%0 Journal Article %1 Castillo-Chavez1989233 %A Castillo-Chavez, C. %A Hethcote, H.W. %A Andreasen, V. %A Levin, S.A. %A Liu, W.M. %D 1989 %I Springer-Verlag %J Journal of Mathematical Biology %K Aging; Epidemiologic Gov't, Gov't; Human; Immunity; Influenza; Methods; Models, Non-P.H.S. Non-U.S. Support, Theoretical; U.S. aging; article; epidemiology; human; immunity; influenza; model, theoretical %N 3 %P 233-258 %R http://dx.doi.org/10.1007/BF00275810 %T Epidemiological models with age structure, proportionate mixing, and cross-immunity %U http://dx.doi.org/10.1007/BF00275810 %V 27 %X Infection by one strain of influenza type A provides some protection (cross-immunity) against infection by a related strain. It is important to determine how this influences the observed co-circulation of comparatively minor variants of the H1N1 and H3N2 subtypes. To this end, we formulate discrete and continuous time models with two viral strains, cross-immunity, age structure, and infectious disease dynamics. Simulation and analysis of models with cross-immunity indicate that sustained oscillations cannot be maintained by age-specific infection activity level rates when the mortality rate is constant; but are possible if mortalities are age-specific, even if activity levels are independent of age. Sustained oscillations do not seem possible for a single-strain model, even in the presence of age-specific mortalities; and thus it is suggested that the interplay between cross-immunity and age-specific mortalities may underlie observed oscillations. Â\copyright 1989 Springer-Verlag.

@article{Castillo-Chavez1989233, abstract = {Infection by one strain of influenza type A provides some protection (cross-immunity) against infection by a related strain. It is important to determine how this influences the observed co-circulation of comparatively minor variants of the H1N1 and H3N2 subtypes. To this end, we formulate discrete and continuous time models with two viral strains, cross-immunity, age structure, and infectious disease dynamics. Simulation and analysis of models with cross-immunity indicate that sustained oscillations cannot be maintained by age-specific infection activity level rates when the mortality rate is constant; but are possible if mortalities are age-specific, even if activity levels are independent of age. Sustained oscillations do not seem possible for a single-strain model, even in the presence of age-specific mortalities; and thus it is suggested that the interplay between cross-immunity and age-specific mortalities may underlie observed oscillations. {\^A}{\copyright} 1989 Springer-Verlag.}, added-at = {2017-11-10T22:48:29.000+0100}, affiliation = {Ecology and Systematics, Cornell University, Corson Hall, Ithaca, 14853, NY, United States; Center for Applied Mathematics, Cornell University, United States; Biometrics Unit, Cornell University, Warren Hall, United States; Department of Mathematics, University of Iowa, Iowa City, 52242, IA, United States; Ecosystems Research Center, Cornell University, United States}, author = {Castillo-Chavez, C. and Hethcote, H.W. and Andreasen, V. and Levin, S.A. and Liu, W.M.}, author_keywords = {Age structure; Cross-immunity; Infectious diseases; Influenza; Proportionate mixing}, biburl = {https://www.bibsonomy.org/bibtex/24ba64c73e9ebc2b082794e89c0779e0a/ccchavez}, correspondence_address1 = {Castillo-Chavez, C.; Ecology and Systematics, Cornell University, Corson Hall, Ithaca, 14853, NY, United States}, date-added = {2017-11-10 21:45:26 +0000}, date-modified = {2017-11-10 21:45:26 +0000}, document_type = {Article}, doi = {http://dx.doi.org/10.1007/BF00275810}, interhash = {6fb02c60ef76e2bc1eab49023110ae26}, intrahash = {4ba64c73e9ebc2b082794e89c0779e0a}, issn = {03036812}, journal = {Journal of Mathematical Biology}, keywords = {Aging; Epidemiologic Gov't, Gov't; Human; Immunity; Influenza; Methods; Models, Non-P.H.S. Non-U.S. Support, Theoretical; U.S. aging; article; epidemiology; human; immunity; influenza; model, theoretical}, language = {English}, number = 3, pages = {233-258}, publisher = {Springer-Verlag}, pubmed_id = {2746140}, timestamp = {2017-11-10T22:48:29.000+0100}, title = {Epidemiological models with age structure, proportionate mixing, and cross-immunity}, url = {http://dx.doi.org/10.1007/BF00275810}, volume = 27, year = 1989 }