Endemic infections in growing populations.

*(English)*Zbl 0586.92018For a homogeneously mixing population, the authors consider the effects of an increasing population upon the incidence of a particular infection. This feature of an increasing population differs from most epidemic models with assumption of constant host population.

An age-structured compartmental model is formulated with susceptible, infectious, and recovered/immune categories. The population growth occurs in a fixed finite region so that density and infection rates are increasing over time. The density dependent tranmission has the form \(\beta\) XY, where X is the number of susceptibles and Y is the total number of infectious individuals per unit area.

Asymptotic expressions for the force of infection are obtained explicitly when the death rate is given by (1) everyone dies at age L, or (2) an age-independent mortality rate \(\mu\). For type (1) survivorship, explicit analytic and numerical examples are given to illustrate the age-specific patterns of susceptibility as functions of time.

An age-structured compartmental model is formulated with susceptible, infectious, and recovered/immune categories. The population growth occurs in a fixed finite region so that density and infection rates are increasing over time. The density dependent tranmission has the form \(\beta\) XY, where X is the number of susceptibles and Y is the total number of infectious individuals per unit area.

Asymptotic expressions for the force of infection are obtained explicitly when the death rate is given by (1) everyone dies at age L, or (2) an age-independent mortality rate \(\mu\). For type (1) survivorship, explicit analytic and numerical examples are given to illustrate the age-specific patterns of susceptibility as functions of time.

Reviewer: S.M.Lenhart

##### MSC:

92D25 | Population dynamics (general) |

##### Keywords:

epidemiology; homogeneously mixing population; increasing population; age-structured compartmental model; population growth; infection rates; density dependent tranmission; Asymptotic expressions; age-independent mortality rate
PDF
BibTeX
XML
Cite

\textit{R. M. May} and \textit{R. M. Anderson}, Math. Biosci. 77, 141--156 (1985; Zbl 0586.92018)

Full Text:
DOI

##### References:

[1] | Bailey, N.J.T., The mathematical theory of infectious diseases, (1975), Macmillan New York |

[2] | Hoppensteadt, F.C., Mathematical theories of populations: demographics, genetics and epidemics, () · Zbl 0304.92012 |

[3] | Waltman, P., Deterministic threshold models in the theory of epidemics, () · Zbl 0293.92015 |

[4] | Anderson, R.M.; May, R.M., Vaccination against rubella and measles: quantitative investigations of different policies, J. hyg., 90, 259-325, (1983) |

[5] | Anderson, R.M.; May, R.M., Spatial, temporal and genetic heterogeneity in host populations and the design of immunization programmes, J. math. appl. biol. med., (1985) |

[6] | Anderson, R.M.; May, R.M.; Anderson, R.M.; May, R.M., Population biology of infectious diseases, Nature, Nature, 280, 455-461, (1979) · Zbl 0529.92014 |

[7] | Dietz, K., Transmission and control of arbovirus diseases, (), 104-121 · Zbl 0322.92023 |

[8] | Anderson, R.M.; May, R.M., Directly transmitted infectious diseases: control by vaccination, Science, 215, 1053-1060, (1982) · Zbl 1225.37099 |

[9] | R. M. Anderson, A. McLean, and R. M. May, Epidemiology of measles in growing populations: The force of transmission and the design of vaccination programs, in preparation. |

[10] | A. McLean, Models for the epidemiology of childhood infections in growing populations, in preparation. |

[11] | Krebs, C.J., Ecology: the experimental analysis of distribution and abundance, (1978), Harper and Row New York |

[12] | Keyfitz, N.; Flieger, W., Population: facts and methods of demography, (1971), Freeman San Francisco |

[13] | Anderson, R.M., Transmission dynamics and control of infectious disease agents in population biology of infectious diseases, (), 149-176 |

[14] | D. Schenzle, Manuscript in preparation. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.