Abstract
The classical epidemic models derived from the Kermack-McKendrick model consider the prevalence of the disease only. The host population is partitioned into classes of susceptibles S, infectious I, and recovered R. The transition between these classes is described by ordinary differential equations. The following equations take into account the recruitment of new individuals into the class of susceptibles by birth and a death rate depending on the class. The equations read
Of course these equations are independent of δ1, and P = S + I + R is an invariant. Thus the equations simplify to
The “natural” parameters of the system are β, γ + δ3, α + δ2, α + γ + δ3. In the following we consider only the endemic case γ + δ3 > 0. The state space of the system (2) is the triangle T = {S ≧ 0, I ≧ 0, S + I ≦ P} which is positively invariant with respect to the flow.
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© 1985 Springer-Verlag Berlin Heidelberg
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Hadeler, K.P. (1985). Models for Endemic Diseases. In: Capasso, V., Grosso, E., Paveri-Fontana, S.L. (eds) Mathematics in Biology and Medicine. Lecture Notes in Biomathematics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93287-8_18
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DOI: https://doi.org/10.1007/978-3-642-93287-8_18
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