Analysis of a vector-bias model on malaria transmission

Farida Chamchod, Nicholas F Britton

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

We incorporate a vector-bias term into a malaria-transmission model to account for the greater attractiveness of infectious humans to mosquitoes in terms of differing probabilities that a mosquito arriving at a human at random picks that human depending on whether he is infectious or susceptible. We prove that transcritical bifurcation occurs at the basic reproductive ratio equalling 1 by projecting the flow onto the extended centre manifold. We next study the dynamics of the system when incubation time of malaria parasites in mosquitoes is included, and find that the longer incubation time reduces the prevalence of malaria. Also, we incorporate a random movement of mosquitoes as a diffusion term and a chemically directed movement of mosquitoes to humans expressed in terms of sweat and body odour as a chemotaxis term to study the propagation of infected population to uninfected population. We find that a travelling wave occurs; its speed is calculated numerically and estimated for the lower bound analytically.
Original languageEnglish
Pages (from-to)639-657
Number of pages19
JournalBulletin of Mathematical Biology
Volume73
Issue number3
Early online date21 May 2010
DOIs
Publication statusPublished - Mar 2011

Keywords

  • malaria transmission
  • travelling waves
  • time delay

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