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The General Age‐Dependent Endemic with Age‐Specific Contact Rate
Author(s) -
Knolle H.
Publication year - 1983
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.19830250507
Subject(s) - mathematics , kernel (algebra) , operator (biology) , ordinary differential equation , age groups , differential equation , statistics , mathematical analysis , demography , biology , pure mathematics , sociology , biochemistry , repressor , transcription factor , gene
The time‐independent (i.e. endemic) case of the general deterministic age‐dependent epidemic is treated. The “force of infection” (Muench, 1959) depends on the age density of the infectious via an integral operator whose kernel n ( a , α) is related to the frequency of contact between different age groups. Endemic threshold conditions are derived. For a special case of n ( a , α) suited for the situation of school children, a differential equation is derived and solved numerically. Its parameters are estimated for two sets of rubella data.