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Age-Structured Population Dynamics in Demography and Epidemiology pp 139–179Cite as

Nonlinear One-Sex Models

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Abstract

The stable population model is an age-structured version of the Malthus model. Therefore, any criticism of the Malthus model can also be applied to the stable population model. In reality, if the intrinsic growth rate is positive, asymptotic exponential growth cannot continue forever. In the long term, we should take into account the interactions that exist between the population and its environment. Population parameters such as fertility and mortality could be affected by environmental parameters (resources, seasons, life conditions and so on), while population growth itself will affect the environmental conditions. Therefore, through these feedback loops, demographic parameters generally depend on the population size and structure, resulting in a necessarily nonlinear model. Although there are many nonlinear effects that should be taken into account to reflect the self-regulation of the population, in this chapter, we only consider the mechanism of density-dependence in a one-sex age-structured population. In the first half of this chapter, we discuss the period control model, and in the latter half, we consider the cohort control model.

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Notes

  1. 1.

    \(C_+([0,T]; \mathbb R)\) denotes the set of nonnegative continuous functions on [0, T].

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  1. The University of Tokyo, Tokyo, Japan

    Hisashi Inaba

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  1. Hisashi Inaba
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Inaba, H. (2017). Nonlinear One-Sex Models. In: Age-Structured Population Dynamics in Demography and Epidemiology. Springer, Singapore. https://doi.org/10.1007/978-981-10-0188-8_3

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  • DOI: https://doi.org/10.1007/978-981-10-0188-8_3

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