Stability and Hopf bifurcation of a two species malaria model with time delays

Authors

  • Ephraim Agyingi School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, USA Author
  • Tamas Wiandt School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, USA Author
  • Matthias Ngwa School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, USA Author

DOI:

https://doi.org/10.30707/LiB4.1Agyingi

Keywords:

Malaria transmission, Multiple species, Multiple delays, Stability analysis, Hopf bifurcation

Abstract

We present a mathematical model of the transmission dynamics of two species of malaria with time lags. The model is equally applicable to two strains of a malaria species. The reproduction numbers of the two species are obtained and used as threshold parameters to study the stability and bifurcations of the equilibria of the model. We find that the model has a disease free equilibrium, which is a global attractor when the reproduction number of each species is less than one. Further, we observe that the non-disease free equilibrium of the model contains stability switches and Hopf bifurcations take place when the delays exceed the critical values.

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Published

2017-01-01

Issue

Section

Research

How to Cite

Stability and Hopf bifurcation of a two species malaria model with time delays. (2017). Letters in Biomathematics, 4(1), 59–76. https://doi.org/10.30707/LiB4.1Agyingi

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