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A mathematical model of infectious diseases

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  • Guangping Huang
  • Ling Li

Abstract

In the formulation of models for the spread of communicable diseases which include removal and population dynamics, it is necessary to distinguish between removal through recovery with immunity and removal by death due to disease. This distinction must be made because of the difference in the effect on the population dynamics of the different kinds of removal and because there are significant differences in the behavior of the models. We have formulated a class of models which allow recovery with immunity for a fraction of the infective and permanent removal by death from disease for the remainder. Earlier models of this type have postulated an increased death rate for infective, but such models are restricted to exponentially distributed-infective periods. Because of the differences in behavior between models with recovery and models with permanent removal do not arise when the infective period is exponentially distributed, we have chosen to formulate a different type of model which is sufficiently general to admit qualitative differences. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Guangping Huang & Ling Li, 2009. "A mathematical model of infectious diseases," Annals of Operations Research, Springer, vol. 168(1), pages 41-80, April.
    • Handle: RePEc:spr:annopr:v:168:y:2009:i:1:p:41-80:10.1007/s10479-008-0373-7
    DOI: 10.1007/s10479-008-0373-7
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    Cited by:

    1. Enayati, Shakiba & Özaltın, Osman Y., 2020. "Optimal influenza vaccine distribution with equity," European Journal of Operational Research, Elsevier, vol. 283(2), pages 714-725.
    2. Hyukpyo Hong & Eunjin Eom & Hyojung Lee & Sunhwa Choi & Boseung Choi & Jae Kyoung Kim, 2024. "Overcoming bias in estimating epidemiological parameters with realistic history-dependent disease spread dynamics," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    3. Fang Liu & Zhuming Bi & Eric L. Xu & Qin Ga & Quanyu Yang & Yingzhong Yang & Lan Ma & Tana Wuren & Rili Ge, 2015. "An integrated systems approach to plateau ecosystem management—a scientific application in Qinghai and Tibet plateau," Information Systems Frontiers, Springer, vol. 17(2), pages 337-350, April.

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