Research article Special Issues

Computing human to human Avian influenza $\mathcal{R}_0$ via transmission chains and parameter estimation

  • Received: 14 February 2019 Accepted: 10 April 2019 Published: 19 April 2019
  • The transmission of avian influenza between humans is extremely rare, and it mostly affects individuals who are in contact with infected family member. Although this scenario is uncommon, there have been multiple outbreaks that occur in small infection clusters in Asia with relatively lowtransmissibility, and thus are too weak to cause an epidemic. Still, subcritical transmission from stut-tering chain data is vital for determining whether avian influenza is close to the threshold of $\mathcal{R}_0$ > 1.In this article, we will explore two methods of estimating $\mathcal{R}_0$ using transmission chains and parameterestimation through data fitting. We found that $\mathcal{R}_0$ = 0.2205 when calculating the $\mathcal{R}_0$ using the maxi-mum likelihood method. When we computed the reproduction number for human to human transmis-sion through differential equations and fitted the model to data from the cumulative cases, cumulativedeaths, and cumulative secondary cases, we estimated $\mathcal{R}_0$ = 0.1768. To avoid violating the assumptionof the least square method, we fitted the model to incidence data to obtain $\mathcal{R}_0$ = 0.1520. We tested thestructural and practical identifiability of the model, and concluded that the model is identifiable undercertain assumptions. We further use two more methods to estimate $\mathcal{R}_0$ : by the $\mathcal{R}_0$ definition whichgives an overestimate of 0.28 and by Ferguson approach which yields $\mathcal{R}_0$ = 0.1586. We conclude that $\mathcal{R}_0$ for human to human transmission was about 0.2.

    Citation: Omar Saucedo, Maia Martcheva, Abena Annor. Computing human to human Avian influenza $\mathcal{R}_0$ via transmission chains and parameter estimation[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3465-3487. doi: 10.3934/mbe.2019174

    Related Papers:

  • The transmission of avian influenza between humans is extremely rare, and it mostly affects individuals who are in contact with infected family member. Although this scenario is uncommon, there have been multiple outbreaks that occur in small infection clusters in Asia with relatively lowtransmissibility, and thus are too weak to cause an epidemic. Still, subcritical transmission from stut-tering chain data is vital for determining whether avian influenza is close to the threshold of $\mathcal{R}_0$ > 1.In this article, we will explore two methods of estimating $\mathcal{R}_0$ using transmission chains and parameterestimation through data fitting. We found that $\mathcal{R}_0$ = 0.2205 when calculating the $\mathcal{R}_0$ using the maxi-mum likelihood method. When we computed the reproduction number for human to human transmis-sion through differential equations and fitted the model to data from the cumulative cases, cumulativedeaths, and cumulative secondary cases, we estimated $\mathcal{R}_0$ = 0.1768. To avoid violating the assumptionof the least square method, we fitted the model to incidence data to obtain $\mathcal{R}_0$ = 0.1520. We tested thestructural and practical identifiability of the model, and concluded that the model is identifiable undercertain assumptions. We further use two more methods to estimate $\mathcal{R}_0$ : by the $\mathcal{R}_0$ definition whichgives an overestimate of 0.28 and by Ferguson approach which yields $\mathcal{R}_0$ = 0.1586. We conclude that $\mathcal{R}_0$ for human to human transmission was about 0.2.


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    [1] M. D. R. van Beest Holle and A. Meijer, Human to human transmission of avian influenza /h7n7, the netherlands, Euro Surveill., 10 (2005), 264–268.
    [2] K. Ungchusak, Probable person-to-person transmission of avian influenza a (h5n1), New Engl. J. Med., 352 (2005), 333–340.
    [3] I. Kandum, Three indonesian clusters of h5n1 virus infection in 2005, New Engl. J. Med., 355 (2006), 2186–2194.
    [4] S. Herfst, Airborne transmission of influenza a/h5n1 virus between ferrets, Science, 336 (2012), 1534–1541.
    [5] A. J. Hay, The evolution of human influenza viruses, Philos. T. R. Soc. B, 356 (2001), 1861–1870. 6. Avian influenza (2015).
    [6] 7. Centers for Disease Control and Prevention, Highly pathogenic avian influenza a (h5n1) virus, (2015).
    [7] 8. Y. Yang, Detecting human to human transmission of avian influenza a (h5n1), Emerg. Infect. Dis., 13 (2005), 1348–1353.
    [8] 9. J. K. Taubenberger and D. M Morens, The pathology of influenza virus infections, Annu. Rev. Pathol., 3 (2005), 499–522.
    [9] 10. Mathematical model, Infect. Dis., (2015).
    [10] 11. J. Hyman and L. Jia, An intuitive formulation for the reproductive number for the spread of disease in heterogeneous populations, Math. Biosci., 167 (2000), 65–86.
    [11] 12. Y. Xiao, X. Sun and S. Tang Transmission potential of the novel avian influenza a(h7n9) infection in mainland china, J. Theor. Biol., 352 (2014), 1–5.
    [12] 13. N. Tuncer and M. Martcheva, Modeling seasonality in avian influenza h5n1, J. Biol. Syst., 21 (2013), 1–27.
    [13] 14. G. Chowell, L. Simonsen, S. Towers, et al., Transmission potential of influenza h7n9 february to may 20china, BMC Medicine, 11 (2013), 1–13.
    [14] 15. M. van Boven, M. Koopmans, M. Du Ry van Beest Holle, et al., Detecting emerging transmissi- bility of avian influenza virus in human households, PLoS Comput. Biol., 3 (2007), 1–9.
    [15] 16. M. E. Woolhouse and S. Gowtage-Sequeria, Host range and emerging and reemerging pathogens, Emerg. Reemerg. Pathog., 11 (2005), 1842–1847.
    [16] 17. S. Blumger and J. Lloyd-Smith, Inference of R 0 and transmission heterongeneity from the size distribution of stuttering chains, PLoS Comput. Biol., 9 (2013), 1–17.
    [17] 18. S. Blumberg, S. Funk and J. R. Pulliam, Detecting differential transmissibilities that affect the size of self-limited outbreaks, PloS One, 10 (2014), 1–14.
    [18] 19. S. Blumberg and J. Lloyd-Smith, Comparing methods for estimating R 0 from the size distribution of subcritical transmission chains, Epidemics, 5 (2013), 131–145.
    [19] 20. V. Pitzer, Little evidence for genetic susceptibility to influenza a from family clustering data, Emerg. Infect. Dis., 13 (2007) 1074–1076.
    [20] 21. S. J. Olsen, Family clustering of avian influenza a (h5n1), Emerg. Infect. Dis., 11 (5), 1799– 1801.
    [21] 22. T. Harris, The Theory of Branching Process, Dover, 2002.
    [22] 23. I. Dumitriu, J. Spencer and C. Yan, Branching processes with negative offspring distribution, Ann. Comb., 7 (2003), 35–47.
    [23] 24. J. Lloyd-Smith, S. Schreiber, P. Kopp, et al., Superspreading and the effect of individual variation on disease emergence, Nature, 438 (2005), 355–359.
    [24] 25. M. Dwass, The total progeny in a branching process and a related random walk, J. Appl. Probab., 6 (1969), 682–686.
    [25] 26. World Health Organization, Cumulative number of confirmed human cases of avian influenza a (h5n1) reported to who (2015).
    [26] 27. S. Iwami, Y. Takeuchi and X. Liu, Avian flu pandemic: Can we prevent it?, J. Theor. Biol., 257 (2009), 181–190.
    [27] 28. W. H. O. Commmittee, The writing committee of the who consultation on human influenza a/h5 avian influenza a (h5n1) infection in humans, New Engl. J. Med., 353 (2005), 1374–1385.
    [28] 29. Food and Agriculture Organization of United Nations, Animal production and health division, (2015).
    [29] 30. Centers for Disease Control and Prevention, Avian influenza a (h7n9) virus, (2014).
    [30] 31. C. Hayden, Transmission of avian influenza viruses to and between humans, J. Infect. Dis., 192 (2005), 1311–1314.
    [31] 32. L. A. Reperant, T. Kuiken and A. D. Osterhaus, Influenza viruses, J. Hum. Vaccin. Immunother., 8 (2012), 7–16.
    [32] 33. A. A. King, M. Domenech de Cells, F. M. G. Magpantay, et al., Avoidable errors in modelling of outbreaks of emerging pathogens with special reference to ebola, P. Roy. Soc. B, 282 (2015), 143–151.
    [33] 34. M.C.Eisenberg, S.L.Robertson, J.H.Tien, Identifiabilityandestimationofmultipletransmission pathways in cholera and waterborne disease, J. Theor. Biol., 324 (2013), 84–102.
    [34] 35. N. Meshkat, M. Eisenberg and J. DiStefano, An algorithm for finding globally identifiable pa- rameter combinations of nonlinear ode models using grobner bases, Math. Biosci., 222 (2009), 61–72.
    [35] 36. M. C. Eisenberg and M. A. L. Hayashi, Determining identifiable parameter combinations using subset profiling, Math. Biosci., 256 (2014), 116–126.
    [36] 37. N. D. Evans, L. J. White, M. J. Chapman, et al., The structural identifiability of the susceptible infected recovered model with seasonal forcing, Math. Biosci., 194 (2005), 175–197.
    [37] 38. H. Kelejian, Random parameters in a simultaneous equation framework: Identification and esti- mation, Econometrica, 42 (1974), 517–527.
    [38] 39. H. Maio, X. Xia, A. Perelson, et al., On identifiability of nonlinear ode models and applications in viral dynamics, SIAM Rev. Soc. Ind. Appl. Math., 53 (2011), 3–39.
    [39] 40. N. Meshkat, C. Anderson, S. J. Rd, Alternative to ritt's pseudodivision for finding the input-output equations of multi-output models, Math. Biosci., 2(2012), 117–123.
    [40] 41. G. S. Bellu, M. Audoly and S. D'Angio, Daisy: A new software tool to test global identifiability of biological and physiological systems, Comput. Meth. Prog. Bio., 88 (2007), 52–61.
    [41] 42. A. Raue, J. Karlsson and M. Jirstrand, Comparison of approaches for parameter identifiability analysis of biological systems, Bioinformatics, 30 (2014), 1440–1448.
    [42] 43. H. T. Banks, J. E. Banks, C. Jackson, et al., Modeling the east coast akalat population: Model com- parison and parameter estimation, Center for Research in Scientific Computation Report, (2013), 1–39.
    [43] 44. A. Raue and C. Kreutz, Structural and practical identifiability analysis of partially observed dy- namical models by exploiting the profile likelihood, Oxford University Press, 25 (2009), 1923– 1929.
    [44] 45. N. M. Ferguson and C. Fraser, Public health risk from the avian h5n1 influenza epidemic, Science, 304 (2004), 968–969.
    [45] 46. Y. H. Hsieh, J. Wu, J. Fang, et al., Quantification of bird to bird and bird to human infections during 2013 novel h7n9 avian influenza outbreak in china, Lancet, 383 (2014), 541–548.
    [46] 47. N. Marquetoux, M. Paul, S. Wongnarkpet, et al., Estimating spatial and temporal variations of the reproductive number for highly pathogenic avian influenza h5n1 epidemic in thailand, Prev. Vet. Med., 106 (2012), 143–151.
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