2,355
Views
10
CrossRef citations to date
0
Altmetric
Articles

Epidemic models with heterogeneous mixing and indirect transmission

Pages 375-399 | Received 21 Jul 2017, Accepted 13 Apr 2018, Published online: 05 May 2018

References

  • G. Brankston, L. Gutterman, Z. Hirji, C. Lemieux, and M. Gardam, Transmission of influenza A in human beings, Lancet Infect Dis. 7 (2007), pp. 257–265. doi: 10.1016/S1473-3099(07)70029-4
  • F. Brauer, Epidemic models with heterogeneous mixing and treatment, Bull. Math. Biol. 70 (2008), pp. 1869–1885. doi: 10.1007/s11538-008-9326-1
  • F. Brauer, Age-of-infection and the final size relation, Math. Biosci. Eng. 5 (2008), pp. 681–690. doi: 10.3934/mbe.2008.5.681
  • F. Brauer, A new epidemic model with indirect transmission, J. Biol. Dyn. 11 (2016), pp. 1–10.
  • F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Vol. 41, Springer, New York, 2012.
  • F. Brauer, Z. Feng, and C. Castillo-Chavez, Discrete epidemic models, Math. Biosci. Eng. 7 (2010), pp. 1–15. doi: 10.3934/mbe.2010.7.1
  • F. Brauer, C. Castillo-Chavez, A. Mubayi, and S. Towers, Some models for epidemics of vector-transmitted diseases, Infect. Dis. Model. 1 (2016), pp. 79–87.
  • C.B. Bridges, M.J. Kuehnert, and C.B. Hall, Transmission of influenza: Implications for control in health care settings, Clin. Infect. Dis. 42 (2003), pp. 1094–1101.
  • C. Castillo-Chavez, D. Bichara, and B.R. Morin, Perspectives on the role of mobility, behavior, and time scales in the spread of diseases, Proc. Natl. Acad. Sci. 113 (2016), pp. 14582–14588. doi: 10.1073/pnas.1604994113
  • Y.K. Derdei Bichara, C. Castillo-Chavez, R. Horan, and C. Perrings, SIS and SIR epidemic models under virtual dispersal, Bull. Math. Biol. 77 (2015), pp. 2004–2034. doi: 10.1007/s11538-015-0113-5
  • B. Espinoza, V. Moreno, D. Bichara, and C. Castillo-Chavez, Assessing the efficiency of movement restriction as a control strategy of Ebola, in Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases, Springer International Publishing, Cham, 2016, pp. 123–145.
  • B. Fred, Heterogeneous mixing in epidemic models, Canad. Appl. Math. Q. 20 (2012), pp. 1–14.
  • B. Fred and G. Chowell, On epidemic growth rates and the estimation of the basic reproduction number, pp. 1–27. Available at http://chowell.lab.asu.edu/publication_pdfs/notas_cimat.pdf.
  • A. Jaichuang and W. Chinviriyasit, Numerical modelling of influenza model with diffusion, Int. J. Appl. Phys. Math. 4 (2014), pp. 15–21. doi: 10.7763/IJAPM.2014.V4.247
  • W.O. Kermack and A.G. McKendrick, A contribution to the mathematical theory of epidemics. Part I, Proc. R. Soc. A 115 (1927), pp. 700–721. doi: 10.1098/rspa.1927.0118
  • W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics . II. The problem of endemicity, Proc. R. Soc. A 138 (1932), pp. 55–83. doi: 10.1098/rspa.1932.0171
  • W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics . III. Further studies of the problem of endemicity, Proc. R. Soc. A 141 (1932), pp. 94–122. doi: 10.1098/rspa.1933.0106
  • J.J. Levin and D.F. Shea, On the asymptotic behaviour of the bounded solutions of some integral equations, I, J. Math. Anal. Appl. 37 (1972), pp. 42–82, 288–326, 537–575. doi: 10.1016/0022-247X(72)90258-2
  • Z. Liang, Z.-C. Wang, and Y. Zhang, Dynamics of a reaction–diffusion waterborne pathogen model with direct and indirect transmission, J. Comput. Math. Appl. 72 (2016), pp. 202–215. doi: 10.1016/j.camwa.2016.05.013
  • S. Mubareka, A.C. Lowen, J. Steel, A.L. Coates, A. Garcia-Sastre, and P. Palese, Transmission of influenza virus via aerosols and fomites in the guinea pig model, J. Infect. Dis. 199 (2009), pp. 858–865. doi: 10.1086/597073
  • J.H. Tien and D.J.D. Earn, Multiple transmission pathways and disease dynamics in a waterborne pathogen model, Bull. Math. Biol. 72 (2010), pp. 1506–1533. doi: 10.1007/s11538-010-9507-6
  • 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