Transmission model for Plasmodium vivax malaria

  • Authors:

  • Puntani Pongsumpun;I-Ming Tang

  • Affiliations:

  • Department of Mathematics and Computer Science, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok, Thailand;Department of Physics, Faculty of Science, Mahidol University, Bangkok, Thailand

  • Venue:
  • CONTROL'07 Proceedings of the 3rd WSEAS/IASME international conference on Dynamical systems and control
  • Year:
  • 2007

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Abstract

Plasmodium vivax malaria differs from P. falciparum malaria in that a person suffering from P. vivax malaria can experience relapses of the disease. Between the relapses, the malaria parasite will remain dormant in the liver of the patient, leading to the patient being classified as being in the dormant class. A mathematical model for the transmission of P. vivax is developed in which the human population is divided into four classes, the susceptible, the infected, the dormant and the recovered. Two stable equilibrium states, a disease free state E0 and an endemic state E1, are found to be possible. It is found that the E0 state is stable when a newly defined basic reproduction number R0 is less than one. If R0 is more than one then endemic state E1 is stable. The conditions for the second equilibrium state E1 to be a stable spiral node are established. It is found that solutions in phase space are trajectories spiraling into the endemic state. The different behavior of our numerical results are shown for the different values of parameters.