Spatial heterogeneity and the design of immunization programs.

*(English)*Zbl 0564.92016The paper deals with the situation when the population is subdivided into n groups and the transmission rate of an infectious disease among individuals within one group is different from the transmission rate between groups. An optimal eradication program is studied in which different groups are treated differently. It is shown that this program requires fewer immunizations than in the case we assume that the population is homogeneously mixed.

Reviewer: U.Wilczyńska

##### MSC:

92D25 | Population dynamics (general) |

##### Keywords:

spatial heterogeneity; immunization programs; transmission rate within groups; transmission rate between groups; optimal eradication program
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\textit{R. M. May} and \textit{R. M. Anderson}, Math. Biosci. 72, 83--111 (1984; Zbl 0564.92016)

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##### References:

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

[2] | Anderson, R.M.; May, R.M., Population biology of infectious diseases: part I, Nature, 280, 361-367, (1979) |

[3] | Macdonald, G., The analysis of equilibrium in malaria, Trop. dis. bull., 49, 813-829, (1952) |

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

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

[6] | Nold, A., The infectee number at equilibrium for a communicable disease, Math. biosci., 46, 131-138, (1979) |

[7] | Smith, C.E.G., Prospects for the control of infectious disease, Proc. roy. soc. med., 63, 1181-1190, (1970) |

[8] | Hethcote, H.W., An immunization model for a heterogeneous population, Theoret. population biol., 14, 338-349, (1978) · Zbl 0392.92009 |

[9] | Fine, P.E.M.; Clarkson, J.A., Measles in england and wales, II: the impact of the measles vaccination programme on the distribution of immunity in the population, Internat. J. epidemiol., 11, 15-25, (1982) |

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

[11] | () |

[12] | Hethcote, H.W., Measles and rubella in the united states, Amer. J. epidemiol., (1983) |

[13] | Dietz, K., The incidence of infectious diseases under the influence of seasonal fluctuations, (), 1-15 · Zbl 0333.92014 |

[14] | Hoppensteadt, F., An age dependent epidemic model, J. franklin inst., 297, 325-333, (1974) · Zbl 0305.92010 |

[15] | Longini, I.M.; Ackerman, E.; Elveback, L.R., An optimization model for influenza A epidemics, Math. biosci., 38, 141-157, (1978) |

[16] | Schenzle, D., Control of virus transmission in age-structured populations, () · Zbl 0565.92023 |

[17] | May, R.M., Population biology of microparasitic infections, (), to appear. |

[18] | R. M. Anderson and R. M. May, Vaccination against microparasitic infections: Age-specific transmission rates, J. Hyg., to appear. |

[19] | Becker, N.; Angulo, J., On estimating the contagiousness of a disease transmitted from person to person, Math. biosci., 54, 137-154, (1981) · Zbl 0455.92017 |

[20] | Yorke, J.A.; Hethcote, H.W.; Nold, A., Dynamics and control of the transmission of gonorrhea, J. sex. trans. dis., 5, 51-56, (1978) |

[21] | Murray, G.D.; Cliff, A.D., A stochastic model for measles epidemics in a multi-region setting, Inst. brit. geog., 2, 158-174, (1975) |

[22] | Lajmanovich, A.; Yorke, J.A., A deterministic model for gonorrhea in a nonhomogeneous population, Math. biosci., 28, 221-236, (1976) · Zbl 0344.92016 |

[23] | Nold, A., Heterogeneity in disease-transmission modeling, Math. biosci., 52, 227-240, (1980) · Zbl 0454.92020 |

[24] | Post, W.M.; DeAngelis, D.L.; Travis, C.C., Endemic disease in environments with spatially heterogeneous host populations, Math. biosci., 63, 289-302, (1983) · Zbl 0528.92018 |

[25] | C.C. Travis and S.M. Lenhart, private communication, 1984. |

[26] | Barbour, A.D., Macdonald’s model and the transmission of bilharzia, Trans. roy. soc. trop. med. hyg., 72, 6-15, (1978) · Zbl 0377.92013 |

[27] | C. Dye and G. Hasibeder, Patterns of mosquito-host contact and disease population dynamics, to appear. · Zbl 0647.92015 |

[28] | Dietz, K., Models for vector-borne parasitic diseases, (), 264-277 · Zbl 0441.92020 |

[29] | Fine, P.E.M., Control of infectious diseases, (), 121-148, (group report) |

[30] | Anderson, R.M., Transmission dynamics and control of infectious disease agents, (), 149-176 |

[31] | Sethi, S.P., Quantitative guidelines for communicable disease control program: A complete synthesis, Biometrics, 30, 681-691, (1974) · Zbl 0292.92011 |

[32] | Wickwire, K., Mathematical models for the control of pests and infectious diseases: A survey, Theoret. population biol., 11, 182-238, (1977) · Zbl 0356.92001 |

[33] | Anscombe, F.J., Sampling theory of the negative binomial and logarithmic series distributions, Biometrica, 37, 358-382, (1950) · Zbl 0039.14202 |

[34] | Southwood, T.R.E., Ecological methods, with particular reference to the study of insect populations, (1966), Methuen London |

[35] | May, R.M., Host-parasitoid systems in patchy environments: A phenomenological model, J. anim. ecol., 47, 833-843, (1978) |

[36] | Hopkins, D.R.; Hinman, A.R.; Koplan, J.P.; Lane, J.M., The case for global eradication, Lancet, 1396-1398, (19 June 1982) |

[37] | Hinman, A.R., World eradication of measles, Rev. infectious dis., 4, 933-939, (1982) |

[38] | Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions, (1965), Dover New York · Zbl 0515.33001 |

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