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Computation of $\mathcal R $ in age-structured epidemiological models with maternal and temporary immunity
1. | Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, United States, United States |
2. | Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094 |
3. | National Center for HIV/AIDS, Viral Hepatitis, STD, and TB Prevention, 1600 Clifton Road, NE, Atlanta, GA 30333, United States |
4. | National Center for Immunization and Respiratory Diseases, 1600 Clifton Road, NE, Atlanta, GA 30333, United States |
References:
[1] |
O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases Model Building, Analysis and Interpretation, Wiley Series in Mathematical and Computational Biology, Wiley, Chichester, 2000. |
[2] |
C. Dye and B. G. Williams, Eliminating human tuberculosis in the twenty-first century, J. R. Soc. Interface, 5 (2008), 653-662.
doi: 10.1098/rsif.2007.1138. |
[3] |
Z. Feng, J. W. Glasser, A. N. Hill, M. A. Franko, R. M. Carlsson, H. Hallander, P. Tull and P. Olin, Modeling rates of infection with transient maternal antibodies and waning active immunity: Applicationto Bordetella pertussis in Sweden, J. Theor. Biol., 356 (2014), 123-132.
doi: 10.1016/j.jtbi.2014.04.020. |
[4] |
J. Glasser, Z. Feng, A. Moylan, S. Del Valled and C. Castillo-Chavez, Mixing in age-structured population models of infectious diseases, Math. Biosci., 235 (2012), 1-7.
doi: 10.1016/j.mbs.2011.10.001. |
[5] |
H. W. Hethcote, An age-structured model for pertussis transmission, Math. Biosci., 145 (1997), 89-136.
doi: 10.1016/S0025-5564(97)00014-X. |
[6] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653.
doi: 10.1137/S0036144500371907. |
[7] |
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University, Cambridge, 1991.
doi: 10.1017/CBO9780511840371. |
[8] |
J. A. Jacquez, C. P. Simon, J. Koopman, L. Sattenspiel and T. Perry, Modeling and analyzing HIV transmission: The effect of contact patterns, Math. Biosci., 92 (1988), 119-199.
doi: 10.1016/0025-5564(88)90031-4. |
[9] |
H. Inaba, Age-structured homogeneous epidemic systems with application to the MSEIR epidemic model, J. Math. Biol., 54 (2007), 101-146.
doi: 10.1007/s00285-006-0033-y. |
[10] |
T. Kuniya and H. Inaba, Endemic threshold results for an agestructured SIS epidemic model with periodic parameters, J. Math. Anal. Appl., 402 (2013), 477-492.
doi: 10.1016/j.jmaa.2013.01.044. |
[11] |
J. Mossong, N. Hens and M. Jit, et al., Social contacts and mixing patterns relevant to the spread of infectious diseases, PLoS Med., 5 (2008), e74.
doi: 10.1371/journal.pmed.0050074. |
[12] |
H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time-heterogeneity, SIAM J. Appl. Math., 70 (2009), 188-211.
doi: 10.1137/080732870. |
[13] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
show all references
References:
[1] |
O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases Model Building, Analysis and Interpretation, Wiley Series in Mathematical and Computational Biology, Wiley, Chichester, 2000. |
[2] |
C. Dye and B. G. Williams, Eliminating human tuberculosis in the twenty-first century, J. R. Soc. Interface, 5 (2008), 653-662.
doi: 10.1098/rsif.2007.1138. |
[3] |
Z. Feng, J. W. Glasser, A. N. Hill, M. A. Franko, R. M. Carlsson, H. Hallander, P. Tull and P. Olin, Modeling rates of infection with transient maternal antibodies and waning active immunity: Applicationto Bordetella pertussis in Sweden, J. Theor. Biol., 356 (2014), 123-132.
doi: 10.1016/j.jtbi.2014.04.020. |
[4] |
J. Glasser, Z. Feng, A. Moylan, S. Del Valled and C. Castillo-Chavez, Mixing in age-structured population models of infectious diseases, Math. Biosci., 235 (2012), 1-7.
doi: 10.1016/j.mbs.2011.10.001. |
[5] |
H. W. Hethcote, An age-structured model for pertussis transmission, Math. Biosci., 145 (1997), 89-136.
doi: 10.1016/S0025-5564(97)00014-X. |
[6] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653.
doi: 10.1137/S0036144500371907. |
[7] |
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University, Cambridge, 1991.
doi: 10.1017/CBO9780511840371. |
[8] |
J. A. Jacquez, C. P. Simon, J. Koopman, L. Sattenspiel and T. Perry, Modeling and analyzing HIV transmission: The effect of contact patterns, Math. Biosci., 92 (1988), 119-199.
doi: 10.1016/0025-5564(88)90031-4. |
[9] |
H. Inaba, Age-structured homogeneous epidemic systems with application to the MSEIR epidemic model, J. Math. Biol., 54 (2007), 101-146.
doi: 10.1007/s00285-006-0033-y. |
[10] |
T. Kuniya and H. Inaba, Endemic threshold results for an agestructured SIS epidemic model with periodic parameters, J. Math. Anal. Appl., 402 (2013), 477-492.
doi: 10.1016/j.jmaa.2013.01.044. |
[11] |
J. Mossong, N. Hens and M. Jit, et al., Social contacts and mixing patterns relevant to the spread of infectious diseases, PLoS Med., 5 (2008), e74.
doi: 10.1371/journal.pmed.0050074. |
[12] |
H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time-heterogeneity, SIAM J. Appl. Math., 70 (2009), 188-211.
doi: 10.1137/080732870. |
[13] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
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