On some epidemic models

Gripenberg, Gustaf

doi:10.1090/qam/636238

Author: Gustaf Gripenberg
Journal: Quart. Appl. Math. 39 (1981), 317-327
MSC: Primary 92A15; Secondary 45M05
DOI: https://doi.org/10.1090/qam/636238
MathSciNet review: 636238
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Abstract: The qualitative behavior of the solution $x$ of the equation \[ x\left ( t \right ) = k\left ( {p\left ( t \right ) - \smallint _0^tA\left ( {t - s} \right )x\left ( s \right )ds} \right )\left ( {f\left ( t \right ) + \smallint _0^ta(t - s)x(s)ds} \right ),t \ge 0\] is studied. This equation arises in the study of the spread of an infectious disease that does not induce permanent immunity.

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