Lipsitch M. How generation intervals shape the relationship between growth rates and reproductive numbers. Proc. R. Soc. B 2007, 274:599-604.
45. Yan P. Separate roles of the latent and infectious periods in shaping the relation between the basic reproduction number and the intrinsic growth rate of infectious disease outbreaks. J. Theor. Biol. 2008, 251:238-252.
46. Yang C.K., Brauer F. Calculation of R0 for age-at-infection models. Math. Biosci. Eng. 2008, 5:585-599.
47. Zanette D.H., Risau-Gusmán S. Infection spreading in a population with evolving contacts. J. Biol. Phys. 2008, 34:135-148.