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Epidemics and Demography

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The Basic Approach to Age-Structured Population Dynamics

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Abstract

This chapter deals with the modeling of epidemics with demographic age-structure. Apart from the dramatic family scenario described by Lucretius, showing that a disease such as the plague does not distinguish among ages, the importance of considering the age of the individuals in an epidemic model arises from the fact that, for many diseases, the rate of infection varies significantly with age.

Praeterea iam pastor et armentarius omnis

et robustus item curvi moderator aratri

languebat, penitusque casa contrusa iacebant

corpora paupertate et morbo dedita morti.

Exanimis pueris super examinata parentum

corpora nonnumquam posses retroque videre

matribus et patribus natos super edere vitam.

Lucretius, “De Rerum Natura”, Liber VI, 1252–1258

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Notes

  1. 1.

    Moreover, by now the shepherd and every herdsman, and likewise the sturdy steersman of the curving plough, would fall drooping, and their bodies would lie thrust together in the recess of a hut, given over to death by poverty and disease. On lifeless children you might often have seen the lifeless bodies of parents, and again, children breathing out their life upon mothers and fathers.

  2. 2.

    Note that if J is constant, i.e. J(t) ≡ J, then Ψ(a, t, a; J) = ψ(a, J).

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Authors and Affiliations

  1. Department of Mathematics, University of Trento, Trento, Italy

    Mimmo Iannelli

  2. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona, USA

    Fabio Milner

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Iannelli, M., Milner, F. (2017). Epidemics and Demography. In: The Basic Approach to Age-Structured Population Dynamics. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1146-1_10

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