Issue
Math. Model. Nat. Phenom.
Volume 17, 2022
Modelling of Communicable Diseases
Article Number 35
Number of page(s) 24
DOI https://doi.org/10.1051/mmnp/2022035
Published online 05 September 2022
  1. D.F. Anderson, A modified next reaction method for simulating chemical systems with time dependent propensities and delays. J. Chew,. Phys. 127 (2007) 214107. [CrossRef] [PubMed] [Google Scholar]
  2. D.F. Anderson, Incorporating postleap checks in tau-leaping. J. Chew,. Phys. 128 (2008) 054103. [CrossRef] [PubMed] [Google Scholar]
  3. D.F. Anderson, A. Ganguly and T.G. Kurtz, Error analysis of tau-leap simulation methods. Ann. Appl. Probab. 21 (2011) 2226–2262. [CrossRef] [MathSciNet] [Google Scholar]
  4. S. Bansal, B.T. Grenfell and L.A. Meyers, When individual behaviour matters: homogeneous and network models in epidemiology. J.R. Soc. Interface 4 (2007) 879–91. [CrossRef] [PubMed] [Google Scholar]
  5. M. Boguîiâ, L.F. Lafuerza, R. Toral and M.A. Serrano, Simulating non-Markovian stochastic processes. Phys. Rev. E 90 (2014) 042108. [Google Scholar]
  6. M.-C. Boily, R.F. Baggaley, L. Wang, B. Masse, R.G. White, R.J. Hayes and M. Alary, Heterosexual risk of HIV-1 infection per sexual act: systematic review and meta-analysis of observational studies. Lancet Infect Dis. 9 (2009) 118–29. [CrossRef] [PubMed] [Google Scholar]
  7. F. Brauer, Mathematical epidemiology: past, present, and future. Infect Dis. Model 2 (2017) 113–127. [Google Scholar]
  8. J. Butcher, Numerical Methods for Ordinary Differential Equations, Second Edition, Wiley (2008). [Google Scholar]
  9. Y. Cao, D.T. Gillespie and L.R. Petzold, Efficient step size selection for the tau-leaping simulation method. J. Chem. Phys. 124 (2006) 044109. [CrossRef] [PubMed] [Google Scholar]
  10. M.S. Cohen, Y.Q. Chen, M. McCauley, T. Gamble, M.C. Hosseinipour, N. Kumarasamy, J.G. Hakim, J. Kumwenda, B. Grinsztejn, J.H.S. Pilotto, S.V. Godbole, S. Mehendale, S. Chariyalertsak, B.R. Santos, K.H. Mayer, I.F. Hoffman, S.H. Eshleman, E. Piwowar-Manning, L. Wang, J. Makhema, L.A. Mills, G. de Bruyn, I. Sanne, J. Eron, J. Gallant, D. Havlir, S. Swindells, H. Ribaudo, V. Elharrar, D. Burns, T.E. Taha, K. Nielsen-Saines, D. Celentano, M. Essex, T.R. Fleming and HPTN 052 Study Team, Prevention of HIV-1 infection with early antiretroviral therapy. N. Engl. J. Med. 365 (2011) 493–505. [CrossRef] [PubMed] [Google Scholar]
  11. C.E. Dangerfield, J.V. Ross and M.J. Keeling, Integrating stochasticity and network structure into an epidemic model. J. R. Soc. Interface 6 (2009) 761–74. [CrossRef] [PubMed] [Google Scholar]
  12. J.T. Davis, M. Chinazzi, N. Perra, K. Mu, A. Pastore Y. Piontti, M. Ajelli, N.E. Dean, C. Gioannini, M. Litvinova, S. Merler, L. Rossi, K. Sun, X. Xiong, I.M. Longini, Jr, M.E. Halloran, C. Viboud and A. Vespignani, Cryptic transmission of SARS-CoV-2 and the first COVID-19 wave. Nature 600 (2021) 127–132. [CrossRef] [PubMed] [Google Scholar]
  13. R. Dunbar, Grooming, gossip, and the evolution of language. Harvard University Press (1998). [Google Scholar]
  14. R.I.M. Dunbar, Neocortex size as a constraint on group size in primates. J. Human Evolut. 22 (1992) 469–493. [CrossRef] [Google Scholar]
  15. S. Duwal, L. Dickinson, S. Khoo and M. von Kleist, Hybrid stochastic framework predicts efficacy of prophylaxis against HIV. PLoS Comput. Biol. 14 (2018) e1006155. [CrossRef] [Google Scholar]
  16. S. Duwal, D. Seeler, L. Dickinson, S. Khoo and M. von Kleist, The Utility of Efavirenz-based prophylaxis against hiv infection. A systems pharmacological analysis. Front. Pharmacol. 10 (2019) 199. [CrossRef] [Google Scholar]
  17. S. Duwal, V. Sunkara and M. von Kleist, Multiscale systems-pharmacology pipeline to assess the prophylactic efficacy of NRTIs Against HIV-1. CPT Pharmacometr. Syst. Pharmacol. 5 (2016) 377–87. [CrossRef] [Google Scholar]
  18. S. Duwal, S. Winkelmann, C. Schütte and M. von Kleist, Optimal treatment strategies in the context of 'treatment for prevention' against HIV-1. PLoS Comput. Biol. 11 (2015) e1004200. [CrossRef] [Google Scholar]
  19. J. Enright and R.R. Kao, Epidemics on dynamic networks. Epidemics 24 (2018) 88–97. [CrossRef] [PubMed] [Google Scholar]
  20. E. Fehlberg, Classical fifth-, sixth-, seventh-, and eighth-order Runge-Kutta formulas with stepsize control. NASA Technical Report (TR) (1968). [Google Scholar]
  21. S.C. Ferreira, C. Castellano and R. Pastor-Satorras, Epidemic thresholds of the susceptible-infected-susceptible model on networks: a comparison of numerical and theoretical results. Phys. Rev. E 86 (2012) 041125. [CrossRef] [PubMed] [Google Scholar]
  22. S. Funk, M. Salathe and V.A.A. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: a review. J.R. Soc. Interface 7 (2010) 1247–1256. [CrossRef] [PubMed] [Google Scholar]
  23. D.T. Gillespie, Exact stochastic simulation of coupled chemical-reactions. J. Phys. Chem. 81 (1977) 2340–2361. [CrossRef] [Google Scholar]
  24. D.T. Gillespie, Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115 (2001) 1716–1733. [CrossRef] [Google Scholar]
  25. S.M. Goodreau, S. Cassels, D. Kasprzyk, D.E. Montano, A. Greek and M. Morris, Concurrent partnerships, acute infection and HIV epidemic dynamics among young adults in Zimbabwe. AIDS Behav. 16 (2012) 312–322. [CrossRef] [PubMed] [Google Scholar]
  26. R.M. Grant, J.R. Lama, P.L. Anderson, V. McMahan, A.Y. Liu, L. Vargas, P. Goicochea, M. Casapia, J.V. Guanira-Carranza, M.E. Ramirez-Cardich, O. Montoya-Herrera, T. Fernandez, V.G. Veloso, S.P. Buchbinder, S. Chariyalertsak, M. Schechter, L.-G. Bekker, K.H. Mayer, E.G. Kallas, K.R. Amico, K. Mulligan, L.R. Bushman, R.J. Hance, C. Ganoza, P. Defechereux, B. Postle, F. Wang, J.J. McConnell, J.-H. Zheng, J. Lee, J.F. Rooney, H.S. Jaffe, A.I. Martinez, D.N. Burns, D.V. Glidden and iPrEx Study Team, Preexposure chemoprophylaxis for HIV prevention in men who have sex with men. N. Engl. J. Med. 363 (2010) 2587–2599. [CrossRef] [PubMed] [Google Scholar]
  27. T. Gross and B. Blasius, Adaptive coevolutionary networks: a review. J.R. Soc. Interface 5 (2008) 259–271. [CrossRef] [PubMed] [Google Scholar]
  28. T. Gross and H. Sayama, Adaptive Networks: Theory, Models and Applications. Springer (2009). [Google Scholar]
  29. S.L. Hakimi, On realizability of a set of integers as degrees of the vertices of a linear graph. I. J. Soc. Indust. Appl. Math. 10 (1962) 496–506. [CrossRef] [MathSciNet] [Google Scholar]
  30. R. Hinch, W.J.M. Probert, A. Nurtay, M. Kendall, C. Wymant, M. Hall, K. Lythgoe, A. Bulas Cruz, L. Zhao, A. Stewart, L. Ferretti, D. Montero, J. Warren, N. Mather, M. Abueg, N. Wu, O. Legat, K. Bentley, T. Mead, K. Van-Vuuren, D. Feldner-Busztin, T. Ristori, A. Finkelstein, D.G. Bonsall, L. Abeler-Doürner and C. Fraser, OpenABM-Covid19-An agent-based model for non-pharmaceutical interventions against COVID-19 including contact tracing. PLoS Comput. Biol. 17 (2021) e1009146. [CrossRef] [Google Scholar]
  31. T. Hladish, E. Melamud, L.A. Barrera, A. Galvani and L.A. Meyers, EpiFire: An open source CH-+ library and application for contact network epidemiology. BMC Bioinform. 13 (2012) 76. [CrossRef] [Google Scholar]
  32. P. Holme, Epidemiologically optimal static networks from temporal network data. PLoS Comput. Biol. 9 (2013) e1003142. [CrossRef] [Google Scholar]
  33. P. Holme and J. Saramüaki, Temporal Networks. Springer (2013). [Google Scholar]
  34. R. Huerta and L.S. Tsimring, Contact tracing and epidemics control in social networks. Phys. Rev. E 66 (2002) 056115. [CrossRef] [Google Scholar]
  35. S.M. Jenness, S.M. Goodreau and M. Morris, EpiModel: an R package for mathematical modeling of infectious disease over networks. J. Stat. Software 84 (2018) 10.18637/jss.v084.i08. [CrossRef] [Google Scholar]
  36. M.J. Keeling and K.T.D. Eames, Networks and epidemic models. J.R. Soc. Interface 2 (2005) 295–307. [CrossRef] [PubMed] [Google Scholar]
  37. M.J. Keeling, T. House, A.J. Cooper and L. Pellis, Systematic approximations to susceptible-infectious-susceptible dynamics on networks. PLoS Comput. Biol. 12 (2016) e1005296. [CrossRef] [Google Scholar]
  38. W. Kermack and A. McKendrick, A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. A 115 (1927) 700–721. [Google Scholar]
  39. C.C. Kerr, R.M. Stuart, D. Mistry, R.G. Abeysuriya, K. Rosenfeld, G.R. Hart, R.C. Nünez, J.A. Cohen, P. Selvaraj, B. Hagedorn, L. George, M. Jastrzebski, A.S. Izzo, G. Fowler, A. Palmer, D. Delport, N. Scott, S.L. Kelly, C.S. Bennette, B.G. Wagner, S.T. Chang, A.P. Oron, E.A. Wenger, J. Panovska-Griffiths, M. Famulare and D.J. Klein, Covasim: an agent-based model of COVID-19 dynamics and interventions. PLOS Comput. Biol. 17 (2021) 1–32. [Google Scholar]
  40. M. Kretzschmar and M. Morris, Measures of concurrency in networks and the spread of infectious disease. Math. Biosci. 133 (1996) 165–195. [CrossRef] [Google Scholar]
  41. T. Leng and M.J. Keeling, Concurrency of partnerships, consistency with data, and control of sexually transmitted infections. Epidemics 25 (2018) 35–46. [CrossRef] [PubMed] [Google Scholar]
  42. N.H.L. Leung, D.K.W. Chu, E.Y.C. Shiu, K.-H. Chan, J.J. McDevitt, B.J.P. Hau, H.-L. Yen, Y. Li, D.K.M. Ip, J.S.M. Peiris, W.-H. Seto, G.M. Leung, D.K. Milton and B.J. Cowling, Respiratory virus shedding in exhaled breath and efficacy of face masks. Nat. Med. 26 (2020) 676–680. [CrossRef] [PubMed] [Google Scholar]
  43. P. Lindenfors, A. Wartel and J. Lind, 'Dunbar's number' deconstructed. Biol. Lett. 17 (2021) 20210158. [CrossRef] [Google Scholar]
  44. I.M. Longini, Jr, M.E. Halloran, A. Nizam and Y. Yang, Containing pandemic influenza with antiviral agents. Am,. J. Epidemiol. 159 (2004) 623–633. [CrossRef] [PubMed] [Google Scholar]
  45. L. Marchetti, C. Priami and V.H. Thanh, Simulation Algorithms for Computational Systems Biology. Springer (2017). [Google Scholar]
  46. F. Morone and H. Makse, Influence maximization in complex networks through optimal percolation. Nature 524 (2015) 65–68. [CrossRef] [PubMed] [Google Scholar]
  47. M. Nadini, L. Zino, A. Rizzo and M. Porfiri, A multi-agent model to study epidemic spreading and vaccination strategies in an urban-like environment. Appl. Netw. Sci. 5 (2020) 68. [CrossRef] [Google Scholar]
  48. D.-Y. Oh, S. Buda, B. Biere, J. Reiche, F. Schlosser, S. Duwe, M. Wedde, M. von Kleist, M. Mielke, T. Wolffand R. Dürrwald, Trends in respiratory virus circulation following COVID-19-targeted nonpharmaceutical interventions in Germany, January-September 2020: analysis of national surveillance data. Lancet Reg. Health Eur. 6 (2021) 100112. [CrossRef] [Google Scholar]
  49. S. Osat, A. Faqeeh and F. Radicchi, Optimal percolation on multiplex networks. Nat. Commun. 8 (2017) 1540. [CrossRef] [Google Scholar]
  50. R. Pastor-Satorras, C. Castellano, P.V. Mieghem and A. Vespignani, Epidemic processes in complex networks. Rev. Mod. Phys. 87 (2015) 925–979. [CrossRef] [Google Scholar]
  51. F.P. Polack, S.J. Thomas, N. Kitchin, J. Absalon, A. Gurtman, S. Lockhart, J.L. Perez, G. Perez Marc, E.D. Moreira, C. Zerbini, R. Bailey, K.A. Swanson, S. Roychoudhury, K. Koury, P. Li, W.V. Kalina, D. Cooper, R.W. Frenck, Jr, L.L. Hammitt, O. Türeci, H. Nell, A. Schaefer, S. Ünal, D.B. Tresnan, S. Mather, P.R. Dormitzer, U. Sahin, K.U. Jansen, W.C. Gruber and C4591001 Clinical Trial Group, Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine. N. Engl. J. Med. 383 (2020) 2603–2615. [CrossRef] [PubMed] [Google Scholar]
  52. R.A. Royce, A. Sena, W. Cates, Jr and M.S. Cohen, Sexual transmission of HIV. N. Engl. J. Med. 336 (1997) 1072–1078. [CrossRef] [PubMed] [Google Scholar]
  53. P. Rue, J. Villa-Freixa and K. Burrage, Simulation methods with extended stability for stiff biochemical Kinetics. BMC Syst. Biol. 4 (2010) 110. [CrossRef] [Google Scholar]
  54. E. Silverman, Ü. Gostoli, S. Picascia, J. Almagor, M. McCann, R. Shaw and C. Angione, Situating agent-based modelling in population health research. Emerg. Themes Epidemiol. 18 (2021) 10. [CrossRef] [Google Scholar]
  55. W. van der Toorn, D.-Y. Oh, D. Bourquain, J. Michel, E. Krause, A. Nitsche, M. von Kleist and Working Group on SARS-CoV-2 Diagnostics at RKI, An intra-host SARS-CoV-2 dynamics model to assess testing and quarantine strategies for incoming travelers, contact management, and de-isolation. Patterns (N Y) 2 (2021) 100262. [CrossRef] [PubMed] [Google Scholar]
  56. W. van der Toorn, D.-Y. Oh, M. von Kleist and Working Group on SARS-CoV-2 Diagnostics at RKI, COVIDStrategyCal-culator: a software to assess testing and quarantine strategies for incoming travelers, contact management, and de-isolation. Patterns (N Y) 2 (2021) 100264. [CrossRef] [PubMed] [Google Scholar]
  57. C.L. Vestergaard and M. Genois, Temporal gillespie algorithm: fast simulation of contagion processes on time-varying networks. PLoS Comput. Biol. 11 (2015) e1004579. [CrossRef] [Google Scholar]
  58. M. Voliotis, P. Thomas, R. Grima and C. Bowsher, Stochastic simulation of biomolecular networks in dynamic environments. PLoS Comput. Biol. 12 (2016) e1004923. [CrossRef] [Google Scholar]
  59. S. Weller and K. Davis, Condom effectiveness in reducing heterosexual HIV transmission. Cochrane Database Syst. Rev. 2002 (2002) CD003255. [Google Scholar]
  60. L. Zhang, J. Wang and M. von Kleist, Numerical approaches for the rapid analysis of prophylactic efficacy against HIV with arbitrary drug-dosing schemes. PLoS Comput. Biol. 17 (2021) 1009295. [Google Scholar]
  61. G. Zschaler and T. Gross, Largenet2: an object-oriented programming library for simulating large adaptive networks. Bioinformatics 29 (2013) 277–278. [CrossRef] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.