A mathematical model for the dynamics of malaria in a human host and mosquito vector with temporary immunity

  • Tumwiine J
  • Mugisha J
  • Luboobi L
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Abstract

In the paper, we propose a model that tracks the dynamics of malaria in the human host and mosquito vector. Our model incorporates some infected humans that recover from infection and immune humans after loss of immunity to the disease to join the susceptible class again. All the new borne are susceptible to the infection and there is no vertical transmission. The stability of the system is analyzed for the existence of the disease-free and endemic equilibria points. We established that the disease-free equilibrium point is globally asymptotically stable when the reproduction number, R0≤ 1 and the disease always dies out. For R0> 1 the disease-free equilibrium becomes unstable and the endemic equilibrium is globally asymptotically stable. Thus, due to new births and immunity loss to malaria, the susceptible class will always be refilled and the disease becomes more endemic. © 2007 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Compound matrices
  • Immunity
  • Reproduction number
  • Stability

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Authors

  • J. Tumwiine

  • J. Y.T. Mugisha

  • L. S. Luboobi

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