Journal Article

The <i>basic reproduction ratio</i> for a model of directly transmitted infections considering the virus charge and the immunological response


in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 17, issue 1, pages 15-31
Published in print January 2000 | ISSN: 1477-8599
Published online January 2000 | e-ISSN: 1477-8602 | DOI:
The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response

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  • Applied Mathematics
  • Biomathematics and Statistics


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In order to describe mathematically the transmission of microparasites, especially directly transmitted infections, it is usual to set up differential equations assuming the mass action law and a homogeneously mixed population. In this paper we analyze such a model taking into account heterogeneity with respect to the infectivity, that is, the variability in the evolution of the interaction between parasite and the human host during the infectious period. The well established biological phenomenon of initial increase in parasite abundance followed by its decrease, due to the interaction between the host's immunological response and the parasite, has thus been taken into account The variable amount of microparasites eliminated by an infectious individual, and the different (heterogeneous) immunological response build up by the host when in interaction with parasite are present in the model. The analytical expression for the basic reproduction ratio is derived through stability analysis.

Keywords: mathematical model; heterogeneous infectivity; amount of parasites; immunity; stability; basic reproduction ratio

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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