Ducrot2009 - Malaria transmission in two host types

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MODEL1808280013
Short description
The main purpose of this article is to formulate a deterministic mathematical model for the transmission of malaria that considers two host types in the human population. The first type is called "non-immune" comprising all humans who have never acquired immunity against malaria and the second type is called "semi-immune". Non-immune are divided into susceptible, exposed and infectious and semi-immune are divided into susceptible, exposed, infectious and immune. We obtain an explicit formula for the reproductive number, R(0) which is a function of the weight of the transmission semi-immune-mosquito-semi-immune, R(0a), and the weight of the transmission non-immune-mosquito-non-immune, R(0e). Then, we study the existence of endemic equilibria by using bifurcation analysis. We give a simple criterion when R(0) crosses one for forward and backward bifurcation. We explore the possibility of a control for malaria through a specific sub-group such as non-immune or semi-immune or mosquitoes
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SBML (L2V4)
Related Publication
  • A mathematical model for malaria involving differential susceptibility, exposedness and infectivity of human host.
  • Ducrot A, Sirima SB, Somé B, Zongo P
  • Journal of biological dynamics , 11/ 2009 , Volume 3 , Issue 6 , pages: 574-598 , PubMed ID: 22880962
  • INRIA-Anubis Sud-Ouest futurs, Université de Bordeaux, UFR Sciences et Modélisation, 146 rue Leo Saignat BP 26, Bordeaux Cedex, France. arnaud.ducrot@u-bordeaux2.fr
  • The main purpose of this article is to formulate a deterministic mathematical model for the transmission of malaria that considers two host types in the human population. The first type is called "non-immune" comprising all humans who have never acquired immunity against malaria and the second type is called "semi-immune". Non-immune are divided into susceptible, exposed and infectious and semi-immune are divided into susceptible, exposed, infectious and immune. We obtain an explicit formula for the reproductive number, R(0) which is a function of the weight of the transmission semi-immune-mosquito-semi-immune, R(0a), and the weight of the transmission non-immune-mosquito-non-immune, R(0e). Then, we study the existence of endemic equilibria by using bifurcation analysis. We give a simple criterion when R(0) crosses one for forward and backward bifurcation. We explore the possibility of a control for malaria through a specific sub-group such as non-immune or semi-immune or mosquitoes.
Contributors
Submitter of the first revision: Sarubini Kananathan
Submitter of this revision: Krishna Kumar Tiwari
Modellers: Sarubini Kananathan, Krishna Kumar Tiwari

Metadata information

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BioModels Database MODEL1808280013

hasProperty (1 statement)
Mathematical Modelling Ontology Ordinary differential equation model

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Non-curated
Modelling approach(es)
ordinary differential equation model
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Model files
Final Version.xml SBML L2V4 representation of Ducrot2009 - Malaria transmission in two host types 84.50 KB Preview | Download

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Final Version.cps Copasi file for the model. Figure produced is similar to publication. 133.44 KB Preview | Download

  • Model originally submitted by : Sarubini Kananathan
  • Submitted: Aug 28, 2018 4:51:49 PM
  • Last Modified: Jul 9, 2020 1:30:53 PM
Revisions
  • Version: 6 public model Download this version
    • Submitted on: Jul 9, 2020 1:30:53 PM
    • Submitted by: Krishna Kumar Tiwari
    • With comment: Edited model metadata online.
  • Version: 4 public model Download this version
    • Submitted on: Aug 28, 2018 4:51:49 PM
    • Submitted by: Sarubini Kananathan
    • With comment: Edited model metadata online.

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