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Effective and ineffective treatment in a malaria model for humans in an endemic region

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Abstract

A mathematical model for malaria in humans was developed to explore the effect of treatment on the transmission and control of malaria. The model incorporates effective antimalarial and substandard drugs as treatment for infectious humans. The reproduction number \(R_{0}\) is evaluated, and shown to increase due to the presence of partially recovered humans. The disease free equilibrium is locally asymptotically stable when \(R_{0}<1\) and unstable when \(R_{0}>1\). The model exhibits backward, imperfect or transcritical bifurcation depending on the value of the disease induced death rate and \(R_{0}\). The numerical simulations, local and global sensitivity analysis suggest that the combination of effective control measures and the prompt use of effective antimalarial drugs that clear parasites quickly and give a long post-treatment prophylaxis may not only prevent transmission of infection to mosquitoes, but significantly reduce the number of infectious humans and the overall sources of infection.

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu Natal, P.M.B X01, Pietermaritzburg, South Africa

    B. A. Danquah & F. Chirove

  2. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

    Jacek Banasiak

Authors
  1. B. A. Danquah
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  2. F. Chirove
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  3. Jacek Banasiak
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Correspondence to B. A. Danquah.

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Danquah, B.A., Chirove, F. & Banasiak, J. Effective and ineffective treatment in a malaria model for humans in an endemic region. Afr. Mat. 30, 1181–1204 (2019). https://doi.org/10.1007/s13370-019-00713-z

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