Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes

Math Biosci Eng. 2012 Jan 1;9(1):165-74. doi: 10.3934/mbe.2012.9.165.

Abstract

A delayed vector-bias model for malaria transmission with incubation period in mosquitoes is studied. The delay t corresponds to the time necessary for a latently infected vector to become an infectious vector. We prove that the global stability is completely determined by the threshold parameter, R₀(τ). If R₀(τ) ≥ 1, the disease-free equilibrium is globally asymptotically stable. If R₀(τ) > 1 a unique endemic equilibrium exists and is globally asymptotically stable. We apply our results to Ross-MacDonald malaria models with an incubation period (extrinsic or intrinsic).

MeSH terms

  • Animals
  • Basic Reproduction Number
  • Culicidae / parasitology*
  • Humans
  • Insect Vectors / parasitology*
  • Malaria / parasitology*
  • Malaria / transmission
  • Models, Biological*
  • Plasmodium / growth & development*