An Age-Structured Model for Transmission Dynamics of Malaria with Infected Immigrants and Asymptomatic Carriers

Authors

  • Asha S Kalula Department of Mathematics, University of Dar es Salaam, P. O. Box 35062, Tanzania.
  • Eunice Mureithi Department of Mathematics, University of Dar es Salaam, P. O. Box 35062, Tanzania.
  • Theresia Marijani Department of Mathematics, University of Dar es Salaam, P. O. Box 35062, Tanzania.
  • Isambi Mbalawata African Institute for Mathematical Sciences (AIMS), Cellule Kamatamu, Rue KG590 ST No 1 Kigali, Rwanda

DOI:

https://doi.org/10.4314/tjs.v47i3.7

Keywords:

Age-structure, malaria, immigrants, asymptomatic carrier, nonlinear ODE model

Abstract

Abstract

An age-structured (children and adults) model for the transmission dynamics of malaria with asymptomatic carriers and infected immigrants has been analyzed. We first analyze a model without infected immigrants. It shows that the disease-free equilibrium exists and is stable when and unstable for . Also, we compute the sensitivity indices of the basic reproduction number. The basic reproduction number is most sensitive to the mosquito biting rate. Besides, the sensitivity of the basic reproduction number shows that the children's class parameters are more sensitive than those of adults. In the presence of infected immigrants, the model does not admit a disease-free equilibrium. The sensitivity of endemic equilibrium shows that the asymptomatic carrier parameters are more critical than that of infected immigrants. Also, the inflow of infectious immigrants is sensitive than that of infected immigrants. The results obtained indicate that strategies that target asymptomatic carriers and infected immigrants can help control malaria.

Keywords: Age-structure, malaria, immigrants, asymptomatic carrier, nonlinear ODE model.

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Published

2021-08-31

Issue

Vol. 47 No. 3 (2021)

Section

Articles

License

Authors who publish in The Eastern Africa Law Review retain the copyright to their work and grant the University of Dar es Salaam a non-exclusive license to publish, reproduce, and distribute the article.

This article is published under the Creative Commons Attribution 4.0 International (CC BY 4.0) License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided the original work is properly cited.