Stochastic two-group models with transmission dependent on host infectivity or susceptibility

References

• L.J.S. Allen, An Introduction to Stochastic Processes with Applications to Biology, 2nd ed., CRC Press, Boca Raton, Fl., 2010.
   Google Scholar
• L.J.S. Allen, Stochastic Population and Epidemic Models Persistence and Extinction, Springer International Publishing, Switzerland, 2015.
   Google Scholar
• L.J.S. Allen, A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis, Infect. Dis. Model. 2 (2017), pp. 128–142.
   PubMedGoogle Scholar
• L.J.S. Allen and P. van den Driessche, Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models, Math. Biosci. 243 (2013), pp. 99–108. doi: 10.1016/j.mbs.2013.02.006
   PubMed Web of Science ®Google Scholar
• K.B. Athreya and A.P. Ney, Branching Processes, Springer-Verlag, New York, 1972.
   Google Scholar
• L. Bolzoni, L. Real, and G. De Leo, Transmission heterogeneity and control strategies for infectious disease emergence, PLoS. One 2 (2007), pp. 747. Available at https://doi.org/10.1371/journal.pone.0000747.
   Web of Science ®Google Scholar
• N. Chitnis, J.M. Hyman, and J.M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol. 70 (2008), pp. 1272–1296. doi: 10.1007/s11538-008-9299-0
   PubMed Web of Science ®Google Scholar
• S.Y. Cho, J. Kang, Y.E. Ha, G.E. Park, J.Y. Lee, J.H. Ko, J.Y. Lee, J.M. Kim, C. Kang, I.J. Jo, J.G. Ryu, J.R. Choi, S. Kim, H.J. Huh, C.S. Ki, E.S. Kang, K.R. Peck, H.J. Dhong, J.H. Song, D.R.Chung, and Y.J. Kim, MERS-CoV outbreak following a single patient exposure in an emergency room in South Korea: An epidemiological outbreak study, Lancet 388 (2016), pp. 994–1001. doi: 10.1016/S0140-6736(16)30623-7
   PubMed Web of Science ®Google Scholar
• G. Chowell, S. Blumberg, L. Simonsen, M. Miller, and C. Viboud, Synthesizing data and models for the spread of MERS-CoV, 2013: Key role of index cases and hospital transmission, Epidemics 9 (2014), pp. 40–51. doi: 10.1016/j.epidem.2014.09.011
   PubMed Web of Science ®Google Scholar
• G. Chowell, C. Castillo-Chavez, P.W. Fenimore, C.M. Kribs-Zaleta, L. Arriola, and J.M. Hyman, Model parameters and outbreak control for SARS, Emerg. Infect. Dis. 10 (2004), pp. 1258–1263. doi: 10.3201/eid1007.030647
   PubMed Web of Science ®Google Scholar
• G. De Serres, N. Boulianne, N. Brousseau, M. Benoit, S. Lacoursiere, F. Guillemette, J. Soto, M.Ouakki, B. Ward, and D. Skowronski, Higher risk of measles when the first dose of a 2-dose schedule of measles vaccine is given at 12–14 months versus 15 months of age, Clin. Infect. Dis. 55 (2012), pp. 394–402. doi: 10.1093/cid/cis439
   PubMed Web of Science ®Google Scholar
• O. Diekmann, J. Heesterbeek, and J. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990), pp. 365–382. doi: 10.1007/BF00178324
   PubMed Web of Science ®Google Scholar
• C.J. Edholm, B.O. Emerenini, A.L. Murillo2018 Searching for superspreaders: Identifying epidemic patterns associated with superspreading events in stochastic models, in Understanding Complex Biological Systems with Mathematics, Chapter 1, pp. 1–29, Springer Nature, Switzerland
   Google Scholar
• Z. Feng, A.N. Hill, A.T. Curns, and J.W. Glasser, Evaluating targeted interventions via meta-population models with multi-level mixing, Math. Biosci. 287 (2017), pp. 93–104. doi: 10.1016/j.mbs.2016.09.013
   PubMed Web of Science ®Google Scholar
• A.P. Galvani and R.M. May, Dimensions of superspreading, Nature 438 (2005), pp. 293–295. doi: 10.1038/438293a
   PubMed Web of Science ®Google Scholar
• G. Gopalakrishna, P. Choo, Y. Leo, B.K. Tay, Y.T. Lim, A.S. Khan, and C.C. Tan, SARS transmission and hospital containment, Emerg. Infect. Dis. 10 (2004), pp. 395–400. doi: 10.3201/eid1003.030650
   PubMed Web of Science ®Google Scholar
• F.M. Guerra, S. Bolotin, G. Lim, J. Heffernan, S.L. Deeks, Y. Li, and N.S. Crowcroft, The basic reproduction number (R0) of measles: A systematic review, Lancet Infect. Dis. 17 (2017), pp. e420–e428. doi: 10.1016/S1473-3099(17)30307-9
   PubMed Web of Science ®Google Scholar
• T.E. Harris, The Theory of Branching Processes, Springer-Verlag, Berlin, Heidelberg, 1963.
   Google Scholar
• H. Hethcote, The mathematics of infectious disease, SIAM Rev. 42 (2000), pp. 599–653. doi: 10.1137/S0036144500371907
   Web of Science ®Google Scholar
• A. James, J.W. Pitchford, and M.J. Plank, An event-based model of superspreading in epidemics, Proc. R. Soc. Lond. [Biol] 274 (2007), pp. 741–747. doi: 10.1098/rspb.2006.0219
   PubMed Web of Science ®Google Scholar
• S. Karlin and H. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, 1981.
   Google Scholar
• M. Kontio, S. Jokinen, M. Paunio, H. Peltola, and I. Davidkin, Waning antibody levels and avidity: Implications for MMR vaccine-induced protection, J. Infect. Dis. 206 (2012), pp. 1542–1548. doi: 10.1093/infdis/jis568
   PubMed Web of Science ®Google Scholar
• J.W. Leavitt, Typhoid Mary: Captive to the Public's Health, Beacon Press, Boston, 1996.
   Google Scholar
• J. Lee, G. Chowell, and E. Jung, A dynamic compartmental model for the Middle East respiratory syndrome outbreak in the Republic of Korea: A retrospective analysis on control interventions and superspreading events., J. Theoret. Biol. 408 (2016), pp. 118–126. doi: 10.1016/j.jtbi.2016.08.009
   PubMed Web of Science ®Google Scholar
• J.O. Lloyd-Smith, S.J. Schreiber, P.E. Kopp, and W.M. Getz, Superspreading and the effect of individual variation on disease emergence, Nature 438 (2005), pp. 355–359. doi: 10.1038/nature04153
   PubMed Web of Science ®Google Scholar
• P. Magal, O. Seydi, and G. Webb, Final size of an epidemic for a two group SIR model, SIAM J. Appl. Math. 76 (2016), pp. 2042–2059. doi: 10.1137/16M1065392
   Web of Science ®Google Scholar
• T. Mkhatshwa and A. Mummert, Modeling super-spreading events for infectious disease: Case study SARS, Int. J. Acad. Med. 41 (2011), pp. 82–88. doi: 10.1111/j.1445-5994.2010.02339.x
   PubMedGoogle Scholar
• National Center for Immunization and Respiratory Diseases, Epidemiology and prevention of vaccine-preventable diseases. Available at https://www.cdc.gov/vaccines/pubs/pinkbook/meas.html (last access date 2/1/2018).
   Google Scholar
• National Center for Immunization and Respiratory Diseases, Division of Viral Diseases, Severe Acute Respiratory Syndrome (SARS). Available at https://www.cdc.gov/sars/about/faq.html (last access date 2/1/2018).
   Google Scholar
• National Institutes of Health (US), Biological Sciences Curriculum Study, Bethesda (MD). Available at https://www.ncbi.nlm.nih.gov/books/nbk20370/ (last access date 2/1/2018).
   Google Scholar
• N.I. Nii-Trebi, Emerging and neglected infectious diseases: Insights, advances, and challenges, Biomed. Res. Int. 2017 (2017), pp. ID 5245021, 15 pages. doi: 10.1155/2017/5245021
   PubMedGoogle Scholar
• E. Rothstein and K. Edwards, Health burden of pertussis in adolescents and adults, Pediatr. Infect. Dis. J. 24 (2005), pp. S44–S47. doi: 10.1097/01.inf.0000160912.58660.87
   PubMed Web of Science ®Google Scholar
• Z. Shen, F. Ning, W. Zhou, X. He, C. Lin, D.P. Chin, Z. Zhu, and A. Schuchat, Superspreading SARS events, Beijing 2003, Emerg. Infect. Dis. 10 (2004), pp. 256–260. doi: 10.3201/eid1002.030732
   PubMed Web of Science ®Google Scholar
• R.A. Stein, Super-spreaders in infectious diseases, Int. J. Infect. Dis. 15 (2011), pp. e510–e513. Available at https://www.ncbi.nlm.nih.gov/pubmed/21737332. doi: 10.1016/j.ijid.2010.06.020
   PubMed Web of Science ®Google Scholar
• A.J. Tatem, D.J. Rodgers, and S.I. Hay, Global transport networks and infectious disease spread, Adv. Parasit. 62 (2006), pp. 293–343. doi: 10.1016/S0065-308X(05)62009-X
   PubMed Web of Science ®Google Scholar
• P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), pp. 29–48. doi: 10.1016/S0025-5564(02)00108-6
   PubMed Web of Science ®Google Scholar
• J. Wallinga and P. Teunis, Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures, Amer. J. Epidemiol. 160 (2004), pp. 509–516. doi: 10.1093/aje/kwh255
   PubMed Web of Science ®Google Scholar
• A.M. Wendelboe, A. van Rie, S. Salmaso, and J.A. Englund, Duration of immunity against pertussis after natural infection or vaccination, Pediatr. Infect. Dis. J. 24 (2005), pp. S58–S61. doi: 10.1097/01.inf.0000160914.59160.41
   PubMedGoogle Scholar
• P. Whittle, The outcome of a stochastic epidemic: A note on Bailey's paper, Biometrika 42 (1955), pp. 116–122.
   Web of Science ®Google Scholar
• G. Wong, W. Liu, Y. Liu, B. Zhou, Y. Bi, and G.F. Gao, MERS, SARS, and Ebola: The role of super-spreaders in infectious disease, Cell Host Microbe 18 (2015), pp. 398–401. doi: 10.1016/j.chom.2015.09.013
   PubMed Web of Science ®Google Scholar