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Dynamics of an age-structured two-strain model for malaria transmission

Author

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  • Forouzannia, Farinaz
  • Gumel, A.

Abstract

A new age-structured deterministic model for assessing the impact of anti-malaria drugs on the transmission dynamics of malaria is designed and qualitatively analysed. The resulting two-strain age-structured model undergoes backward bifurcation, which arises due to malaria-induced mortality in humans. Conditions for the existence of unique resistant strain-only and low-endemicity equilibria are derived for special cases. It is shown, for the case when treatment does not cause drug resistance, that the disease-free equilibrium of the wild strain-only component of the model is globally-asymptotically stable whenever the associated reproduction number of the model is less than unity. Similar result is established for the resistant strain-only component of the model for this case. Numerical simulations of the model, for the case when treatment does not cause drug resistance, show that the model undergoes competitive exclusion (where the malaria strain with the higher reproduction number drives the other to extinction).

Suggested Citation

  • Forouzannia, Farinaz & Gumel, A., 2015. "Dynamics of an age-structured two-strain model for malaria transmission," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 860-886.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:860-886
    DOI: 10.1016/j.amc.2014.09.117
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    References listed on IDEAS

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    1. Chiyaka, Christinah & Garira, Winston & Dube, Shadreck, 2009. "Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas," Theoretical Population Biology, Elsevier, vol. 75(1), pages 14-29.
    2. anonymous, 2001. "Creating critical mass," Banking and Community Perspectives, Federal Reserve Bank of Dallas, issue 1, pages 2-3,8.
    3. Ashrafi Niger & Abba Gumel, 2011. "Immune Response and Imperfect Vaccine in Malaria Dynamics," Mathematical Population Studies, Taylor & Francis Journals, vol. 18(2), pages 55-86.
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